Initial revision

darcs-hash:20010301114010-f6438-12fb8a9ffcc80e86c0a97e37b5b0dae0dbc59b79.gz

24 files changed, 5312 insertions, 0 deletions

diff --git a/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/cart3d_x.xl b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/cart3d_x.xl
new file mode 100644
index 000000000..4e6fc8f78
--- /dev/null
+++ b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/cart3d_x.xl
@@ -0,0 +1,170 @@
+# GRID::cart3d_x x (cart3d_x)
+#
+# iteration 0
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+0 0 0 0 0 0 12 16 -5.4
+0 0 0 0 0 1 12 16 -4.8
+0 0 0 0 0 2 12 16 -4.2
+0 0 0 0 0 3 12 16 -3.6
+0 0 0 0 0 4 12 16 -3
+0 0 0 0 0 5 12 16 -2.4
+0 0 0 0 0 6 12 16 -1.8
+0 0 0 0 0 7 12 16 -1.2
+0 0 0 0 0 8 12 16 -0.6
+0 0 0 0 0 9 12 16 4.44089209850063e-16
+0 0 0 0 0 10 12 16 0.600000000000001
+0 0 0 0 0 11 12 16 1.2
+0 0 0 0 0 12 12 16 1.8
+0 0 0 0 0 13 12 16 2.4
+0 0 0 0 0 14 12 16 3
+0 0 0 0 0 15 12 16 3.6
+0 0 0 0 0 16 12 16 4.2
+0 0 0 0 0 17 12 16 4.8
+0 0 0 0 0 18 12 16 5.4
+
+
+# iteration 1
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+1 0 0 0 0 0 12 16 -5.4
+1 0 0 0 0 1 12 16 -4.8
+1 0 0 0 0 2 12 16 -4.2
+1 0 0 0 0 3 12 16 -3.6
+1 0 0 0 0 4 12 16 -3
+1 0 0 0 0 5 12 16 -2.4
+1 0 0 0 0 6 12 16 -1.8
+1 0 0 0 0 7 12 16 -1.2
+1 0 0 0 0 8 12 16 -0.6
+1 0 0 0 0 9 12 16 4.44089209850063e-16
+1 0 0 0 0 10 12 16 0.600000000000001
+1 0 0 0 0 11 12 16 1.2
+1 0 0 0 0 12 12 16 1.8
+1 0 0 0 0 13 12 16 2.4
+1 0 0 0 0 14 12 16 3
+1 0 0 0 0 15 12 16 3.6
+1 0 0 0 0 16 12 16 4.2
+1 0 0 0 0 17 12 16 4.8
+1 0 0 0 0 18 12 16 5.4
+
+
+# iteration 2
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+2 0 0 0 0 0 12 16 -5.4
+2 0 0 0 0 1 12 16 -4.8
+2 0 0 0 0 2 12 16 -4.2
+2 0 0 0 0 3 12 16 -3.6
+2 0 0 0 0 4 12 16 -3
+2 0 0 0 0 5 12 16 -2.4
+2 0 0 0 0 6 12 16 -1.8
+2 0 0 0 0 7 12 16 -1.2
+2 0 0 0 0 8 12 16 -0.6
+2 0 0 0 0 9 12 16 4.44089209850063e-16
+2 0 0 0 0 10 12 16 0.600000000000001
+2 0 0 0 0 11 12 16 1.2
+2 0 0 0 0 12 12 16 1.8
+2 0 0 0 0 13 12 16 2.4
+2 0 0 0 0 14 12 16 3
+2 0 0 0 0 15 12 16 3.6
+2 0 0 0 0 16 12 16 4.2
+2 0 0 0 0 17 12 16 4.8
+2 0 0 0 0 18 12 16 5.4
+
+
+# iteration 3
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+3 0 0 0 0 0 12 16 -5.4
+3 0 0 0 0 1 12 16 -4.8
+3 0 0 0 0 2 12 16 -4.2
+3 0 0 0 0 3 12 16 -3.6
+3 0 0 0 0 4 12 16 -3
+3 0 0 0 0 5 12 16 -2.4
+3 0 0 0 0 6 12 16 -1.8
+3 0 0 0 0 7 12 16 -1.2
+3 0 0 0 0 8 12 16 -0.6
+3 0 0 0 0 9 12 16 4.44089209850063e-16
+3 0 0 0 0 10 12 16 0.600000000000001
+3 0 0 0 0 11 12 16 1.2
+3 0 0 0 0 12 12 16 1.8
+3 0 0 0 0 13 12 16 2.4
+3 0 0 0 0 14 12 16 3
+3 0 0 0 0 15 12 16 3.6
+3 0 0 0 0 16 12 16 4.2
+3 0 0 0 0 17 12 16 4.8
+3 0 0 0 0 18 12 16 5.4
+
+
+# iteration 4
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+4 0 0 0 0 0 12 16 -5.4
+4 0 0 0 0 1 12 16 -4.8
+4 0 0 0 0 2 12 16 -4.2
+4 0 0 0 0 3 12 16 -3.6
+4 0 0 0 0 4 12 16 -3
+4 0 0 0 0 5 12 16 -2.4
+4 0 0 0 0 6 12 16 -1.8
+4 0 0 0 0 7 12 16 -1.2
+4 0 0 0 0 8 12 16 -0.6
+4 0 0 0 0 9 12 16 4.44089209850063e-16
+4 0 0 0 0 10 12 16 0.600000000000001
+4 0 0 0 0 11 12 16 1.2
+4 0 0 0 0 12 12 16 1.8
+4 0 0 0 0 13 12 16 2.4
+4 0 0 0 0 14 12 16 3
+4 0 0 0 0 15 12 16 3.6
+4 0 0 0 0 16 12 16 4.2
+4 0 0 0 0 17 12 16 4.8
+4 0 0 0 0 18 12 16 5.4
+
+
+# iteration 5
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+5 0 0 0 0 0 12 16 -5.4
+5 0 0 0 0 1 12 16 -4.8
+5 0 0 0 0 2 12 16 -4.2
+5 0 0 0 0 3 12 16 -3.6
+5 0 0 0 0 4 12 16 -3
+5 0 0 0 0 5 12 16 -2.4
+5 0 0 0 0 6 12 16 -1.8
+5 0 0 0 0 7 12 16 -1.2
+5 0 0 0 0 8 12 16 -0.6
+5 0 0 0 0 9 12 16 4.44089209850063e-16
+5 0 0 0 0 10 12 16 0.600000000000001
+5 0 0 0 0 11 12 16 1.2
+5 0 0 0 0 12 12 16 1.8
+5 0 0 0 0 13 12 16 2.4
+5 0 0 0 0 14 12 16 3
+5 0 0 0 0 15 12 16 3.6
+5 0 0 0 0 16 12 16 4.2
+5 0 0 0 0 17 12 16 4.8
+5 0 0 0 0 18 12 16 5.4
+
+
+# iteration 6
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+6 0 0 0 0 0 12 16 -5.4
+6 0 0 0 0 1 12 16 -4.8
+6 0 0 0 0 2 12 16 -4.2
+6 0 0 0 0 3 12 16 -3.6
+6 0 0 0 0 4 12 16 -3
+6 0 0 0 0 5 12 16 -2.4
+6 0 0 0 0 6 12 16 -1.8
+6 0 0 0 0 7 12 16 -1.2
+6 0 0 0 0 8 12 16 -0.6
+6 0 0 0 0 9 12 16 4.44089209850063e-16
+6 0 0 0 0 10 12 16 0.600000000000001
+6 0 0 0 0 11 12 16 1.2
+6 0 0 0 0 12 12 16 1.8
+6 0 0 0 0 13 12 16 2.4
+6 0 0 0 0 14 12 16 3
+6 0 0 0 0 15 12 16 3.6
+6 0 0 0 0 16 12 16 4.2
+6 0 0 0 0 17 12 16 4.8
+6 0 0 0 0 18 12 16 5.4
+
+
diff --git a/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/cart3d_x.yl b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/cart3d_x.yl
new file mode 100644
index 000000000..467676ecc
--- /dev/null
+++ b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/cart3d_x.yl
@@ -0,0 +1,219 @@
+# GRID::cart3d_x y (cart3d_x)
+#
+# iteration 0
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+0 0 0 0 0 9 0 16 4.44089209850063e-16
+0 0 0 0 0 9 1 16 4.44089209850063e-16
+0 0 0 0 0 9 2 16 4.44089209850063e-16
+0 0 0 0 0 9 3 16 4.44089209850063e-16
+0 0 0 0 0 9 4 16 4.44089209850063e-16
+0 0 0 0 0 9 5 16 4.44089209850063e-16
+0 0 0 0 0 9 6 16 4.44089209850063e-16
+0 0 0 0 0 9 7 16 4.44089209850063e-16
+0 0 0 0 0 9 8 16 4.44089209850063e-16
+0 0 0 0 0 9 9 16 4.44089209850063e-16
+0 0 0 0 0 9 10 16 4.44089209850063e-16
+0 0 0 0 0 9 11 16 4.44089209850063e-16
+0 0 0 0 0 9 12 16 4.44089209850063e-16
+0 0 0 0 0 9 13 16 4.44089209850063e-16
+0 0 0 0 0 9 14 16 4.44089209850063e-16
+0 0 0 0 0 9 15 16 4.44089209850063e-16
+0 0 0 0 0 9 16 16 4.44089209850063e-16
+0 0 0 0 0 9 17 16 4.44089209850063e-16
+0 0 0 0 0 9 18 16 4.44089209850063e-16
+0 0 0 0 0 9 19 16 4.44089209850063e-16
+0 0 0 0 0 9 20 16 4.44089209850063e-16
+0 0 0 0 0 9 21 16 4.44089209850063e-16
+0 0 0 0 0 9 22 16 4.44089209850063e-16
+0 0 0 0 0 9 23 16 4.44089209850063e-16
+0 0 0 0 0 9 24 16 4.44089209850063e-16
+0 0 0 0 0 9 25 16 4.44089209850063e-16
+
+
+# iteration 1
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+1 0 0 0 0 9 0 16 4.44089209850063e-16
+1 0 0 0 0 9 1 16 4.44089209850063e-16
+1 0 0 0 0 9 2 16 4.44089209850063e-16
+1 0 0 0 0 9 3 16 4.44089209850063e-16
+1 0 0 0 0 9 4 16 4.44089209850063e-16
+1 0 0 0 0 9 5 16 4.44089209850063e-16
+1 0 0 0 0 9 6 16 4.44089209850063e-16
+1 0 0 0 0 9 7 16 4.44089209850063e-16
+1 0 0 0 0 9 8 16 4.44089209850063e-16
+1 0 0 0 0 9 9 16 4.44089209850063e-16
+1 0 0 0 0 9 10 16 4.44089209850063e-16
+1 0 0 0 0 9 11 16 4.44089209850063e-16
+1 0 0 0 0 9 12 16 4.44089209850063e-16
+1 0 0 0 0 9 13 16 4.44089209850063e-16
+1 0 0 0 0 9 14 16 4.44089209850063e-16
+1 0 0 0 0 9 15 16 4.44089209850063e-16
+1 0 0 0 0 9 16 16 4.44089209850063e-16
+1 0 0 0 0 9 17 16 4.44089209850063e-16
+1 0 0 0 0 9 18 16 4.44089209850063e-16
+1 0 0 0 0 9 19 16 4.44089209850063e-16
+1 0 0 0 0 9 20 16 4.44089209850063e-16
+1 0 0 0 0 9 21 16 4.44089209850063e-16
+1 0 0 0 0 9 22 16 4.44089209850063e-16
+1 0 0 0 0 9 23 16 4.44089209850063e-16
+1 0 0 0 0 9 24 16 4.44089209850063e-16
+1 0 0 0 0 9 25 16 4.44089209850063e-16
+
+
+# iteration 2
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+2 0 0 0 0 9 0 16 4.44089209850063e-16
+2 0 0 0 0 9 1 16 4.44089209850063e-16
+2 0 0 0 0 9 2 16 4.44089209850063e-16
+2 0 0 0 0 9 3 16 4.44089209850063e-16
+2 0 0 0 0 9 4 16 4.44089209850063e-16
+2 0 0 0 0 9 5 16 4.44089209850063e-16
+2 0 0 0 0 9 6 16 4.44089209850063e-16
+2 0 0 0 0 9 7 16 4.44089209850063e-16
+2 0 0 0 0 9 8 16 4.44089209850063e-16
+2 0 0 0 0 9 9 16 4.44089209850063e-16
+2 0 0 0 0 9 10 16 4.44089209850063e-16
+2 0 0 0 0 9 11 16 4.44089209850063e-16
+2 0 0 0 0 9 12 16 4.44089209850063e-16
+2 0 0 0 0 9 13 16 4.44089209850063e-16
+2 0 0 0 0 9 14 16 4.44089209850063e-16
+2 0 0 0 0 9 15 16 4.44089209850063e-16
+2 0 0 0 0 9 16 16 4.44089209850063e-16
+2 0 0 0 0 9 17 16 4.44089209850063e-16
+2 0 0 0 0 9 18 16 4.44089209850063e-16
+2 0 0 0 0 9 19 16 4.44089209850063e-16
+2 0 0 0 0 9 20 16 4.44089209850063e-16
+2 0 0 0 0 9 21 16 4.44089209850063e-16
+2 0 0 0 0 9 22 16 4.44089209850063e-16
+2 0 0 0 0 9 23 16 4.44089209850063e-16
+2 0 0 0 0 9 24 16 4.44089209850063e-16
+2 0 0 0 0 9 25 16 4.44089209850063e-16
+
+
+# iteration 3
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+3 0 0 0 0 9 0 16 4.44089209850063e-16
+3 0 0 0 0 9 1 16 4.44089209850063e-16
+3 0 0 0 0 9 2 16 4.44089209850063e-16
+3 0 0 0 0 9 3 16 4.44089209850063e-16
+3 0 0 0 0 9 4 16 4.44089209850063e-16
+3 0 0 0 0 9 5 16 4.44089209850063e-16
+3 0 0 0 0 9 6 16 4.44089209850063e-16
+3 0 0 0 0 9 7 16 4.44089209850063e-16
+3 0 0 0 0 9 8 16 4.44089209850063e-16
+3 0 0 0 0 9 9 16 4.44089209850063e-16
+3 0 0 0 0 9 10 16 4.44089209850063e-16
+3 0 0 0 0 9 11 16 4.44089209850063e-16
+3 0 0 0 0 9 12 16 4.44089209850063e-16
+3 0 0 0 0 9 13 16 4.44089209850063e-16
+3 0 0 0 0 9 14 16 4.44089209850063e-16
+3 0 0 0 0 9 15 16 4.44089209850063e-16
+3 0 0 0 0 9 16 16 4.44089209850063e-16
+3 0 0 0 0 9 17 16 4.44089209850063e-16
+3 0 0 0 0 9 18 16 4.44089209850063e-16
+3 0 0 0 0 9 19 16 4.44089209850063e-16
+3 0 0 0 0 9 20 16 4.44089209850063e-16
+3 0 0 0 0 9 21 16 4.44089209850063e-16
+3 0 0 0 0 9 22 16 4.44089209850063e-16
+3 0 0 0 0 9 23 16 4.44089209850063e-16
+3 0 0 0 0 9 24 16 4.44089209850063e-16
+3 0 0 0 0 9 25 16 4.44089209850063e-16
+
+
+# iteration 4
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+4 0 0 0 0 9 0 16 4.44089209850063e-16
+4 0 0 0 0 9 1 16 4.44089209850063e-16
+4 0 0 0 0 9 2 16 4.44089209850063e-16
+4 0 0 0 0 9 3 16 4.44089209850063e-16
+4 0 0 0 0 9 4 16 4.44089209850063e-16
+4 0 0 0 0 9 5 16 4.44089209850063e-16
+4 0 0 0 0 9 6 16 4.44089209850063e-16
+4 0 0 0 0 9 7 16 4.44089209850063e-16
+4 0 0 0 0 9 8 16 4.44089209850063e-16
+4 0 0 0 0 9 9 16 4.44089209850063e-16
+4 0 0 0 0 9 10 16 4.44089209850063e-16
+4 0 0 0 0 9 11 16 4.44089209850063e-16
+4 0 0 0 0 9 12 16 4.44089209850063e-16
+4 0 0 0 0 9 13 16 4.44089209850063e-16
+4 0 0 0 0 9 14 16 4.44089209850063e-16
+4 0 0 0 0 9 15 16 4.44089209850063e-16
+4 0 0 0 0 9 16 16 4.44089209850063e-16
+4 0 0 0 0 9 17 16 4.44089209850063e-16
+4 0 0 0 0 9 18 16 4.44089209850063e-16
+4 0 0 0 0 9 19 16 4.44089209850063e-16
+4 0 0 0 0 9 20 16 4.44089209850063e-16
+4 0 0 0 0 9 21 16 4.44089209850063e-16
+4 0 0 0 0 9 22 16 4.44089209850063e-16
+4 0 0 0 0 9 23 16 4.44089209850063e-16
+4 0 0 0 0 9 24 16 4.44089209850063e-16
+4 0 0 0 0 9 25 16 4.44089209850063e-16
+
+
+# iteration 5
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+5 0 0 0 0 9 0 16 4.44089209850063e-16
+5 0 0 0 0 9 1 16 4.44089209850063e-16
+5 0 0 0 0 9 2 16 4.44089209850063e-16
+5 0 0 0 0 9 3 16 4.44089209850063e-16
+5 0 0 0 0 9 4 16 4.44089209850063e-16
+5 0 0 0 0 9 5 16 4.44089209850063e-16
+5 0 0 0 0 9 6 16 4.44089209850063e-16
+5 0 0 0 0 9 7 16 4.44089209850063e-16
+5 0 0 0 0 9 8 16 4.44089209850063e-16
+5 0 0 0 0 9 9 16 4.44089209850063e-16
+5 0 0 0 0 9 10 16 4.44089209850063e-16
+5 0 0 0 0 9 11 16 4.44089209850063e-16
+5 0 0 0 0 9 12 16 4.44089209850063e-16
+5 0 0 0 0 9 13 16 4.44089209850063e-16
+5 0 0 0 0 9 14 16 4.44089209850063e-16
+5 0 0 0 0 9 15 16 4.44089209850063e-16
+5 0 0 0 0 9 16 16 4.44089209850063e-16
+5 0 0 0 0 9 17 16 4.44089209850063e-16
+5 0 0 0 0 9 18 16 4.44089209850063e-16
+5 0 0 0 0 9 19 16 4.44089209850063e-16
+5 0 0 0 0 9 20 16 4.44089209850063e-16
+5 0 0 0 0 9 21 16 4.44089209850063e-16
+5 0 0 0 0 9 22 16 4.44089209850063e-16
+5 0 0 0 0 9 23 16 4.44089209850063e-16
+5 0 0 0 0 9 24 16 4.44089209850063e-16
+5 0 0 0 0 9 25 16 4.44089209850063e-16
+
+
+# iteration 6
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+6 0 0 0 0 9 0 16 4.44089209850063e-16
+6 0 0 0 0 9 1 16 4.44089209850063e-16
+6 0 0 0 0 9 2 16 4.44089209850063e-16
+6 0 0 0 0 9 3 16 4.44089209850063e-16
+6 0 0 0 0 9 4 16 4.44089209850063e-16
+6 0 0 0 0 9 5 16 4.44089209850063e-16
+6 0 0 0 0 9 6 16 4.44089209850063e-16
+6 0 0 0 0 9 7 16 4.44089209850063e-16
+6 0 0 0 0 9 8 16 4.44089209850063e-16
+6 0 0 0 0 9 9 16 4.44089209850063e-16
+6 0 0 0 0 9 10 16 4.44089209850063e-16
+6 0 0 0 0 9 11 16 4.44089209850063e-16
+6 0 0 0 0 9 12 16 4.44089209850063e-16
+6 0 0 0 0 9 13 16 4.44089209850063e-16
+6 0 0 0 0 9 14 16 4.44089209850063e-16
+6 0 0 0 0 9 15 16 4.44089209850063e-16
+6 0 0 0 0 9 16 16 4.44089209850063e-16
+6 0 0 0 0 9 17 16 4.44089209850063e-16
+6 0 0 0 0 9 18 16 4.44089209850063e-16
+6 0 0 0 0 9 19 16 4.44089209850063e-16
+6 0 0 0 0 9 20 16 4.44089209850063e-16
+6 0 0 0 0 9 21 16 4.44089209850063e-16
+6 0 0 0 0 9 22 16 4.44089209850063e-16
+6 0 0 0 0 9 23 16 4.44089209850063e-16
+6 0 0 0 0 9 24 16 4.44089209850063e-16
+6 0 0 0 0 9 25 16 4.44089209850063e-16
+
+
diff --git a/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/cart3d_x.zl b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/cart3d_x.zl
new file mode 100644
index 000000000..a9d72ade1
--- /dev/null
+++ b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/cart3d_x.zl
@@ -0,0 +1,275 @@
+# GRID::cart3d_x z (cart3d_x)
+#
+# iteration 0
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+0 0 0 0 0 9 12 0 4.44089209850063e-16
+0 0 0 0 0 9 12 1 4.44089209850063e-16
+0 0 0 0 0 9 12 2 4.44089209850063e-16
+0 0 0 0 0 9 12 3 4.44089209850063e-16
+0 0 0 0 0 9 12 4 4.44089209850063e-16
+0 0 0 0 0 9 12 5 4.44089209850063e-16
+0 0 0 0 0 9 12 6 4.44089209850063e-16
+0 0 0 0 0 9 12 7 4.44089209850063e-16
+0 0 0 0 0 9 12 8 4.44089209850063e-16
+0 0 0 0 0 9 12 9 4.44089209850063e-16
+0 0 0 0 0 9 12 10 4.44089209850063e-16
+0 0 0 0 0 9 12 11 4.44089209850063e-16
+0 0 0 0 0 9 12 12 4.44089209850063e-16
+0 0 0 0 0 9 12 13 4.44089209850063e-16
+0 0 0 0 0 9 12 14 4.44089209850063e-16
+0 0 0 0 0 9 12 15 4.44089209850063e-16
+0 0 0 0 0 9 12 16 4.44089209850063e-16
+0 0 0 0 0 9 12 17 4.44089209850063e-16
+0 0 0 0 0 9 12 18 4.44089209850063e-16
+0 0 0 0 0 9 12 19 4.44089209850063e-16
+0 0 0 0 0 9 12 20 4.44089209850063e-16
+0 0 0 0 0 9 12 21 4.44089209850063e-16
+0 0 0 0 0 9 12 22 4.44089209850063e-16
+0 0 0 0 0 9 12 23 4.44089209850063e-16
+0 0 0 0 0 9 12 24 4.44089209850063e-16
+0 0 0 0 0 9 12 25 4.44089209850063e-16
+0 0 0 0 0 9 12 26 4.44089209850063e-16
+0 0 0 0 0 9 12 27 4.44089209850063e-16
+0 0 0 0 0 9 12 28 4.44089209850063e-16
+0 0 0 0 0 9 12 29 4.44089209850063e-16
+0 0 0 0 0 9 12 30 4.44089209850063e-16
+0 0 0 0 0 9 12 31 4.44089209850063e-16
+0 0 0 0 0 9 12 32 4.44089209850063e-16
+0 0 0 0 0 9 12 33 4.44089209850063e-16
+
+
+# iteration 1
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+1 0 0 0 0 9 12 0 4.44089209850063e-16
+1 0 0 0 0 9 12 1 4.44089209850063e-16
+1 0 0 0 0 9 12 2 4.44089209850063e-16
+1 0 0 0 0 9 12 3 4.44089209850063e-16
+1 0 0 0 0 9 12 4 4.44089209850063e-16
+1 0 0 0 0 9 12 5 4.44089209850063e-16
+1 0 0 0 0 9 12 6 4.44089209850063e-16
+1 0 0 0 0 9 12 7 4.44089209850063e-16
+1 0 0 0 0 9 12 8 4.44089209850063e-16
+1 0 0 0 0 9 12 9 4.44089209850063e-16
+1 0 0 0 0 9 12 10 4.44089209850063e-16
+1 0 0 0 0 9 12 11 4.44089209850063e-16
+1 0 0 0 0 9 12 12 4.44089209850063e-16
+1 0 0 0 0 9 12 13 4.44089209850063e-16
+1 0 0 0 0 9 12 14 4.44089209850063e-16
+1 0 0 0 0 9 12 15 4.44089209850063e-16
+1 0 0 0 0 9 12 16 4.44089209850063e-16
+1 0 0 0 0 9 12 17 4.44089209850063e-16
+1 0 0 0 0 9 12 18 4.44089209850063e-16
+1 0 0 0 0 9 12 19 4.44089209850063e-16
+1 0 0 0 0 9 12 20 4.44089209850063e-16
+1 0 0 0 0 9 12 21 4.44089209850063e-16
+1 0 0 0 0 9 12 22 4.44089209850063e-16
+1 0 0 0 0 9 12 23 4.44089209850063e-16
+1 0 0 0 0 9 12 24 4.44089209850063e-16
+1 0 0 0 0 9 12 25 4.44089209850063e-16
+1 0 0 0 0 9 12 26 4.44089209850063e-16
+1 0 0 0 0 9 12 27 4.44089209850063e-16
+1 0 0 0 0 9 12 28 4.44089209850063e-16
+1 0 0 0 0 9 12 29 4.44089209850063e-16
+1 0 0 0 0 9 12 30 4.44089209850063e-16
+1 0 0 0 0 9 12 31 4.44089209850063e-16
+1 0 0 0 0 9 12 32 4.44089209850063e-16
+1 0 0 0 0 9 12 33 4.44089209850063e-16
+
+
+# iteration 2
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+2 0 0 0 0 9 12 0 4.44089209850063e-16
+2 0 0 0 0 9 12 1 4.44089209850063e-16
+2 0 0 0 0 9 12 2 4.44089209850063e-16
+2 0 0 0 0 9 12 3 4.44089209850063e-16
+2 0 0 0 0 9 12 4 4.44089209850063e-16
+2 0 0 0 0 9 12 5 4.44089209850063e-16
+2 0 0 0 0 9 12 6 4.44089209850063e-16
+2 0 0 0 0 9 12 7 4.44089209850063e-16
+2 0 0 0 0 9 12 8 4.44089209850063e-16
+2 0 0 0 0 9 12 9 4.44089209850063e-16
+2 0 0 0 0 9 12 10 4.44089209850063e-16
+2 0 0 0 0 9 12 11 4.44089209850063e-16
+2 0 0 0 0 9 12 12 4.44089209850063e-16
+2 0 0 0 0 9 12 13 4.44089209850063e-16
+2 0 0 0 0 9 12 14 4.44089209850063e-16
+2 0 0 0 0 9 12 15 4.44089209850063e-16
+2 0 0 0 0 9 12 16 4.44089209850063e-16
+2 0 0 0 0 9 12 17 4.44089209850063e-16
+2 0 0 0 0 9 12 18 4.44089209850063e-16
+2 0 0 0 0 9 12 19 4.44089209850063e-16
+2 0 0 0 0 9 12 20 4.44089209850063e-16
+2 0 0 0 0 9 12 21 4.44089209850063e-16
+2 0 0 0 0 9 12 22 4.44089209850063e-16
+2 0 0 0 0 9 12 23 4.44089209850063e-16
+2 0 0 0 0 9 12 24 4.44089209850063e-16
+2 0 0 0 0 9 12 25 4.44089209850063e-16
+2 0 0 0 0 9 12 26 4.44089209850063e-16
+2 0 0 0 0 9 12 27 4.44089209850063e-16
+2 0 0 0 0 9 12 28 4.44089209850063e-16
+2 0 0 0 0 9 12 29 4.44089209850063e-16
+2 0 0 0 0 9 12 30 4.44089209850063e-16
+2 0 0 0 0 9 12 31 4.44089209850063e-16
+2 0 0 0 0 9 12 32 4.44089209850063e-16
+2 0 0 0 0 9 12 33 4.44089209850063e-16
+
+
+# iteration 3
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+3 0 0 0 0 9 12 0 4.44089209850063e-16
+3 0 0 0 0 9 12 1 4.44089209850063e-16
+3 0 0 0 0 9 12 2 4.44089209850063e-16
+3 0 0 0 0 9 12 3 4.44089209850063e-16
+3 0 0 0 0 9 12 4 4.44089209850063e-16
+3 0 0 0 0 9 12 5 4.44089209850063e-16
+3 0 0 0 0 9 12 6 4.44089209850063e-16
+3 0 0 0 0 9 12 7 4.44089209850063e-16
+3 0 0 0 0 9 12 8 4.44089209850063e-16
+3 0 0 0 0 9 12 9 4.44089209850063e-16
+3 0 0 0 0 9 12 10 4.44089209850063e-16
+3 0 0 0 0 9 12 11 4.44089209850063e-16
+3 0 0 0 0 9 12 12 4.44089209850063e-16
+3 0 0 0 0 9 12 13 4.44089209850063e-16
+3 0 0 0 0 9 12 14 4.44089209850063e-16
+3 0 0 0 0 9 12 15 4.44089209850063e-16
+3 0 0 0 0 9 12 16 4.44089209850063e-16
+3 0 0 0 0 9 12 17 4.44089209850063e-16
+3 0 0 0 0 9 12 18 4.44089209850063e-16
+3 0 0 0 0 9 12 19 4.44089209850063e-16
+3 0 0 0 0 9 12 20 4.44089209850063e-16
+3 0 0 0 0 9 12 21 4.44089209850063e-16
+3 0 0 0 0 9 12 22 4.44089209850063e-16
+3 0 0 0 0 9 12 23 4.44089209850063e-16
+3 0 0 0 0 9 12 24 4.44089209850063e-16
+3 0 0 0 0 9 12 25 4.44089209850063e-16
+3 0 0 0 0 9 12 26 4.44089209850063e-16
+3 0 0 0 0 9 12 27 4.44089209850063e-16
+3 0 0 0 0 9 12 28 4.44089209850063e-16
+3 0 0 0 0 9 12 29 4.44089209850063e-16
+3 0 0 0 0 9 12 30 4.44089209850063e-16
+3 0 0 0 0 9 12 31 4.44089209850063e-16
+3 0 0 0 0 9 12 32 4.44089209850063e-16
+3 0 0 0 0 9 12 33 4.44089209850063e-16
+
+
+# iteration 4
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+4 0 0 0 0 9 12 0 4.44089209850063e-16
+4 0 0 0 0 9 12 1 4.44089209850063e-16
+4 0 0 0 0 9 12 2 4.44089209850063e-16
+4 0 0 0 0 9 12 3 4.44089209850063e-16
+4 0 0 0 0 9 12 4 4.44089209850063e-16
+4 0 0 0 0 9 12 5 4.44089209850063e-16
+4 0 0 0 0 9 12 6 4.44089209850063e-16
+4 0 0 0 0 9 12 7 4.44089209850063e-16
+4 0 0 0 0 9 12 8 4.44089209850063e-16
+4 0 0 0 0 9 12 9 4.44089209850063e-16
+4 0 0 0 0 9 12 10 4.44089209850063e-16
+4 0 0 0 0 9 12 11 4.44089209850063e-16
+4 0 0 0 0 9 12 12 4.44089209850063e-16
+4 0 0 0 0 9 12 13 4.44089209850063e-16
+4 0 0 0 0 9 12 14 4.44089209850063e-16
+4 0 0 0 0 9 12 15 4.44089209850063e-16
+4 0 0 0 0 9 12 16 4.44089209850063e-16
+4 0 0 0 0 9 12 17 4.44089209850063e-16
+4 0 0 0 0 9 12 18 4.44089209850063e-16
+4 0 0 0 0 9 12 19 4.44089209850063e-16
+4 0 0 0 0 9 12 20 4.44089209850063e-16
+4 0 0 0 0 9 12 21 4.44089209850063e-16
+4 0 0 0 0 9 12 22 4.44089209850063e-16
+4 0 0 0 0 9 12 23 4.44089209850063e-16
+4 0 0 0 0 9 12 24 4.44089209850063e-16
+4 0 0 0 0 9 12 25 4.44089209850063e-16
+4 0 0 0 0 9 12 26 4.44089209850063e-16
+4 0 0 0 0 9 12 27 4.44089209850063e-16
+4 0 0 0 0 9 12 28 4.44089209850063e-16
+4 0 0 0 0 9 12 29 4.44089209850063e-16
+4 0 0 0 0 9 12 30 4.44089209850063e-16
+4 0 0 0 0 9 12 31 4.44089209850063e-16
+4 0 0 0 0 9 12 32 4.44089209850063e-16
+4 0 0 0 0 9 12 33 4.44089209850063e-16
+
+
+# iteration 5
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+5 0 0 0 0 9 12 0 4.44089209850063e-16
+5 0 0 0 0 9 12 1 4.44089209850063e-16
+5 0 0 0 0 9 12 2 4.44089209850063e-16
+5 0 0 0 0 9 12 3 4.44089209850063e-16
+5 0 0 0 0 9 12 4 4.44089209850063e-16
+5 0 0 0 0 9 12 5 4.44089209850063e-16
+5 0 0 0 0 9 12 6 4.44089209850063e-16
+5 0 0 0 0 9 12 7 4.44089209850063e-16
+5 0 0 0 0 9 12 8 4.44089209850063e-16
+5 0 0 0 0 9 12 9 4.44089209850063e-16
+5 0 0 0 0 9 12 10 4.44089209850063e-16
+5 0 0 0 0 9 12 11 4.44089209850063e-16
+5 0 0 0 0 9 12 12 4.44089209850063e-16
+5 0 0 0 0 9 12 13 4.44089209850063e-16
+5 0 0 0 0 9 12 14 4.44089209850063e-16
+5 0 0 0 0 9 12 15 4.44089209850063e-16
+5 0 0 0 0 9 12 16 4.44089209850063e-16
+5 0 0 0 0 9 12 17 4.44089209850063e-16
+5 0 0 0 0 9 12 18 4.44089209850063e-16
+5 0 0 0 0 9 12 19 4.44089209850063e-16
+5 0 0 0 0 9 12 20 4.44089209850063e-16
+5 0 0 0 0 9 12 21 4.44089209850063e-16
+5 0 0 0 0 9 12 22 4.44089209850063e-16
+5 0 0 0 0 9 12 23 4.44089209850063e-16
+5 0 0 0 0 9 12 24 4.44089209850063e-16
+5 0 0 0 0 9 12 25 4.44089209850063e-16
+5 0 0 0 0 9 12 26 4.44089209850063e-16
+5 0 0 0 0 9 12 27 4.44089209850063e-16
+5 0 0 0 0 9 12 28 4.44089209850063e-16
+5 0 0 0 0 9 12 29 4.44089209850063e-16
+5 0 0 0 0 9 12 30 4.44089209850063e-16
+5 0 0 0 0 9 12 31 4.44089209850063e-16
+5 0 0 0 0 9 12 32 4.44089209850063e-16
+5 0 0 0 0 9 12 33 4.44089209850063e-16
+
+
+# iteration 6
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+6 0 0 0 0 9 12 0 4.44089209850063e-16
+6 0 0 0 0 9 12 1 4.44089209850063e-16
+6 0 0 0 0 9 12 2 4.44089209850063e-16
+6 0 0 0 0 9 12 3 4.44089209850063e-16
+6 0 0 0 0 9 12 4 4.44089209850063e-16
+6 0 0 0 0 9 12 5 4.44089209850063e-16
+6 0 0 0 0 9 12 6 4.44089209850063e-16
+6 0 0 0 0 9 12 7 4.44089209850063e-16
+6 0 0 0 0 9 12 8 4.44089209850063e-16
+6 0 0 0 0 9 12 9 4.44089209850063e-16
+6 0 0 0 0 9 12 10 4.44089209850063e-16
+6 0 0 0 0 9 12 11 4.44089209850063e-16
+6 0 0 0 0 9 12 12 4.44089209850063e-16
+6 0 0 0 0 9 12 13 4.44089209850063e-16
+6 0 0 0 0 9 12 14 4.44089209850063e-16
+6 0 0 0 0 9 12 15 4.44089209850063e-16
+6 0 0 0 0 9 12 16 4.44089209850063e-16
+6 0 0 0 0 9 12 17 4.44089209850063e-16
+6 0 0 0 0 9 12 18 4.44089209850063e-16
+6 0 0 0 0 9 12 19 4.44089209850063e-16
+6 0 0 0 0 9 12 20 4.44089209850063e-16
+6 0 0 0 0 9 12 21 4.44089209850063e-16
+6 0 0 0 0 9 12 22 4.44089209850063e-16
+6 0 0 0 0 9 12 23 4.44089209850063e-16
+6 0 0 0 0 9 12 24 4.44089209850063e-16
+6 0 0 0 0 9 12 25 4.44089209850063e-16
+6 0 0 0 0 9 12 26 4.44089209850063e-16
+6 0 0 0 0 9 12 27 4.44089209850063e-16
+6 0 0 0 0 9 12 28 4.44089209850063e-16
+6 0 0 0 0 9 12 29 4.44089209850063e-16
+6 0 0 0 0 9 12 30 4.44089209850063e-16
+6 0 0 0 0 9 12 31 4.44089209850063e-16
+6 0 0 0 0 9 12 32 4.44089209850063e-16
+6 0 0 0 0 9 12 33 4.44089209850063e-16
+
+
diff --git a/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/cart3d_y.xl b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/cart3d_y.xl
new file mode 100644
index 000000000..d4d13f446
--- /dev/null
+++ b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/cart3d_y.xl
@@ -0,0 +1,170 @@
+# GRID::cart3d_y x (cart3d_y)
+#
+# iteration 0
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+0 0 0 0 0 0 12 16 -4.44089209850063e-16
+0 0 0 0 0 1 12 16 -4.44089209850063e-16
+0 0 0 0 0 2 12 16 -4.44089209850063e-16
+0 0 0 0 0 3 12 16 -4.44089209850063e-16
+0 0 0 0 0 4 12 16 -4.44089209850063e-16
+0 0 0 0 0 5 12 16 -4.44089209850063e-16
+0 0 0 0 0 6 12 16 -4.44089209850063e-16
+0 0 0 0 0 7 12 16 -4.44089209850063e-16
+0 0 0 0 0 8 12 16 -4.44089209850063e-16
+0 0 0 0 0 9 12 16 -4.44089209850063e-16
+0 0 0 0 0 10 12 16 -4.44089209850063e-16
+0 0 0 0 0 11 12 16 -4.44089209850063e-16
+0 0 0 0 0 12 12 16 -4.44089209850063e-16
+0 0 0 0 0 13 12 16 -4.44089209850063e-16
+0 0 0 0 0 14 12 16 -4.44089209850063e-16
+0 0 0 0 0 15 12 16 -4.44089209850063e-16
+0 0 0 0 0 16 12 16 -4.44089209850063e-16
+0 0 0 0 0 17 12 16 -4.44089209850063e-16
+0 0 0 0 0 18 12 16 -4.44089209850063e-16
+
+
+# iteration 1
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+1 0 0 0 0 0 12 16 -4.44089209850063e-16
+1 0 0 0 0 1 12 16 -4.44089209850063e-16
+1 0 0 0 0 2 12 16 -4.44089209850063e-16
+1 0 0 0 0 3 12 16 -4.44089209850063e-16
+1 0 0 0 0 4 12 16 -4.44089209850063e-16
+1 0 0 0 0 5 12 16 -4.44089209850063e-16
+1 0 0 0 0 6 12 16 -4.44089209850063e-16
+1 0 0 0 0 7 12 16 -4.44089209850063e-16
+1 0 0 0 0 8 12 16 -4.44089209850063e-16
+1 0 0 0 0 9 12 16 -4.44089209850063e-16
+1 0 0 0 0 10 12 16 -4.44089209850063e-16
+1 0 0 0 0 11 12 16 -4.44089209850063e-16
+1 0 0 0 0 12 12 16 -4.44089209850063e-16
+1 0 0 0 0 13 12 16 -4.44089209850063e-16
+1 0 0 0 0 14 12 16 -4.44089209850063e-16
+1 0 0 0 0 15 12 16 -4.44089209850063e-16
+1 0 0 0 0 16 12 16 -4.44089209850063e-16
+1 0 0 0 0 17 12 16 -4.44089209850063e-16
+1 0 0 0 0 18 12 16 -4.44089209850063e-16
+
+
+# iteration 2
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+2 0 0 0 0 0 12 16 -4.44089209850063e-16
+2 0 0 0 0 1 12 16 -4.44089209850063e-16
+2 0 0 0 0 2 12 16 -4.44089209850063e-16
+2 0 0 0 0 3 12 16 -4.44089209850063e-16
+2 0 0 0 0 4 12 16 -4.44089209850063e-16
+2 0 0 0 0 5 12 16 -4.44089209850063e-16
+2 0 0 0 0 6 12 16 -4.44089209850063e-16
+2 0 0 0 0 7 12 16 -4.44089209850063e-16
+2 0 0 0 0 8 12 16 -4.44089209850063e-16
+2 0 0 0 0 9 12 16 -4.44089209850063e-16
+2 0 0 0 0 10 12 16 -4.44089209850063e-16
+2 0 0 0 0 11 12 16 -4.44089209850063e-16
+2 0 0 0 0 12 12 16 -4.44089209850063e-16
+2 0 0 0 0 13 12 16 -4.44089209850063e-16
+2 0 0 0 0 14 12 16 -4.44089209850063e-16
+2 0 0 0 0 15 12 16 -4.44089209850063e-16
+2 0 0 0 0 16 12 16 -4.44089209850063e-16
+2 0 0 0 0 17 12 16 -4.44089209850063e-16
+2 0 0 0 0 18 12 16 -4.44089209850063e-16
+
+
+# iteration 3
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+3 0 0 0 0 0 12 16 -4.44089209850063e-16
+3 0 0 0 0 1 12 16 -4.44089209850063e-16
+3 0 0 0 0 2 12 16 -4.44089209850063e-16
+3 0 0 0 0 3 12 16 -4.44089209850063e-16
+3 0 0 0 0 4 12 16 -4.44089209850063e-16
+3 0 0 0 0 5 12 16 -4.44089209850063e-16
+3 0 0 0 0 6 12 16 -4.44089209850063e-16
+3 0 0 0 0 7 12 16 -4.44089209850063e-16
+3 0 0 0 0 8 12 16 -4.44089209850063e-16
+3 0 0 0 0 9 12 16 -4.44089209850063e-16
+3 0 0 0 0 10 12 16 -4.44089209850063e-16
+3 0 0 0 0 11 12 16 -4.44089209850063e-16
+3 0 0 0 0 12 12 16 -4.44089209850063e-16
+3 0 0 0 0 13 12 16 -4.44089209850063e-16
+3 0 0 0 0 14 12 16 -4.44089209850063e-16
+3 0 0 0 0 15 12 16 -4.44089209850063e-16
+3 0 0 0 0 16 12 16 -4.44089209850063e-16
+3 0 0 0 0 17 12 16 -4.44089209850063e-16
+3 0 0 0 0 18 12 16 -4.44089209850063e-16
+
+
+# iteration 4
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+4 0 0 0 0 0 12 16 -4.44089209850063e-16
+4 0 0 0 0 1 12 16 -4.44089209850063e-16
+4 0 0 0 0 2 12 16 -4.44089209850063e-16
+4 0 0 0 0 3 12 16 -4.44089209850063e-16
+4 0 0 0 0 4 12 16 -4.44089209850063e-16
+4 0 0 0 0 5 12 16 -4.44089209850063e-16
+4 0 0 0 0 6 12 16 -4.44089209850063e-16
+4 0 0 0 0 7 12 16 -4.44089209850063e-16
+4 0 0 0 0 8 12 16 -4.44089209850063e-16
+4 0 0 0 0 9 12 16 -4.44089209850063e-16
+4 0 0 0 0 10 12 16 -4.44089209850063e-16
+4 0 0 0 0 11 12 16 -4.44089209850063e-16
+4 0 0 0 0 12 12 16 -4.44089209850063e-16
+4 0 0 0 0 13 12 16 -4.44089209850063e-16
+4 0 0 0 0 14 12 16 -4.44089209850063e-16
+4 0 0 0 0 15 12 16 -4.44089209850063e-16
+4 0 0 0 0 16 12 16 -4.44089209850063e-16
+4 0 0 0 0 17 12 16 -4.44089209850063e-16
+4 0 0 0 0 18 12 16 -4.44089209850063e-16
+
+
+# iteration 5
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+5 0 0 0 0 0 12 16 -4.44089209850063e-16
+5 0 0 0 0 1 12 16 -4.44089209850063e-16
+5 0 0 0 0 2 12 16 -4.44089209850063e-16
+5 0 0 0 0 3 12 16 -4.44089209850063e-16
+5 0 0 0 0 4 12 16 -4.44089209850063e-16
+5 0 0 0 0 5 12 16 -4.44089209850063e-16
+5 0 0 0 0 6 12 16 -4.44089209850063e-16
+5 0 0 0 0 7 12 16 -4.44089209850063e-16
+5 0 0 0 0 8 12 16 -4.44089209850063e-16
+5 0 0 0 0 9 12 16 -4.44089209850063e-16
+5 0 0 0 0 10 12 16 -4.44089209850063e-16
+5 0 0 0 0 11 12 16 -4.44089209850063e-16
+5 0 0 0 0 12 12 16 -4.44089209850063e-16
+5 0 0 0 0 13 12 16 -4.44089209850063e-16
+5 0 0 0 0 14 12 16 -4.44089209850063e-16
+5 0 0 0 0 15 12 16 -4.44089209850063e-16
+5 0 0 0 0 16 12 16 -4.44089209850063e-16
+5 0 0 0 0 17 12 16 -4.44089209850063e-16
+5 0 0 0 0 18 12 16 -4.44089209850063e-16
+
+
+# iteration 6
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+6 0 0 0 0 0 12 16 -4.44089209850063e-16
+6 0 0 0 0 1 12 16 -4.44089209850063e-16
+6 0 0 0 0 2 12 16 -4.44089209850063e-16
+6 0 0 0 0 3 12 16 -4.44089209850063e-16
+6 0 0 0 0 4 12 16 -4.44089209850063e-16
+6 0 0 0 0 5 12 16 -4.44089209850063e-16
+6 0 0 0 0 6 12 16 -4.44089209850063e-16
+6 0 0 0 0 7 12 16 -4.44089209850063e-16
+6 0 0 0 0 8 12 16 -4.44089209850063e-16
+6 0 0 0 0 9 12 16 -4.44089209850063e-16
+6 0 0 0 0 10 12 16 -4.44089209850063e-16
+6 0 0 0 0 11 12 16 -4.44089209850063e-16
+6 0 0 0 0 12 12 16 -4.44089209850063e-16
+6 0 0 0 0 13 12 16 -4.44089209850063e-16
+6 0 0 0 0 14 12 16 -4.44089209850063e-16
+6 0 0 0 0 15 12 16 -4.44089209850063e-16
+6 0 0 0 0 16 12 16 -4.44089209850063e-16
+6 0 0 0 0 17 12 16 -4.44089209850063e-16
+6 0 0 0 0 18 12 16 -4.44089209850063e-16
+
+
diff --git a/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/cart3d_y.yl b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/cart3d_y.yl
new file mode 100644
index 000000000..f9b213254
--- /dev/null
+++ b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/cart3d_y.yl
@@ -0,0 +1,219 @@
+# GRID::cart3d_y y (cart3d_y)
+#
+# iteration 0
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+0 0 0 0 0 9 0 16 -7.2
+0 0 0 0 0 9 1 16 -6.6
+0 0 0 0 0 9 2 16 -6
+0 0 0 0 0 9 3 16 -5.4
+0 0 0 0 0 9 4 16 -4.8
+0 0 0 0 0 9 5 16 -4.2
+0 0 0 0 0 9 6 16 -3.6
+0 0 0 0 0 9 7 16 -3
+0 0 0 0 0 9 8 16 -2.4
+0 0 0 0 0 9 9 16 -1.8
+0 0 0 0 0 9 10 16 -1.2
+0 0 0 0 0 9 11 16 -0.6
+0 0 0 0 0 9 12 16 -4.44089209850063e-16
+0 0 0 0 0 9 13 16 0.6
+0 0 0 0 0 9 14 16 1.2
+0 0 0 0 0 9 15 16 1.8
+0 0 0 0 0 9 16 16 2.4
+0 0 0 0 0 9 17 16 3
+0 0 0 0 0 9 18 16 3.6
+0 0 0 0 0 9 19 16 4.2
+0 0 0 0 0 9 20 16 4.8
+0 0 0 0 0 9 21 16 5.4
+0 0 0 0 0 9 22 16 6
+0 0 0 0 0 9 23 16 6.6
+0 0 0 0 0 9 24 16 7.2
+0 0 0 0 0 9 25 16 7.8
+
+
+# iteration 1
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+1 0 0 0 0 9 0 16 -7.2
+1 0 0 0 0 9 1 16 -6.6
+1 0 0 0 0 9 2 16 -6
+1 0 0 0 0 9 3 16 -5.4
+1 0 0 0 0 9 4 16 -4.8
+1 0 0 0 0 9 5 16 -4.2
+1 0 0 0 0 9 6 16 -3.6
+1 0 0 0 0 9 7 16 -3
+1 0 0 0 0 9 8 16 -2.4
+1 0 0 0 0 9 9 16 -1.8
+1 0 0 0 0 9 10 16 -1.2
+1 0 0 0 0 9 11 16 -0.6
+1 0 0 0 0 9 12 16 -4.44089209850063e-16
+1 0 0 0 0 9 13 16 0.6
+1 0 0 0 0 9 14 16 1.2
+1 0 0 0 0 9 15 16 1.8
+1 0 0 0 0 9 16 16 2.4
+1 0 0 0 0 9 17 16 3
+1 0 0 0 0 9 18 16 3.6
+1 0 0 0 0 9 19 16 4.2
+1 0 0 0 0 9 20 16 4.8
+1 0 0 0 0 9 21 16 5.4
+1 0 0 0 0 9 22 16 6
+1 0 0 0 0 9 23 16 6.6
+1 0 0 0 0 9 24 16 7.2
+1 0 0 0 0 9 25 16 7.8
+
+
+# iteration 2
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+2 0 0 0 0 9 0 16 -7.2
+2 0 0 0 0 9 1 16 -6.6
+2 0 0 0 0 9 2 16 -6
+2 0 0 0 0 9 3 16 -5.4
+2 0 0 0 0 9 4 16 -4.8
+2 0 0 0 0 9 5 16 -4.2
+2 0 0 0 0 9 6 16 -3.6
+2 0 0 0 0 9 7 16 -3
+2 0 0 0 0 9 8 16 -2.4
+2 0 0 0 0 9 9 16 -1.8
+2 0 0 0 0 9 10 16 -1.2
+2 0 0 0 0 9 11 16 -0.6
+2 0 0 0 0 9 12 16 -4.44089209850063e-16
+2 0 0 0 0 9 13 16 0.6
+2 0 0 0 0 9 14 16 1.2
+2 0 0 0 0 9 15 16 1.8
+2 0 0 0 0 9 16 16 2.4
+2 0 0 0 0 9 17 16 3
+2 0 0 0 0 9 18 16 3.6
+2 0 0 0 0 9 19 16 4.2
+2 0 0 0 0 9 20 16 4.8
+2 0 0 0 0 9 21 16 5.4
+2 0 0 0 0 9 22 16 6
+2 0 0 0 0 9 23 16 6.6
+2 0 0 0 0 9 24 16 7.2
+2 0 0 0 0 9 25 16 7.8
+
+
+# iteration 3
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+3 0 0 0 0 9 0 16 -7.2
+3 0 0 0 0 9 1 16 -6.6
+3 0 0 0 0 9 2 16 -6
+3 0 0 0 0 9 3 16 -5.4
+3 0 0 0 0 9 4 16 -4.8
+3 0 0 0 0 9 5 16 -4.2
+3 0 0 0 0 9 6 16 -3.6
+3 0 0 0 0 9 7 16 -3
+3 0 0 0 0 9 8 16 -2.4
+3 0 0 0 0 9 9 16 -1.8
+3 0 0 0 0 9 10 16 -1.2
+3 0 0 0 0 9 11 16 -0.6
+3 0 0 0 0 9 12 16 -4.44089209850063e-16
+3 0 0 0 0 9 13 16 0.6
+3 0 0 0 0 9 14 16 1.2
+3 0 0 0 0 9 15 16 1.8
+3 0 0 0 0 9 16 16 2.4
+3 0 0 0 0 9 17 16 3
+3 0 0 0 0 9 18 16 3.6
+3 0 0 0 0 9 19 16 4.2
+3 0 0 0 0 9 20 16 4.8
+3 0 0 0 0 9 21 16 5.4
+3 0 0 0 0 9 22 16 6
+3 0 0 0 0 9 23 16 6.6
+3 0 0 0 0 9 24 16 7.2
+3 0 0 0 0 9 25 16 7.8
+
+
+# iteration 4
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+4 0 0 0 0 9 0 16 -7.2
+4 0 0 0 0 9 1 16 -6.6
+4 0 0 0 0 9 2 16 -6
+4 0 0 0 0 9 3 16 -5.4
+4 0 0 0 0 9 4 16 -4.8
+4 0 0 0 0 9 5 16 -4.2
+4 0 0 0 0 9 6 16 -3.6
+4 0 0 0 0 9 7 16 -3
+4 0 0 0 0 9 8 16 -2.4
+4 0 0 0 0 9 9 16 -1.8
+4 0 0 0 0 9 10 16 -1.2
+4 0 0 0 0 9 11 16 -0.6
+4 0 0 0 0 9 12 16 -4.44089209850063e-16
+4 0 0 0 0 9 13 16 0.6
+4 0 0 0 0 9 14 16 1.2
+4 0 0 0 0 9 15 16 1.8
+4 0 0 0 0 9 16 16 2.4
+4 0 0 0 0 9 17 16 3
+4 0 0 0 0 9 18 16 3.6
+4 0 0 0 0 9 19 16 4.2
+4 0 0 0 0 9 20 16 4.8
+4 0 0 0 0 9 21 16 5.4
+4 0 0 0 0 9 22 16 6
+4 0 0 0 0 9 23 16 6.6
+4 0 0 0 0 9 24 16 7.2
+4 0 0 0 0 9 25 16 7.8
+
+
+# iteration 5
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+5 0 0 0 0 9 0 16 -7.2
+5 0 0 0 0 9 1 16 -6.6
+5 0 0 0 0 9 2 16 -6
+5 0 0 0 0 9 3 16 -5.4
+5 0 0 0 0 9 4 16 -4.8
+5 0 0 0 0 9 5 16 -4.2
+5 0 0 0 0 9 6 16 -3.6
+5 0 0 0 0 9 7 16 -3
+5 0 0 0 0 9 8 16 -2.4
+5 0 0 0 0 9 9 16 -1.8
+5 0 0 0 0 9 10 16 -1.2
+5 0 0 0 0 9 11 16 -0.6
+5 0 0 0 0 9 12 16 -4.44089209850063e-16
+5 0 0 0 0 9 13 16 0.6
+5 0 0 0 0 9 14 16 1.2
+5 0 0 0 0 9 15 16 1.8
+5 0 0 0 0 9 16 16 2.4
+5 0 0 0 0 9 17 16 3
+5 0 0 0 0 9 18 16 3.6
+5 0 0 0 0 9 19 16 4.2
+5 0 0 0 0 9 20 16 4.8
+5 0 0 0 0 9 21 16 5.4
+5 0 0 0 0 9 22 16 6
+5 0 0 0 0 9 23 16 6.6
+5 0 0 0 0 9 24 16 7.2
+5 0 0 0 0 9 25 16 7.8
+
+
+# iteration 6
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+6 0 0 0 0 9 0 16 -7.2
+6 0 0 0 0 9 1 16 -6.6
+6 0 0 0 0 9 2 16 -6
+6 0 0 0 0 9 3 16 -5.4
+6 0 0 0 0 9 4 16 -4.8
+6 0 0 0 0 9 5 16 -4.2
+6 0 0 0 0 9 6 16 -3.6
+6 0 0 0 0 9 7 16 -3
+6 0 0 0 0 9 8 16 -2.4
+6 0 0 0 0 9 9 16 -1.8
+6 0 0 0 0 9 10 16 -1.2
+6 0 0 0 0 9 11 16 -0.6
+6 0 0 0 0 9 12 16 -4.44089209850063e-16
+6 0 0 0 0 9 13 16 0.6
+6 0 0 0 0 9 14 16 1.2
+6 0 0 0 0 9 15 16 1.8
+6 0 0 0 0 9 16 16 2.4
+6 0 0 0 0 9 17 16 3
+6 0 0 0 0 9 18 16 3.6
+6 0 0 0 0 9 19 16 4.2
+6 0 0 0 0 9 20 16 4.8
+6 0 0 0 0 9 21 16 5.4
+6 0 0 0 0 9 22 16 6
+6 0 0 0 0 9 23 16 6.6
+6 0 0 0 0 9 24 16 7.2
+6 0 0 0 0 9 25 16 7.8
+
+
diff --git a/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/cart3d_y.zl b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/cart3d_y.zl
new file mode 100644
index 000000000..5eb528a02
--- /dev/null
+++ b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/cart3d_y.zl
@@ -0,0 +1,275 @@
+# GRID::cart3d_y z (cart3d_y)
+#
+# iteration 0
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+0 0 0 0 0 9 12 0 -4.44089209850063e-16
+0 0 0 0 0 9 12 1 -4.44089209850063e-16
+0 0 0 0 0 9 12 2 -4.44089209850063e-16
+0 0 0 0 0 9 12 3 -4.44089209850063e-16
+0 0 0 0 0 9 12 4 -4.44089209850063e-16
+0 0 0 0 0 9 12 5 -4.44089209850063e-16
+0 0 0 0 0 9 12 6 -4.44089209850063e-16
+0 0 0 0 0 9 12 7 -4.44089209850063e-16
+0 0 0 0 0 9 12 8 -4.44089209850063e-16
+0 0 0 0 0 9 12 9 -4.44089209850063e-16
+0 0 0 0 0 9 12 10 -4.44089209850063e-16
+0 0 0 0 0 9 12 11 -4.44089209850063e-16
+0 0 0 0 0 9 12 12 -4.44089209850063e-16
+0 0 0 0 0 9 12 13 -4.44089209850063e-16
+0 0 0 0 0 9 12 14 -4.44089209850063e-16
+0 0 0 0 0 9 12 15 -4.44089209850063e-16
+0 0 0 0 0 9 12 16 -4.44089209850063e-16
+0 0 0 0 0 9 12 17 -4.44089209850063e-16
+0 0 0 0 0 9 12 18 -4.44089209850063e-16
+0 0 0 0 0 9 12 19 -4.44089209850063e-16
+0 0 0 0 0 9 12 20 -4.44089209850063e-16
+0 0 0 0 0 9 12 21 -4.44089209850063e-16
+0 0 0 0 0 9 12 22 -4.44089209850063e-16
+0 0 0 0 0 9 12 23 -4.44089209850063e-16
+0 0 0 0 0 9 12 24 -4.44089209850063e-16
+0 0 0 0 0 9 12 25 -4.44089209850063e-16
+0 0 0 0 0 9 12 26 -4.44089209850063e-16
+0 0 0 0 0 9 12 27 -4.44089209850063e-16
+0 0 0 0 0 9 12 28 -4.44089209850063e-16
+0 0 0 0 0 9 12 29 -4.44089209850063e-16
+0 0 0 0 0 9 12 30 -4.44089209850063e-16
+0 0 0 0 0 9 12 31 -4.44089209850063e-16
+0 0 0 0 0 9 12 32 -4.44089209850063e-16
+0 0 0 0 0 9 12 33 -4.44089209850063e-16
+
+
+# iteration 1
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+1 0 0 0 0 9 12 0 -4.44089209850063e-16
+1 0 0 0 0 9 12 1 -4.44089209850063e-16
+1 0 0 0 0 9 12 2 -4.44089209850063e-16
+1 0 0 0 0 9 12 3 -4.44089209850063e-16
+1 0 0 0 0 9 12 4 -4.44089209850063e-16
+1 0 0 0 0 9 12 5 -4.44089209850063e-16
+1 0 0 0 0 9 12 6 -4.44089209850063e-16
+1 0 0 0 0 9 12 7 -4.44089209850063e-16
+1 0 0 0 0 9 12 8 -4.44089209850063e-16
+1 0 0 0 0 9 12 9 -4.44089209850063e-16
+1 0 0 0 0 9 12 10 -4.44089209850063e-16
+1 0 0 0 0 9 12 11 -4.44089209850063e-16
+1 0 0 0 0 9 12 12 -4.44089209850063e-16
+1 0 0 0 0 9 12 13 -4.44089209850063e-16
+1 0 0 0 0 9 12 14 -4.44089209850063e-16
+1 0 0 0 0 9 12 15 -4.44089209850063e-16
+1 0 0 0 0 9 12 16 -4.44089209850063e-16
+1 0 0 0 0 9 12 17 -4.44089209850063e-16
+1 0 0 0 0 9 12 18 -4.44089209850063e-16
+1 0 0 0 0 9 12 19 -4.44089209850063e-16
+1 0 0 0 0 9 12 20 -4.44089209850063e-16
+1 0 0 0 0 9 12 21 -4.44089209850063e-16
+1 0 0 0 0 9 12 22 -4.44089209850063e-16
+1 0 0 0 0 9 12 23 -4.44089209850063e-16
+1 0 0 0 0 9 12 24 -4.44089209850063e-16
+1 0 0 0 0 9 12 25 -4.44089209850063e-16
+1 0 0 0 0 9 12 26 -4.44089209850063e-16
+1 0 0 0 0 9 12 27 -4.44089209850063e-16
+1 0 0 0 0 9 12 28 -4.44089209850063e-16
+1 0 0 0 0 9 12 29 -4.44089209850063e-16
+1 0 0 0 0 9 12 30 -4.44089209850063e-16
+1 0 0 0 0 9 12 31 -4.44089209850063e-16
+1 0 0 0 0 9 12 32 -4.44089209850063e-16
+1 0 0 0 0 9 12 33 -4.44089209850063e-16
+
+
+# iteration 2
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+2 0 0 0 0 9 12 0 -4.44089209850063e-16
+2 0 0 0 0 9 12 1 -4.44089209850063e-16
+2 0 0 0 0 9 12 2 -4.44089209850063e-16
+2 0 0 0 0 9 12 3 -4.44089209850063e-16
+2 0 0 0 0 9 12 4 -4.44089209850063e-16
+2 0 0 0 0 9 12 5 -4.44089209850063e-16
+2 0 0 0 0 9 12 6 -4.44089209850063e-16
+2 0 0 0 0 9 12 7 -4.44089209850063e-16
+2 0 0 0 0 9 12 8 -4.44089209850063e-16
+2 0 0 0 0 9 12 9 -4.44089209850063e-16
+2 0 0 0 0 9 12 10 -4.44089209850063e-16
+2 0 0 0 0 9 12 11 -4.44089209850063e-16
+2 0 0 0 0 9 12 12 -4.44089209850063e-16
+2 0 0 0 0 9 12 13 -4.44089209850063e-16
+2 0 0 0 0 9 12 14 -4.44089209850063e-16
+2 0 0 0 0 9 12 15 -4.44089209850063e-16
+2 0 0 0 0 9 12 16 -4.44089209850063e-16
+2 0 0 0 0 9 12 17 -4.44089209850063e-16
+2 0 0 0 0 9 12 18 -4.44089209850063e-16
+2 0 0 0 0 9 12 19 -4.44089209850063e-16
+2 0 0 0 0 9 12 20 -4.44089209850063e-16
+2 0 0 0 0 9 12 21 -4.44089209850063e-16
+2 0 0 0 0 9 12 22 -4.44089209850063e-16
+2 0 0 0 0 9 12 23 -4.44089209850063e-16
+2 0 0 0 0 9 12 24 -4.44089209850063e-16
+2 0 0 0 0 9 12 25 -4.44089209850063e-16
+2 0 0 0 0 9 12 26 -4.44089209850063e-16
+2 0 0 0 0 9 12 27 -4.44089209850063e-16
+2 0 0 0 0 9 12 28 -4.44089209850063e-16
+2 0 0 0 0 9 12 29 -4.44089209850063e-16
+2 0 0 0 0 9 12 30 -4.44089209850063e-16
+2 0 0 0 0 9 12 31 -4.44089209850063e-16
+2 0 0 0 0 9 12 32 -4.44089209850063e-16
+2 0 0 0 0 9 12 33 -4.44089209850063e-16
+
+
+# iteration 3
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+3 0 0 0 0 9 12 0 -4.44089209850063e-16
+3 0 0 0 0 9 12 1 -4.44089209850063e-16
+3 0 0 0 0 9 12 2 -4.44089209850063e-16
+3 0 0 0 0 9 12 3 -4.44089209850063e-16
+3 0 0 0 0 9 12 4 -4.44089209850063e-16
+3 0 0 0 0 9 12 5 -4.44089209850063e-16
+3 0 0 0 0 9 12 6 -4.44089209850063e-16
+3 0 0 0 0 9 12 7 -4.44089209850063e-16
+3 0 0 0 0 9 12 8 -4.44089209850063e-16
+3 0 0 0 0 9 12 9 -4.44089209850063e-16
+3 0 0 0 0 9 12 10 -4.44089209850063e-16
+3 0 0 0 0 9 12 11 -4.44089209850063e-16
+3 0 0 0 0 9 12 12 -4.44089209850063e-16
+3 0 0 0 0 9 12 13 -4.44089209850063e-16
+3 0 0 0 0 9 12 14 -4.44089209850063e-16
+3 0 0 0 0 9 12 15 -4.44089209850063e-16
+3 0 0 0 0 9 12 16 -4.44089209850063e-16
+3 0 0 0 0 9 12 17 -4.44089209850063e-16
+3 0 0 0 0 9 12 18 -4.44089209850063e-16
+3 0 0 0 0 9 12 19 -4.44089209850063e-16
+3 0 0 0 0 9 12 20 -4.44089209850063e-16
+3 0 0 0 0 9 12 21 -4.44089209850063e-16
+3 0 0 0 0 9 12 22 -4.44089209850063e-16
+3 0 0 0 0 9 12 23 -4.44089209850063e-16
+3 0 0 0 0 9 12 24 -4.44089209850063e-16
+3 0 0 0 0 9 12 25 -4.44089209850063e-16
+3 0 0 0 0 9 12 26 -4.44089209850063e-16
+3 0 0 0 0 9 12 27 -4.44089209850063e-16
+3 0 0 0 0 9 12 28 -4.44089209850063e-16
+3 0 0 0 0 9 12 29 -4.44089209850063e-16
+3 0 0 0 0 9 12 30 -4.44089209850063e-16
+3 0 0 0 0 9 12 31 -4.44089209850063e-16
+3 0 0 0 0 9 12 32 -4.44089209850063e-16
+3 0 0 0 0 9 12 33 -4.44089209850063e-16
+
+
+# iteration 4
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+4 0 0 0 0 9 12 0 -4.44089209850063e-16
+4 0 0 0 0 9 12 1 -4.44089209850063e-16
+4 0 0 0 0 9 12 2 -4.44089209850063e-16
+4 0 0 0 0 9 12 3 -4.44089209850063e-16
+4 0 0 0 0 9 12 4 -4.44089209850063e-16
+4 0 0 0 0 9 12 5 -4.44089209850063e-16
+4 0 0 0 0 9 12 6 -4.44089209850063e-16
+4 0 0 0 0 9 12 7 -4.44089209850063e-16
+4 0 0 0 0 9 12 8 -4.44089209850063e-16
+4 0 0 0 0 9 12 9 -4.44089209850063e-16
+4 0 0 0 0 9 12 10 -4.44089209850063e-16
+4 0 0 0 0 9 12 11 -4.44089209850063e-16
+4 0 0 0 0 9 12 12 -4.44089209850063e-16
+4 0 0 0 0 9 12 13 -4.44089209850063e-16
+4 0 0 0 0 9 12 14 -4.44089209850063e-16
+4 0 0 0 0 9 12 15 -4.44089209850063e-16
+4 0 0 0 0 9 12 16 -4.44089209850063e-16
+4 0 0 0 0 9 12 17 -4.44089209850063e-16
+4 0 0 0 0 9 12 18 -4.44089209850063e-16
+4 0 0 0 0 9 12 19 -4.44089209850063e-16
+4 0 0 0 0 9 12 20 -4.44089209850063e-16
+4 0 0 0 0 9 12 21 -4.44089209850063e-16
+4 0 0 0 0 9 12 22 -4.44089209850063e-16
+4 0 0 0 0 9 12 23 -4.44089209850063e-16
+4 0 0 0 0 9 12 24 -4.44089209850063e-16
+4 0 0 0 0 9 12 25 -4.44089209850063e-16
+4 0 0 0 0 9 12 26 -4.44089209850063e-16
+4 0 0 0 0 9 12 27 -4.44089209850063e-16
+4 0 0 0 0 9 12 28 -4.44089209850063e-16
+4 0 0 0 0 9 12 29 -4.44089209850063e-16
+4 0 0 0 0 9 12 30 -4.44089209850063e-16
+4 0 0 0 0 9 12 31 -4.44089209850063e-16
+4 0 0 0 0 9 12 32 -4.44089209850063e-16
+4 0 0 0 0 9 12 33 -4.44089209850063e-16
+
+
+# iteration 5
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+5 0 0 0 0 9 12 0 -4.44089209850063e-16
+5 0 0 0 0 9 12 1 -4.44089209850063e-16
+5 0 0 0 0 9 12 2 -4.44089209850063e-16
+5 0 0 0 0 9 12 3 -4.44089209850063e-16
+5 0 0 0 0 9 12 4 -4.44089209850063e-16
+5 0 0 0 0 9 12 5 -4.44089209850063e-16
+5 0 0 0 0 9 12 6 -4.44089209850063e-16
+5 0 0 0 0 9 12 7 -4.44089209850063e-16
+5 0 0 0 0 9 12 8 -4.44089209850063e-16
+5 0 0 0 0 9 12 9 -4.44089209850063e-16
+5 0 0 0 0 9 12 10 -4.44089209850063e-16
+5 0 0 0 0 9 12 11 -4.44089209850063e-16
+5 0 0 0 0 9 12 12 -4.44089209850063e-16
+5 0 0 0 0 9 12 13 -4.44089209850063e-16
+5 0 0 0 0 9 12 14 -4.44089209850063e-16
+5 0 0 0 0 9 12 15 -4.44089209850063e-16
+5 0 0 0 0 9 12 16 -4.44089209850063e-16
+5 0 0 0 0 9 12 17 -4.44089209850063e-16
+5 0 0 0 0 9 12 18 -4.44089209850063e-16
+5 0 0 0 0 9 12 19 -4.44089209850063e-16
+5 0 0 0 0 9 12 20 -4.44089209850063e-16
+5 0 0 0 0 9 12 21 -4.44089209850063e-16
+5 0 0 0 0 9 12 22 -4.44089209850063e-16
+5 0 0 0 0 9 12 23 -4.44089209850063e-16
+5 0 0 0 0 9 12 24 -4.44089209850063e-16
+5 0 0 0 0 9 12 25 -4.44089209850063e-16
+5 0 0 0 0 9 12 26 -4.44089209850063e-16
+5 0 0 0 0 9 12 27 -4.44089209850063e-16
+5 0 0 0 0 9 12 28 -4.44089209850063e-16
+5 0 0 0 0 9 12 29 -4.44089209850063e-16
+5 0 0 0 0 9 12 30 -4.44089209850063e-16
+5 0 0 0 0 9 12 31 -4.44089209850063e-16
+5 0 0 0 0 9 12 32 -4.44089209850063e-16
+5 0 0 0 0 9 12 33 -4.44089209850063e-16
+
+
+# iteration 6
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+6 0 0 0 0 9 12 0 -4.44089209850063e-16
+6 0 0 0 0 9 12 1 -4.44089209850063e-16
+6 0 0 0 0 9 12 2 -4.44089209850063e-16
+6 0 0 0 0 9 12 3 -4.44089209850063e-16
+6 0 0 0 0 9 12 4 -4.44089209850063e-16
+6 0 0 0 0 9 12 5 -4.44089209850063e-16
+6 0 0 0 0 9 12 6 -4.44089209850063e-16
+6 0 0 0 0 9 12 7 -4.44089209850063e-16
+6 0 0 0 0 9 12 8 -4.44089209850063e-16
+6 0 0 0 0 9 12 9 -4.44089209850063e-16
+6 0 0 0 0 9 12 10 -4.44089209850063e-16
+6 0 0 0 0 9 12 11 -4.44089209850063e-16
+6 0 0 0 0 9 12 12 -4.44089209850063e-16
+6 0 0 0 0 9 12 13 -4.44089209850063e-16
+6 0 0 0 0 9 12 14 -4.44089209850063e-16
+6 0 0 0 0 9 12 15 -4.44089209850063e-16
+6 0 0 0 0 9 12 16 -4.44089209850063e-16
+6 0 0 0 0 9 12 17 -4.44089209850063e-16
+6 0 0 0 0 9 12 18 -4.44089209850063e-16
+6 0 0 0 0 9 12 19 -4.44089209850063e-16
+6 0 0 0 0 9 12 20 -4.44089209850063e-16
+6 0 0 0 0 9 12 21 -4.44089209850063e-16
+6 0 0 0 0 9 12 22 -4.44089209850063e-16
+6 0 0 0 0 9 12 23 -4.44089209850063e-16
+6 0 0 0 0 9 12 24 -4.44089209850063e-16
+6 0 0 0 0 9 12 25 -4.44089209850063e-16
+6 0 0 0 0 9 12 26 -4.44089209850063e-16
+6 0 0 0 0 9 12 27 -4.44089209850063e-16
+6 0 0 0 0 9 12 28 -4.44089209850063e-16
+6 0 0 0 0 9 12 29 -4.44089209850063e-16
+6 0 0 0 0 9 12 30 -4.44089209850063e-16
+6 0 0 0 0 9 12 31 -4.44089209850063e-16
+6 0 0 0 0 9 12 32 -4.44089209850063e-16
+6 0 0 0 0 9 12 33 -4.44089209850063e-16
+
+
diff --git a/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/cart3d_z.xl b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/cart3d_z.xl
new file mode 100644
index 000000000..ec487ca98
--- /dev/null
+++ b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/cart3d_z.xl
@@ -0,0 +1,170 @@
+# GRID::cart3d_z x (cart3d_z)
+#
+# iteration 0
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+0 0 0 0 0 0 12 16 0
+0 0 0 0 0 1 12 16 0
+0 0 0 0 0 2 12 16 0
+0 0 0 0 0 3 12 16 0
+0 0 0 0 0 4 12 16 0
+0 0 0 0 0 5 12 16 0
+0 0 0 0 0 6 12 16 0
+0 0 0 0 0 7 12 16 0
+0 0 0 0 0 8 12 16 0
+0 0 0 0 0 9 12 16 0
+0 0 0 0 0 10 12 16 0
+0 0 0 0 0 11 12 16 0
+0 0 0 0 0 12 12 16 0
+0 0 0 0 0 13 12 16 0
+0 0 0 0 0 14 12 16 0
+0 0 0 0 0 15 12 16 0
+0 0 0 0 0 16 12 16 0
+0 0 0 0 0 17 12 16 0
+0 0 0 0 0 18 12 16 0
+
+
+# iteration 1
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+1 0 0 0 0 0 12 16 0
+1 0 0 0 0 1 12 16 0
+1 0 0 0 0 2 12 16 0
+1 0 0 0 0 3 12 16 0
+1 0 0 0 0 4 12 16 0
+1 0 0 0 0 5 12 16 0
+1 0 0 0 0 6 12 16 0
+1 0 0 0 0 7 12 16 0
+1 0 0 0 0 8 12 16 0
+1 0 0 0 0 9 12 16 0
+1 0 0 0 0 10 12 16 0
+1 0 0 0 0 11 12 16 0
+1 0 0 0 0 12 12 16 0
+1 0 0 0 0 13 12 16 0
+1 0 0 0 0 14 12 16 0
+1 0 0 0 0 15 12 16 0
+1 0 0 0 0 16 12 16 0
+1 0 0 0 0 17 12 16 0
+1 0 0 0 0 18 12 16 0
+
+
+# iteration 2
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+2 0 0 0 0 0 12 16 0
+2 0 0 0 0 1 12 16 0
+2 0 0 0 0 2 12 16 0
+2 0 0 0 0 3 12 16 0
+2 0 0 0 0 4 12 16 0
+2 0 0 0 0 5 12 16 0
+2 0 0 0 0 6 12 16 0
+2 0 0 0 0 7 12 16 0
+2 0 0 0 0 8 12 16 0
+2 0 0 0 0 9 12 16 0
+2 0 0 0 0 10 12 16 0
+2 0 0 0 0 11 12 16 0
+2 0 0 0 0 12 12 16 0
+2 0 0 0 0 13 12 16 0
+2 0 0 0 0 14 12 16 0
+2 0 0 0 0 15 12 16 0
+2 0 0 0 0 16 12 16 0
+2 0 0 0 0 17 12 16 0
+2 0 0 0 0 18 12 16 0
+
+
+# iteration 3
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+3 0 0 0 0 0 12 16 0
+3 0 0 0 0 1 12 16 0
+3 0 0 0 0 2 12 16 0
+3 0 0 0 0 3 12 16 0
+3 0 0 0 0 4 12 16 0
+3 0 0 0 0 5 12 16 0
+3 0 0 0 0 6 12 16 0
+3 0 0 0 0 7 12 16 0
+3 0 0 0 0 8 12 16 0
+3 0 0 0 0 9 12 16 0
+3 0 0 0 0 10 12 16 0
+3 0 0 0 0 11 12 16 0
+3 0 0 0 0 12 12 16 0
+3 0 0 0 0 13 12 16 0
+3 0 0 0 0 14 12 16 0
+3 0 0 0 0 15 12 16 0
+3 0 0 0 0 16 12 16 0
+3 0 0 0 0 17 12 16 0
+3 0 0 0 0 18 12 16 0
+
+
+# iteration 4
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+4 0 0 0 0 0 12 16 0
+4 0 0 0 0 1 12 16 0
+4 0 0 0 0 2 12 16 0
+4 0 0 0 0 3 12 16 0
+4 0 0 0 0 4 12 16 0
+4 0 0 0 0 5 12 16 0
+4 0 0 0 0 6 12 16 0
+4 0 0 0 0 7 12 16 0
+4 0 0 0 0 8 12 16 0
+4 0 0 0 0 9 12 16 0
+4 0 0 0 0 10 12 16 0
+4 0 0 0 0 11 12 16 0
+4 0 0 0 0 12 12 16 0
+4 0 0 0 0 13 12 16 0
+4 0 0 0 0 14 12 16 0
+4 0 0 0 0 15 12 16 0
+4 0 0 0 0 16 12 16 0
+4 0 0 0 0 17 12 16 0
+4 0 0 0 0 18 12 16 0
+
+
+# iteration 5
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+5 0 0 0 0 0 12 16 0
+5 0 0 0 0 1 12 16 0
+5 0 0 0 0 2 12 16 0
+5 0 0 0 0 3 12 16 0
+5 0 0 0 0 4 12 16 0
+5 0 0 0 0 5 12 16 0
+5 0 0 0 0 6 12 16 0
+5 0 0 0 0 7 12 16 0
+5 0 0 0 0 8 12 16 0
+5 0 0 0 0 9 12 16 0
+5 0 0 0 0 10 12 16 0
+5 0 0 0 0 11 12 16 0
+5 0 0 0 0 12 12 16 0
+5 0 0 0 0 13 12 16 0
+5 0 0 0 0 14 12 16 0
+5 0 0 0 0 15 12 16 0
+5 0 0 0 0 16 12 16 0
+5 0 0 0 0 17 12 16 0
+5 0 0 0 0 18 12 16 0
+
+
+# iteration 6
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+6 0 0 0 0 0 12 16 0
+6 0 0 0 0 1 12 16 0
+6 0 0 0 0 2 12 16 0
+6 0 0 0 0 3 12 16 0
+6 0 0 0 0 4 12 16 0
+6 0 0 0 0 5 12 16 0
+6 0 0 0 0 6 12 16 0
+6 0 0 0 0 7 12 16 0
+6 0 0 0 0 8 12 16 0
+6 0 0 0 0 9 12 16 0
+6 0 0 0 0 10 12 16 0
+6 0 0 0 0 11 12 16 0
+6 0 0 0 0 12 12 16 0
+6 0 0 0 0 13 12 16 0
+6 0 0 0 0 14 12 16 0
+6 0 0 0 0 15 12 16 0
+6 0 0 0 0 16 12 16 0
+6 0 0 0 0 17 12 16 0
+6 0 0 0 0 18 12 16 0
+
+
diff --git a/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/cart3d_z.yl b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/cart3d_z.yl
new file mode 100644
index 000000000..c52bfeb8e
--- /dev/null
+++ b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/cart3d_z.yl
@@ -0,0 +1,219 @@
+# GRID::cart3d_z y (cart3d_z)
+#
+# iteration 0
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+0 0 0 0 0 9 0 16 0
+0 0 0 0 0 9 1 16 0
+0 0 0 0 0 9 2 16 0
+0 0 0 0 0 9 3 16 0
+0 0 0 0 0 9 4 16 0
+0 0 0 0 0 9 5 16 0
+0 0 0 0 0 9 6 16 0
+0 0 0 0 0 9 7 16 0
+0 0 0 0 0 9 8 16 0
+0 0 0 0 0 9 9 16 0
+0 0 0 0 0 9 10 16 0
+0 0 0 0 0 9 11 16 0
+0 0 0 0 0 9 12 16 0
+0 0 0 0 0 9 13 16 0
+0 0 0 0 0 9 14 16 0
+0 0 0 0 0 9 15 16 0
+0 0 0 0 0 9 16 16 0
+0 0 0 0 0 9 17 16 0
+0 0 0 0 0 9 18 16 0
+0 0 0 0 0 9 19 16 0
+0 0 0 0 0 9 20 16 0
+0 0 0 0 0 9 21 16 0
+0 0 0 0 0 9 22 16 0
+0 0 0 0 0 9 23 16 0
+0 0 0 0 0 9 24 16 0
+0 0 0 0 0 9 25 16 0
+
+
+# iteration 1
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+1 0 0 0 0 9 0 16 0
+1 0 0 0 0 9 1 16 0
+1 0 0 0 0 9 2 16 0
+1 0 0 0 0 9 3 16 0
+1 0 0 0 0 9 4 16 0
+1 0 0 0 0 9 5 16 0
+1 0 0 0 0 9 6 16 0
+1 0 0 0 0 9 7 16 0
+1 0 0 0 0 9 8 16 0
+1 0 0 0 0 9 9 16 0
+1 0 0 0 0 9 10 16 0
+1 0 0 0 0 9 11 16 0
+1 0 0 0 0 9 12 16 0
+1 0 0 0 0 9 13 16 0
+1 0 0 0 0 9 14 16 0
+1 0 0 0 0 9 15 16 0
+1 0 0 0 0 9 16 16 0
+1 0 0 0 0 9 17 16 0
+1 0 0 0 0 9 18 16 0
+1 0 0 0 0 9 19 16 0
+1 0 0 0 0 9 20 16 0
+1 0 0 0 0 9 21 16 0
+1 0 0 0 0 9 22 16 0
+1 0 0 0 0 9 23 16 0
+1 0 0 0 0 9 24 16 0
+1 0 0 0 0 9 25 16 0
+
+
+# iteration 2
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+2 0 0 0 0 9 0 16 0
+2 0 0 0 0 9 1 16 0
+2 0 0 0 0 9 2 16 0
+2 0 0 0 0 9 3 16 0
+2 0 0 0 0 9 4 16 0
+2 0 0 0 0 9 5 16 0
+2 0 0 0 0 9 6 16 0
+2 0 0 0 0 9 7 16 0
+2 0 0 0 0 9 8 16 0
+2 0 0 0 0 9 9 16 0
+2 0 0 0 0 9 10 16 0
+2 0 0 0 0 9 11 16 0
+2 0 0 0 0 9 12 16 0
+2 0 0 0 0 9 13 16 0
+2 0 0 0 0 9 14 16 0
+2 0 0 0 0 9 15 16 0
+2 0 0 0 0 9 16 16 0
+2 0 0 0 0 9 17 16 0
+2 0 0 0 0 9 18 16 0
+2 0 0 0 0 9 19 16 0
+2 0 0 0 0 9 20 16 0
+2 0 0 0 0 9 21 16 0
+2 0 0 0 0 9 22 16 0
+2 0 0 0 0 9 23 16 0
+2 0 0 0 0 9 24 16 0
+2 0 0 0 0 9 25 16 0
+
+
+# iteration 3
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+3 0 0 0 0 9 0 16 0
+3 0 0 0 0 9 1 16 0
+3 0 0 0 0 9 2 16 0
+3 0 0 0 0 9 3 16 0
+3 0 0 0 0 9 4 16 0
+3 0 0 0 0 9 5 16 0
+3 0 0 0 0 9 6 16 0
+3 0 0 0 0 9 7 16 0
+3 0 0 0 0 9 8 16 0
+3 0 0 0 0 9 9 16 0
+3 0 0 0 0 9 10 16 0
+3 0 0 0 0 9 11 16 0
+3 0 0 0 0 9 12 16 0
+3 0 0 0 0 9 13 16 0
+3 0 0 0 0 9 14 16 0
+3 0 0 0 0 9 15 16 0
+3 0 0 0 0 9 16 16 0
+3 0 0 0 0 9 17 16 0
+3 0 0 0 0 9 18 16 0
+3 0 0 0 0 9 19 16 0
+3 0 0 0 0 9 20 16 0
+3 0 0 0 0 9 21 16 0
+3 0 0 0 0 9 22 16 0
+3 0 0 0 0 9 23 16 0
+3 0 0 0 0 9 24 16 0
+3 0 0 0 0 9 25 16 0
+
+
+# iteration 4
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+4 0 0 0 0 9 0 16 0
+4 0 0 0 0 9 1 16 0
+4 0 0 0 0 9 2 16 0
+4 0 0 0 0 9 3 16 0
+4 0 0 0 0 9 4 16 0
+4 0 0 0 0 9 5 16 0
+4 0 0 0 0 9 6 16 0
+4 0 0 0 0 9 7 16 0
+4 0 0 0 0 9 8 16 0
+4 0 0 0 0 9 9 16 0
+4 0 0 0 0 9 10 16 0
+4 0 0 0 0 9 11 16 0
+4 0 0 0 0 9 12 16 0
+4 0 0 0 0 9 13 16 0
+4 0 0 0 0 9 14 16 0
+4 0 0 0 0 9 15 16 0
+4 0 0 0 0 9 16 16 0
+4 0 0 0 0 9 17 16 0
+4 0 0 0 0 9 18 16 0
+4 0 0 0 0 9 19 16 0
+4 0 0 0 0 9 20 16 0
+4 0 0 0 0 9 21 16 0
+4 0 0 0 0 9 22 16 0
+4 0 0 0 0 9 23 16 0
+4 0 0 0 0 9 24 16 0
+4 0 0 0 0 9 25 16 0
+
+
+# iteration 5
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+5 0 0 0 0 9 0 16 0
+5 0 0 0 0 9 1 16 0
+5 0 0 0 0 9 2 16 0
+5 0 0 0 0 9 3 16 0
+5 0 0 0 0 9 4 16 0
+5 0 0 0 0 9 5 16 0
+5 0 0 0 0 9 6 16 0
+5 0 0 0 0 9 7 16 0
+5 0 0 0 0 9 8 16 0
+5 0 0 0 0 9 9 16 0
+5 0 0 0 0 9 10 16 0
+5 0 0 0 0 9 11 16 0
+5 0 0 0 0 9 12 16 0
+5 0 0 0 0 9 13 16 0
+5 0 0 0 0 9 14 16 0
+5 0 0 0 0 9 15 16 0
+5 0 0 0 0 9 16 16 0
+5 0 0 0 0 9 17 16 0
+5 0 0 0 0 9 18 16 0
+5 0 0 0 0 9 19 16 0
+5 0 0 0 0 9 20 16 0
+5 0 0 0 0 9 21 16 0
+5 0 0 0 0 9 22 16 0
+5 0 0 0 0 9 23 16 0
+5 0 0 0 0 9 24 16 0
+5 0 0 0 0 9 25 16 0
+
+
+# iteration 6
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+6 0 0 0 0 9 0 16 0
+6 0 0 0 0 9 1 16 0
+6 0 0 0 0 9 2 16 0
+6 0 0 0 0 9 3 16 0
+6 0 0 0 0 9 4 16 0
+6 0 0 0 0 9 5 16 0
+6 0 0 0 0 9 6 16 0
+6 0 0 0 0 9 7 16 0
+6 0 0 0 0 9 8 16 0
+6 0 0 0 0 9 9 16 0
+6 0 0 0 0 9 10 16 0
+6 0 0 0 0 9 11 16 0
+6 0 0 0 0 9 12 16 0
+6 0 0 0 0 9 13 16 0
+6 0 0 0 0 9 14 16 0
+6 0 0 0 0 9 15 16 0
+6 0 0 0 0 9 16 16 0
+6 0 0 0 0 9 17 16 0
+6 0 0 0 0 9 18 16 0
+6 0 0 0 0 9 19 16 0
+6 0 0 0 0 9 20 16 0
+6 0 0 0 0 9 21 16 0
+6 0 0 0 0 9 22 16 0
+6 0 0 0 0 9 23 16 0
+6 0 0 0 0 9 24 16 0
+6 0 0 0 0 9 25 16 0
+
+
diff --git a/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/cart3d_z.zl b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/cart3d_z.zl
new file mode 100644
index 000000000..53d0c0b35
--- /dev/null
+++ b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/cart3d_z.zl
@@ -0,0 +1,275 @@
+# GRID::cart3d_z z (cart3d_z)
+#
+# iteration 0
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+0 0 0 0 0 9 12 0 -9.6
+0 0 0 0 0 9 12 1 -9
+0 0 0 0 0 9 12 2 -8.4
+0 0 0 0 0 9 12 3 -7.8
+0 0 0 0 0 9 12 4 -7.2
+0 0 0 0 0 9 12 5 -6.6
+0 0 0 0 0 9 12 6 -6
+0 0 0 0 0 9 12 7 -5.4
+0 0 0 0 0 9 12 8 -4.8
+0 0 0 0 0 9 12 9 -4.2
+0 0 0 0 0 9 12 10 -3.6
+0 0 0 0 0 9 12 11 -3
+0 0 0 0 0 9 12 12 -2.4
+0 0 0 0 0 9 12 13 -1.8
+0 0 0 0 0 9 12 14 -1.2
+0 0 0 0 0 9 12 15 -0.6
+0 0 0 0 0 9 12 16 0
+0 0 0 0 0 9 12 17 0.6
+0 0 0 0 0 9 12 18 1.2
+0 0 0 0 0 9 12 19 1.8
+0 0 0 0 0 9 12 20 2.4
+0 0 0 0 0 9 12 21 3
+0 0 0 0 0 9 12 22 3.6
+0 0 0 0 0 9 12 23 4.2
+0 0 0 0 0 9 12 24 4.8
+0 0 0 0 0 9 12 25 5.4
+0 0 0 0 0 9 12 26 6
+0 0 0 0 0 9 12 27 6.6
+0 0 0 0 0 9 12 28 7.2
+0 0 0 0 0 9 12 29 7.8
+0 0 0 0 0 9 12 30 8.4
+0 0 0 0 0 9 12 31 9
+0 0 0 0 0 9 12 32 9.6
+0 0 0 0 0 9 12 33 10.2
+
+
+# iteration 1
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+1 0 0 0 0 9 12 0 -9.6
+1 0 0 0 0 9 12 1 -9
+1 0 0 0 0 9 12 2 -8.4
+1 0 0 0 0 9 12 3 -7.8
+1 0 0 0 0 9 12 4 -7.2
+1 0 0 0 0 9 12 5 -6.6
+1 0 0 0 0 9 12 6 -6
+1 0 0 0 0 9 12 7 -5.4
+1 0 0 0 0 9 12 8 -4.8
+1 0 0 0 0 9 12 9 -4.2
+1 0 0 0 0 9 12 10 -3.6
+1 0 0 0 0 9 12 11 -3
+1 0 0 0 0 9 12 12 -2.4
+1 0 0 0 0 9 12 13 -1.8
+1 0 0 0 0 9 12 14 -1.2
+1 0 0 0 0 9 12 15 -0.6
+1 0 0 0 0 9 12 16 0
+1 0 0 0 0 9 12 17 0.6
+1 0 0 0 0 9 12 18 1.2
+1 0 0 0 0 9 12 19 1.8
+1 0 0 0 0 9 12 20 2.4
+1 0 0 0 0 9 12 21 3
+1 0 0 0 0 9 12 22 3.6
+1 0 0 0 0 9 12 23 4.2
+1 0 0 0 0 9 12 24 4.8
+1 0 0 0 0 9 12 25 5.4
+1 0 0 0 0 9 12 26 6
+1 0 0 0 0 9 12 27 6.6
+1 0 0 0 0 9 12 28 7.2
+1 0 0 0 0 9 12 29 7.8
+1 0 0 0 0 9 12 30 8.4
+1 0 0 0 0 9 12 31 9
+1 0 0 0 0 9 12 32 9.6
+1 0 0 0 0 9 12 33 10.2
+
+
+# iteration 2
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+2 0 0 0 0 9 12 0 -9.6
+2 0 0 0 0 9 12 1 -9
+2 0 0 0 0 9 12 2 -8.4
+2 0 0 0 0 9 12 3 -7.8
+2 0 0 0 0 9 12 4 -7.2
+2 0 0 0 0 9 12 5 -6.6
+2 0 0 0 0 9 12 6 -6
+2 0 0 0 0 9 12 7 -5.4
+2 0 0 0 0 9 12 8 -4.8
+2 0 0 0 0 9 12 9 -4.2
+2 0 0 0 0 9 12 10 -3.6
+2 0 0 0 0 9 12 11 -3
+2 0 0 0 0 9 12 12 -2.4
+2 0 0 0 0 9 12 13 -1.8
+2 0 0 0 0 9 12 14 -1.2
+2 0 0 0 0 9 12 15 -0.6
+2 0 0 0 0 9 12 16 0
+2 0 0 0 0 9 12 17 0.6
+2 0 0 0 0 9 12 18 1.2
+2 0 0 0 0 9 12 19 1.8
+2 0 0 0 0 9 12 20 2.4
+2 0 0 0 0 9 12 21 3
+2 0 0 0 0 9 12 22 3.6
+2 0 0 0 0 9 12 23 4.2
+2 0 0 0 0 9 12 24 4.8
+2 0 0 0 0 9 12 25 5.4
+2 0 0 0 0 9 12 26 6
+2 0 0 0 0 9 12 27 6.6
+2 0 0 0 0 9 12 28 7.2
+2 0 0 0 0 9 12 29 7.8
+2 0 0 0 0 9 12 30 8.4
+2 0 0 0 0 9 12 31 9
+2 0 0 0 0 9 12 32 9.6
+2 0 0 0 0 9 12 33 10.2
+
+
+# iteration 3
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+3 0 0 0 0 9 12 0 -9.6
+3 0 0 0 0 9 12 1 -9
+3 0 0 0 0 9 12 2 -8.4
+3 0 0 0 0 9 12 3 -7.8
+3 0 0 0 0 9 12 4 -7.2
+3 0 0 0 0 9 12 5 -6.6
+3 0 0 0 0 9 12 6 -6
+3 0 0 0 0 9 12 7 -5.4
+3 0 0 0 0 9 12 8 -4.8
+3 0 0 0 0 9 12 9 -4.2
+3 0 0 0 0 9 12 10 -3.6
+3 0 0 0 0 9 12 11 -3
+3 0 0 0 0 9 12 12 -2.4
+3 0 0 0 0 9 12 13 -1.8
+3 0 0 0 0 9 12 14 -1.2
+3 0 0 0 0 9 12 15 -0.6
+3 0 0 0 0 9 12 16 0
+3 0 0 0 0 9 12 17 0.6
+3 0 0 0 0 9 12 18 1.2
+3 0 0 0 0 9 12 19 1.8
+3 0 0 0 0 9 12 20 2.4
+3 0 0 0 0 9 12 21 3
+3 0 0 0 0 9 12 22 3.6
+3 0 0 0 0 9 12 23 4.2
+3 0 0 0 0 9 12 24 4.8
+3 0 0 0 0 9 12 25 5.4
+3 0 0 0 0 9 12 26 6
+3 0 0 0 0 9 12 27 6.6
+3 0 0 0 0 9 12 28 7.2
+3 0 0 0 0 9 12 29 7.8
+3 0 0 0 0 9 12 30 8.4
+3 0 0 0 0 9 12 31 9
+3 0 0 0 0 9 12 32 9.6
+3 0 0 0 0 9 12 33 10.2
+
+
+# iteration 4
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+4 0 0 0 0 9 12 0 -9.6
+4 0 0 0 0 9 12 1 -9
+4 0 0 0 0 9 12 2 -8.4
+4 0 0 0 0 9 12 3 -7.8
+4 0 0 0 0 9 12 4 -7.2
+4 0 0 0 0 9 12 5 -6.6
+4 0 0 0 0 9 12 6 -6
+4 0 0 0 0 9 12 7 -5.4
+4 0 0 0 0 9 12 8 -4.8
+4 0 0 0 0 9 12 9 -4.2
+4 0 0 0 0 9 12 10 -3.6
+4 0 0 0 0 9 12 11 -3
+4 0 0 0 0 9 12 12 -2.4
+4 0 0 0 0 9 12 13 -1.8
+4 0 0 0 0 9 12 14 -1.2
+4 0 0 0 0 9 12 15 -0.6
+4 0 0 0 0 9 12 16 0
+4 0 0 0 0 9 12 17 0.6
+4 0 0 0 0 9 12 18 1.2
+4 0 0 0 0 9 12 19 1.8
+4 0 0 0 0 9 12 20 2.4
+4 0 0 0 0 9 12 21 3
+4 0 0 0 0 9 12 22 3.6
+4 0 0 0 0 9 12 23 4.2
+4 0 0 0 0 9 12 24 4.8
+4 0 0 0 0 9 12 25 5.4
+4 0 0 0 0 9 12 26 6
+4 0 0 0 0 9 12 27 6.6
+4 0 0 0 0 9 12 28 7.2
+4 0 0 0 0 9 12 29 7.8
+4 0 0 0 0 9 12 30 8.4
+4 0 0 0 0 9 12 31 9
+4 0 0 0 0 9 12 32 9.6
+4 0 0 0 0 9 12 33 10.2
+
+
+# iteration 5
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+5 0 0 0 0 9 12 0 -9.6
+5 0 0 0 0 9 12 1 -9
+5 0 0 0 0 9 12 2 -8.4
+5 0 0 0 0 9 12 3 -7.8
+5 0 0 0 0 9 12 4 -7.2
+5 0 0 0 0 9 12 5 -6.6
+5 0 0 0 0 9 12 6 -6
+5 0 0 0 0 9 12 7 -5.4
+5 0 0 0 0 9 12 8 -4.8
+5 0 0 0 0 9 12 9 -4.2
+5 0 0 0 0 9 12 10 -3.6
+5 0 0 0 0 9 12 11 -3
+5 0 0 0 0 9 12 12 -2.4
+5 0 0 0 0 9 12 13 -1.8
+5 0 0 0 0 9 12 14 -1.2
+5 0 0 0 0 9 12 15 -0.6
+5 0 0 0 0 9 12 16 0
+5 0 0 0 0 9 12 17 0.6
+5 0 0 0 0 9 12 18 1.2
+5 0 0 0 0 9 12 19 1.8
+5 0 0 0 0 9 12 20 2.4
+5 0 0 0 0 9 12 21 3
+5 0 0 0 0 9 12 22 3.6
+5 0 0 0 0 9 12 23 4.2
+5 0 0 0 0 9 12 24 4.8
+5 0 0 0 0 9 12 25 5.4
+5 0 0 0 0 9 12 26 6
+5 0 0 0 0 9 12 27 6.6
+5 0 0 0 0 9 12 28 7.2
+5 0 0 0 0 9 12 29 7.8
+5 0 0 0 0 9 12 30 8.4
+5 0 0 0 0 9 12 31 9
+5 0 0 0 0 9 12 32 9.6
+5 0 0 0 0 9 12 33 10.2
+
+
+# iteration 6
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+6 0 0 0 0 9 12 0 -9.6
+6 0 0 0 0 9 12 1 -9
+6 0 0 0 0 9 12 2 -8.4
+6 0 0 0 0 9 12 3 -7.8
+6 0 0 0 0 9 12 4 -7.2
+6 0 0 0 0 9 12 5 -6.6
+6 0 0 0 0 9 12 6 -6
+6 0 0 0 0 9 12 7 -5.4
+6 0 0 0 0 9 12 8 -4.8
+6 0 0 0 0 9 12 9 -4.2
+6 0 0 0 0 9 12 10 -3.6
+6 0 0 0 0 9 12 11 -3
+6 0 0 0 0 9 12 12 -2.4
+6 0 0 0 0 9 12 13 -1.8
+6 0 0 0 0 9 12 14 -1.2
+6 0 0 0 0 9 12 15 -0.6
+6 0 0 0 0 9 12 16 0
+6 0 0 0 0 9 12 17 0.6
+6 0 0 0 0 9 12 18 1.2
+6 0 0 0 0 9 12 19 1.8
+6 0 0 0 0 9 12 20 2.4
+6 0 0 0 0 9 12 21 3
+6 0 0 0 0 9 12 22 3.6
+6 0 0 0 0 9 12 23 4.2
+6 0 0 0 0 9 12 24 4.8
+6 0 0 0 0 9 12 25 5.4
+6 0 0 0 0 9 12 26 6
+6 0 0 0 0 9 12 27 6.6
+6 0 0 0 0 9 12 28 7.2
+6 0 0 0 0 9 12 29 7.8
+6 0 0 0 0 9 12 30 8.4
+6 0 0 0 0 9 12 31 9
+6 0 0 0 0 9 12 32 9.6
+6 0 0 0 0 9 12 33 10.2
+
+
diff --git a/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/spher3d_r.xl b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/spher3d_r.xl
new file mode 100644
index 000000000..5c26840e3
--- /dev/null
+++ b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/spher3d_r.xl
@@ -0,0 +1,170 @@
+# GRID::spher3d_r x (spher3d_r)
+#
+# iteration 0
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+0 0 0 0 0 0 12 16 5.4
+0 0 0 0 0 1 12 16 4.8
+0 0 0 0 0 2 12 16 4.2
+0 0 0 0 0 3 12 16 3.6
+0 0 0 0 0 4 12 16 3
+0 0 0 0 0 5 12 16 2.4
+0 0 0 0 0 6 12 16 1.8
+0 0 0 0 0 7 12 16 1.2
+0 0 0 0 0 8 12 16 0.6
+0 0 0 0 0 9 12 16 6.2803698347351e-16
+0 0 0 0 0 10 12 16 0.600000000000001
+0 0 0 0 0 11 12 16 1.2
+0 0 0 0 0 12 12 16 1.8
+0 0 0 0 0 13 12 16 2.4
+0 0 0 0 0 14 12 16 3
+0 0 0 0 0 15 12 16 3.6
+0 0 0 0 0 16 12 16 4.2
+0 0 0 0 0 17 12 16 4.8
+0 0 0 0 0 18 12 16 5.4
+
+
+# iteration 1
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+1 0 0 0 0 0 12 16 5.4
+1 0 0 0 0 1 12 16 4.8
+1 0 0 0 0 2 12 16 4.2
+1 0 0 0 0 3 12 16 3.6
+1 0 0 0 0 4 12 16 3
+1 0 0 0 0 5 12 16 2.4
+1 0 0 0 0 6 12 16 1.8
+1 0 0 0 0 7 12 16 1.2
+1 0 0 0 0 8 12 16 0.6
+1 0 0 0 0 9 12 16 6.2803698347351e-16
+1 0 0 0 0 10 12 16 0.600000000000001
+1 0 0 0 0 11 12 16 1.2
+1 0 0 0 0 12 12 16 1.8
+1 0 0 0 0 13 12 16 2.4
+1 0 0 0 0 14 12 16 3
+1 0 0 0 0 15 12 16 3.6
+1 0 0 0 0 16 12 16 4.2
+1 0 0 0 0 17 12 16 4.8
+1 0 0 0 0 18 12 16 5.4
+
+
+# iteration 2
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+2 0 0 0 0 0 12 16 5.4
+2 0 0 0 0 1 12 16 4.8
+2 0 0 0 0 2 12 16 4.2
+2 0 0 0 0 3 12 16 3.6
+2 0 0 0 0 4 12 16 3
+2 0 0 0 0 5 12 16 2.4
+2 0 0 0 0 6 12 16 1.8
+2 0 0 0 0 7 12 16 1.2
+2 0 0 0 0 8 12 16 0.6
+2 0 0 0 0 9 12 16 6.2803698347351e-16
+2 0 0 0 0 10 12 16 0.600000000000001
+2 0 0 0 0 11 12 16 1.2
+2 0 0 0 0 12 12 16 1.8
+2 0 0 0 0 13 12 16 2.4
+2 0 0 0 0 14 12 16 3
+2 0 0 0 0 15 12 16 3.6
+2 0 0 0 0 16 12 16 4.2
+2 0 0 0 0 17 12 16 4.8
+2 0 0 0 0 18 12 16 5.4
+
+
+# iteration 3
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+3 0 0 0 0 0 12 16 5.4
+3 0 0 0 0 1 12 16 4.8
+3 0 0 0 0 2 12 16 4.2
+3 0 0 0 0 3 12 16 3.6
+3 0 0 0 0 4 12 16 3
+3 0 0 0 0 5 12 16 2.4
+3 0 0 0 0 6 12 16 1.8
+3 0 0 0 0 7 12 16 1.2
+3 0 0 0 0 8 12 16 0.6
+3 0 0 0 0 9 12 16 6.2803698347351e-16
+3 0 0 0 0 10 12 16 0.600000000000001
+3 0 0 0 0 11 12 16 1.2
+3 0 0 0 0 12 12 16 1.8
+3 0 0 0 0 13 12 16 2.4
+3 0 0 0 0 14 12 16 3
+3 0 0 0 0 15 12 16 3.6
+3 0 0 0 0 16 12 16 4.2
+3 0 0 0 0 17 12 16 4.8
+3 0 0 0 0 18 12 16 5.4
+
+
+# iteration 4
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+4 0 0 0 0 0 12 16 5.4
+4 0 0 0 0 1 12 16 4.8
+4 0 0 0 0 2 12 16 4.2
+4 0 0 0 0 3 12 16 3.6
+4 0 0 0 0 4 12 16 3
+4 0 0 0 0 5 12 16 2.4
+4 0 0 0 0 6 12 16 1.8
+4 0 0 0 0 7 12 16 1.2
+4 0 0 0 0 8 12 16 0.6
+4 0 0 0 0 9 12 16 6.2803698347351e-16
+4 0 0 0 0 10 12 16 0.600000000000001
+4 0 0 0 0 11 12 16 1.2
+4 0 0 0 0 12 12 16 1.8
+4 0 0 0 0 13 12 16 2.4
+4 0 0 0 0 14 12 16 3
+4 0 0 0 0 15 12 16 3.6
+4 0 0 0 0 16 12 16 4.2
+4 0 0 0 0 17 12 16 4.8
+4 0 0 0 0 18 12 16 5.4
+
+
+# iteration 5
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+5 0 0 0 0 0 12 16 5.4
+5 0 0 0 0 1 12 16 4.8
+5 0 0 0 0 2 12 16 4.2
+5 0 0 0 0 3 12 16 3.6
+5 0 0 0 0 4 12 16 3
+5 0 0 0 0 5 12 16 2.4
+5 0 0 0 0 6 12 16 1.8
+5 0 0 0 0 7 12 16 1.2
+5 0 0 0 0 8 12 16 0.6
+5 0 0 0 0 9 12 16 6.2803698347351e-16
+5 0 0 0 0 10 12 16 0.600000000000001
+5 0 0 0 0 11 12 16 1.2
+5 0 0 0 0 12 12 16 1.8
+5 0 0 0 0 13 12 16 2.4
+5 0 0 0 0 14 12 16 3
+5 0 0 0 0 15 12 16 3.6
+5 0 0 0 0 16 12 16 4.2
+5 0 0 0 0 17 12 16 4.8
+5 0 0 0 0 18 12 16 5.4
+
+
+# iteration 6
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+6 0 0 0 0 0 12 16 5.4
+6 0 0 0 0 1 12 16 4.8
+6 0 0 0 0 2 12 16 4.2
+6 0 0 0 0 3 12 16 3.6
+6 0 0 0 0 4 12 16 3
+6 0 0 0 0 5 12 16 2.4
+6 0 0 0 0 6 12 16 1.8
+6 0 0 0 0 7 12 16 1.2
+6 0 0 0 0 8 12 16 0.6
+6 0 0 0 0 9 12 16 6.2803698347351e-16
+6 0 0 0 0 10 12 16 0.600000000000001
+6 0 0 0 0 11 12 16 1.2
+6 0 0 0 0 12 12 16 1.8
+6 0 0 0 0 13 12 16 2.4
+6 0 0 0 0 14 12 16 3
+6 0 0 0 0 15 12 16 3.6
+6 0 0 0 0 16 12 16 4.2
+6 0 0 0 0 17 12 16 4.8
+6 0 0 0 0 18 12 16 5.4
+
+
diff --git a/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/spher3d_r.yl b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/spher3d_r.yl
new file mode 100644
index 000000000..3dccc92e2
--- /dev/null
+++ b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/spher3d_r.yl
@@ -0,0 +1,219 @@
+# GRID::spher3d_r y (spher3d_r)
+#
+# iteration 0
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+0 0 0 0 0 9 0 16 7.2
+0 0 0 0 0 9 1 16 6.6
+0 0 0 0 0 9 2 16 6
+0 0 0 0 0 9 3 16 5.4
+0 0 0 0 0 9 4 16 4.8
+0 0 0 0 0 9 5 16 4.2
+0 0 0 0 0 9 6 16 3.6
+0 0 0 0 0 9 7 16 3
+0 0 0 0 0 9 8 16 2.4
+0 0 0 0 0 9 9 16 1.8
+0 0 0 0 0 9 10 16 1.2
+0 0 0 0 0 9 11 16 0.6
+0 0 0 0 0 9 12 16 6.2803698347351e-16
+0 0 0 0 0 9 13 16 0.6
+0 0 0 0 0 9 14 16 1.2
+0 0 0 0 0 9 15 16 1.8
+0 0 0 0 0 9 16 16 2.4
+0 0 0 0 0 9 17 16 3
+0 0 0 0 0 9 18 16 3.6
+0 0 0 0 0 9 19 16 4.2
+0 0 0 0 0 9 20 16 4.8
+0 0 0 0 0 9 21 16 5.4
+0 0 0 0 0 9 22 16 6
+0 0 0 0 0 9 23 16 6.6
+0 0 0 0 0 9 24 16 7.2
+0 0 0 0 0 9 25 16 7.8
+
+
+# iteration 1
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+1 0 0 0 0 9 0 16 7.2
+1 0 0 0 0 9 1 16 6.6
+1 0 0 0 0 9 2 16 6
+1 0 0 0 0 9 3 16 5.4
+1 0 0 0 0 9 4 16 4.8
+1 0 0 0 0 9 5 16 4.2
+1 0 0 0 0 9 6 16 3.6
+1 0 0 0 0 9 7 16 3
+1 0 0 0 0 9 8 16 2.4
+1 0 0 0 0 9 9 16 1.8
+1 0 0 0 0 9 10 16 1.2
+1 0 0 0 0 9 11 16 0.6
+1 0 0 0 0 9 12 16 6.2803698347351e-16
+1 0 0 0 0 9 13 16 0.6
+1 0 0 0 0 9 14 16 1.2
+1 0 0 0 0 9 15 16 1.8
+1 0 0 0 0 9 16 16 2.4
+1 0 0 0 0 9 17 16 3
+1 0 0 0 0 9 18 16 3.6
+1 0 0 0 0 9 19 16 4.2
+1 0 0 0 0 9 20 16 4.8
+1 0 0 0 0 9 21 16 5.4
+1 0 0 0 0 9 22 16 6
+1 0 0 0 0 9 23 16 6.6
+1 0 0 0 0 9 24 16 7.2
+1 0 0 0 0 9 25 16 7.8
+
+
+# iteration 2
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+2 0 0 0 0 9 0 16 7.2
+2 0 0 0 0 9 1 16 6.6
+2 0 0 0 0 9 2 16 6
+2 0 0 0 0 9 3 16 5.4
+2 0 0 0 0 9 4 16 4.8
+2 0 0 0 0 9 5 16 4.2
+2 0 0 0 0 9 6 16 3.6
+2 0 0 0 0 9 7 16 3
+2 0 0 0 0 9 8 16 2.4
+2 0 0 0 0 9 9 16 1.8
+2 0 0 0 0 9 10 16 1.2
+2 0 0 0 0 9 11 16 0.6
+2 0 0 0 0 9 12 16 6.2803698347351e-16
+2 0 0 0 0 9 13 16 0.6
+2 0 0 0 0 9 14 16 1.2
+2 0 0 0 0 9 15 16 1.8
+2 0 0 0 0 9 16 16 2.4
+2 0 0 0 0 9 17 16 3
+2 0 0 0 0 9 18 16 3.6
+2 0 0 0 0 9 19 16 4.2
+2 0 0 0 0 9 20 16 4.8
+2 0 0 0 0 9 21 16 5.4
+2 0 0 0 0 9 22 16 6
+2 0 0 0 0 9 23 16 6.6
+2 0 0 0 0 9 24 16 7.2
+2 0 0 0 0 9 25 16 7.8
+
+
+# iteration 3
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+3 0 0 0 0 9 0 16 7.2
+3 0 0 0 0 9 1 16 6.6
+3 0 0 0 0 9 2 16 6
+3 0 0 0 0 9 3 16 5.4
+3 0 0 0 0 9 4 16 4.8
+3 0 0 0 0 9 5 16 4.2
+3 0 0 0 0 9 6 16 3.6
+3 0 0 0 0 9 7 16 3
+3 0 0 0 0 9 8 16 2.4
+3 0 0 0 0 9 9 16 1.8
+3 0 0 0 0 9 10 16 1.2
+3 0 0 0 0 9 11 16 0.6
+3 0 0 0 0 9 12 16 6.2803698347351e-16
+3 0 0 0 0 9 13 16 0.6
+3 0 0 0 0 9 14 16 1.2
+3 0 0 0 0 9 15 16 1.8
+3 0 0 0 0 9 16 16 2.4
+3 0 0 0 0 9 17 16 3
+3 0 0 0 0 9 18 16 3.6
+3 0 0 0 0 9 19 16 4.2
+3 0 0 0 0 9 20 16 4.8
+3 0 0 0 0 9 21 16 5.4
+3 0 0 0 0 9 22 16 6
+3 0 0 0 0 9 23 16 6.6
+3 0 0 0 0 9 24 16 7.2
+3 0 0 0 0 9 25 16 7.8
+
+
+# iteration 4
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+4 0 0 0 0 9 0 16 7.2
+4 0 0 0 0 9 1 16 6.6
+4 0 0 0 0 9 2 16 6
+4 0 0 0 0 9 3 16 5.4
+4 0 0 0 0 9 4 16 4.8
+4 0 0 0 0 9 5 16 4.2
+4 0 0 0 0 9 6 16 3.6
+4 0 0 0 0 9 7 16 3
+4 0 0 0 0 9 8 16 2.4
+4 0 0 0 0 9 9 16 1.8
+4 0 0 0 0 9 10 16 1.2
+4 0 0 0 0 9 11 16 0.6
+4 0 0 0 0 9 12 16 6.2803698347351e-16
+4 0 0 0 0 9 13 16 0.6
+4 0 0 0 0 9 14 16 1.2
+4 0 0 0 0 9 15 16 1.8
+4 0 0 0 0 9 16 16 2.4
+4 0 0 0 0 9 17 16 3
+4 0 0 0 0 9 18 16 3.6
+4 0 0 0 0 9 19 16 4.2
+4 0 0 0 0 9 20 16 4.8
+4 0 0 0 0 9 21 16 5.4
+4 0 0 0 0 9 22 16 6
+4 0 0 0 0 9 23 16 6.6
+4 0 0 0 0 9 24 16 7.2
+4 0 0 0 0 9 25 16 7.8
+
+
+# iteration 5
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+5 0 0 0 0 9 0 16 7.2
+5 0 0 0 0 9 1 16 6.6
+5 0 0 0 0 9 2 16 6
+5 0 0 0 0 9 3 16 5.4
+5 0 0 0 0 9 4 16 4.8
+5 0 0 0 0 9 5 16 4.2
+5 0 0 0 0 9 6 16 3.6
+5 0 0 0 0 9 7 16 3
+5 0 0 0 0 9 8 16 2.4
+5 0 0 0 0 9 9 16 1.8
+5 0 0 0 0 9 10 16 1.2
+5 0 0 0 0 9 11 16 0.6
+5 0 0 0 0 9 12 16 6.2803698347351e-16
+5 0 0 0 0 9 13 16 0.6
+5 0 0 0 0 9 14 16 1.2
+5 0 0 0 0 9 15 16 1.8
+5 0 0 0 0 9 16 16 2.4
+5 0 0 0 0 9 17 16 3
+5 0 0 0 0 9 18 16 3.6
+5 0 0 0 0 9 19 16 4.2
+5 0 0 0 0 9 20 16 4.8
+5 0 0 0 0 9 21 16 5.4
+5 0 0 0 0 9 22 16 6
+5 0 0 0 0 9 23 16 6.6
+5 0 0 0 0 9 24 16 7.2
+5 0 0 0 0 9 25 16 7.8
+
+
+# iteration 6
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+6 0 0 0 0 9 0 16 7.2
+6 0 0 0 0 9 1 16 6.6
+6 0 0 0 0 9 2 16 6
+6 0 0 0 0 9 3 16 5.4
+6 0 0 0 0 9 4 16 4.8
+6 0 0 0 0 9 5 16 4.2
+6 0 0 0 0 9 6 16 3.6
+6 0 0 0 0 9 7 16 3
+6 0 0 0 0 9 8 16 2.4
+6 0 0 0 0 9 9 16 1.8
+6 0 0 0 0 9 10 16 1.2
+6 0 0 0 0 9 11 16 0.6
+6 0 0 0 0 9 12 16 6.2803698347351e-16
+6 0 0 0 0 9 13 16 0.6
+6 0 0 0 0 9 14 16 1.2
+6 0 0 0 0 9 15 16 1.8
+6 0 0 0 0 9 16 16 2.4
+6 0 0 0 0 9 17 16 3
+6 0 0 0 0 9 18 16 3.6
+6 0 0 0 0 9 19 16 4.2
+6 0 0 0 0 9 20 16 4.8
+6 0 0 0 0 9 21 16 5.4
+6 0 0 0 0 9 22 16 6
+6 0 0 0 0 9 23 16 6.6
+6 0 0 0 0 9 24 16 7.2
+6 0 0 0 0 9 25 16 7.8
+
+
diff --git a/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/spher3d_r.zl b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/spher3d_r.zl
new file mode 100644
index 000000000..0d3ac2541
--- /dev/null
+++ b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/spher3d_r.zl
@@ -0,0 +1,275 @@
+# GRID::spher3d_r z (spher3d_r)
+#
+# iteration 0
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+0 0 0 0 0 9 12 0 9.6
+0 0 0 0 0 9 12 1 9
+0 0 0 0 0 9 12 2 8.4
+0 0 0 0 0 9 12 3 7.8
+0 0 0 0 0 9 12 4 7.2
+0 0 0 0 0 9 12 5 6.6
+0 0 0 0 0 9 12 6 6
+0 0 0 0 0 9 12 7 5.4
+0 0 0 0 0 9 12 8 4.8
+0 0 0 0 0 9 12 9 4.2
+0 0 0 0 0 9 12 10 3.6
+0 0 0 0 0 9 12 11 3
+0 0 0 0 0 9 12 12 2.4
+0 0 0 0 0 9 12 13 1.8
+0 0 0 0 0 9 12 14 1.2
+0 0 0 0 0 9 12 15 0.6
+0 0 0 0 0 9 12 16 6.2803698347351e-16
+0 0 0 0 0 9 12 17 0.6
+0 0 0 0 0 9 12 18 1.2
+0 0 0 0 0 9 12 19 1.8
+0 0 0 0 0 9 12 20 2.4
+0 0 0 0 0 9 12 21 3
+0 0 0 0 0 9 12 22 3.6
+0 0 0 0 0 9 12 23 4.2
+0 0 0 0 0 9 12 24 4.8
+0 0 0 0 0 9 12 25 5.4
+0 0 0 0 0 9 12 26 6
+0 0 0 0 0 9 12 27 6.6
+0 0 0 0 0 9 12 28 7.2
+0 0 0 0 0 9 12 29 7.8
+0 0 0 0 0 9 12 30 8.4
+0 0 0 0 0 9 12 31 9
+0 0 0 0 0 9 12 32 9.6
+0 0 0 0 0 9 12 33 10.2
+
+
+# iteration 1
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+1 0 0 0 0 9 12 0 9.6
+1 0 0 0 0 9 12 1 9
+1 0 0 0 0 9 12 2 8.4
+1 0 0 0 0 9 12 3 7.8
+1 0 0 0 0 9 12 4 7.2
+1 0 0 0 0 9 12 5 6.6
+1 0 0 0 0 9 12 6 6
+1 0 0 0 0 9 12 7 5.4
+1 0 0 0 0 9 12 8 4.8
+1 0 0 0 0 9 12 9 4.2
+1 0 0 0 0 9 12 10 3.6
+1 0 0 0 0 9 12 11 3
+1 0 0 0 0 9 12 12 2.4
+1 0 0 0 0 9 12 13 1.8
+1 0 0 0 0 9 12 14 1.2
+1 0 0 0 0 9 12 15 0.6
+1 0 0 0 0 9 12 16 6.2803698347351e-16
+1 0 0 0 0 9 12 17 0.6
+1 0 0 0 0 9 12 18 1.2
+1 0 0 0 0 9 12 19 1.8
+1 0 0 0 0 9 12 20 2.4
+1 0 0 0 0 9 12 21 3
+1 0 0 0 0 9 12 22 3.6
+1 0 0 0 0 9 12 23 4.2
+1 0 0 0 0 9 12 24 4.8
+1 0 0 0 0 9 12 25 5.4
+1 0 0 0 0 9 12 26 6
+1 0 0 0 0 9 12 27 6.6
+1 0 0 0 0 9 12 28 7.2
+1 0 0 0 0 9 12 29 7.8
+1 0 0 0 0 9 12 30 8.4
+1 0 0 0 0 9 12 31 9
+1 0 0 0 0 9 12 32 9.6
+1 0 0 0 0 9 12 33 10.2
+
+
+# iteration 2
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+2 0 0 0 0 9 12 0 9.6
+2 0 0 0 0 9 12 1 9
+2 0 0 0 0 9 12 2 8.4
+2 0 0 0 0 9 12 3 7.8
+2 0 0 0 0 9 12 4 7.2
+2 0 0 0 0 9 12 5 6.6
+2 0 0 0 0 9 12 6 6
+2 0 0 0 0 9 12 7 5.4
+2 0 0 0 0 9 12 8 4.8
+2 0 0 0 0 9 12 9 4.2
+2 0 0 0 0 9 12 10 3.6
+2 0 0 0 0 9 12 11 3
+2 0 0 0 0 9 12 12 2.4
+2 0 0 0 0 9 12 13 1.8
+2 0 0 0 0 9 12 14 1.2
+2 0 0 0 0 9 12 15 0.6
+2 0 0 0 0 9 12 16 6.2803698347351e-16
+2 0 0 0 0 9 12 17 0.6
+2 0 0 0 0 9 12 18 1.2
+2 0 0 0 0 9 12 19 1.8
+2 0 0 0 0 9 12 20 2.4
+2 0 0 0 0 9 12 21 3
+2 0 0 0 0 9 12 22 3.6
+2 0 0 0 0 9 12 23 4.2
+2 0 0 0 0 9 12 24 4.8
+2 0 0 0 0 9 12 25 5.4
+2 0 0 0 0 9 12 26 6
+2 0 0 0 0 9 12 27 6.6
+2 0 0 0 0 9 12 28 7.2
+2 0 0 0 0 9 12 29 7.8
+2 0 0 0 0 9 12 30 8.4
+2 0 0 0 0 9 12 31 9
+2 0 0 0 0 9 12 32 9.6
+2 0 0 0 0 9 12 33 10.2
+
+
+# iteration 3
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+3 0 0 0 0 9 12 0 9.6
+3 0 0 0 0 9 12 1 9
+3 0 0 0 0 9 12 2 8.4
+3 0 0 0 0 9 12 3 7.8
+3 0 0 0 0 9 12 4 7.2
+3 0 0 0 0 9 12 5 6.6
+3 0 0 0 0 9 12 6 6
+3 0 0 0 0 9 12 7 5.4
+3 0 0 0 0 9 12 8 4.8
+3 0 0 0 0 9 12 9 4.2
+3 0 0 0 0 9 12 10 3.6
+3 0 0 0 0 9 12 11 3
+3 0 0 0 0 9 12 12 2.4
+3 0 0 0 0 9 12 13 1.8
+3 0 0 0 0 9 12 14 1.2
+3 0 0 0 0 9 12 15 0.6
+3 0 0 0 0 9 12 16 6.2803698347351e-16
+3 0 0 0 0 9 12 17 0.6
+3 0 0 0 0 9 12 18 1.2
+3 0 0 0 0 9 12 19 1.8
+3 0 0 0 0 9 12 20 2.4
+3 0 0 0 0 9 12 21 3
+3 0 0 0 0 9 12 22 3.6
+3 0 0 0 0 9 12 23 4.2
+3 0 0 0 0 9 12 24 4.8
+3 0 0 0 0 9 12 25 5.4
+3 0 0 0 0 9 12 26 6
+3 0 0 0 0 9 12 27 6.6
+3 0 0 0 0 9 12 28 7.2
+3 0 0 0 0 9 12 29 7.8
+3 0 0 0 0 9 12 30 8.4
+3 0 0 0 0 9 12 31 9
+3 0 0 0 0 9 12 32 9.6
+3 0 0 0 0 9 12 33 10.2
+
+
+# iteration 4
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+4 0 0 0 0 9 12 0 9.6
+4 0 0 0 0 9 12 1 9
+4 0 0 0 0 9 12 2 8.4
+4 0 0 0 0 9 12 3 7.8
+4 0 0 0 0 9 12 4 7.2
+4 0 0 0 0 9 12 5 6.6
+4 0 0 0 0 9 12 6 6
+4 0 0 0 0 9 12 7 5.4
+4 0 0 0 0 9 12 8 4.8
+4 0 0 0 0 9 12 9 4.2
+4 0 0 0 0 9 12 10 3.6
+4 0 0 0 0 9 12 11 3
+4 0 0 0 0 9 12 12 2.4
+4 0 0 0 0 9 12 13 1.8
+4 0 0 0 0 9 12 14 1.2
+4 0 0 0 0 9 12 15 0.6
+4 0 0 0 0 9 12 16 6.2803698347351e-16
+4 0 0 0 0 9 12 17 0.6
+4 0 0 0 0 9 12 18 1.2
+4 0 0 0 0 9 12 19 1.8
+4 0 0 0 0 9 12 20 2.4
+4 0 0 0 0 9 12 21 3
+4 0 0 0 0 9 12 22 3.6
+4 0 0 0 0 9 12 23 4.2
+4 0 0 0 0 9 12 24 4.8
+4 0 0 0 0 9 12 25 5.4
+4 0 0 0 0 9 12 26 6
+4 0 0 0 0 9 12 27 6.6
+4 0 0 0 0 9 12 28 7.2
+4 0 0 0 0 9 12 29 7.8
+4 0 0 0 0 9 12 30 8.4
+4 0 0 0 0 9 12 31 9
+4 0 0 0 0 9 12 32 9.6
+4 0 0 0 0 9 12 33 10.2
+
+
+# iteration 5
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+5 0 0 0 0 9 12 0 9.6
+5 0 0 0 0 9 12 1 9
+5 0 0 0 0 9 12 2 8.4
+5 0 0 0 0 9 12 3 7.8
+5 0 0 0 0 9 12 4 7.2
+5 0 0 0 0 9 12 5 6.6
+5 0 0 0 0 9 12 6 6
+5 0 0 0 0 9 12 7 5.4
+5 0 0 0 0 9 12 8 4.8
+5 0 0 0 0 9 12 9 4.2
+5 0 0 0 0 9 12 10 3.6
+5 0 0 0 0 9 12 11 3
+5 0 0 0 0 9 12 12 2.4
+5 0 0 0 0 9 12 13 1.8
+5 0 0 0 0 9 12 14 1.2
+5 0 0 0 0 9 12 15 0.6
+5 0 0 0 0 9 12 16 6.2803698347351e-16
+5 0 0 0 0 9 12 17 0.6
+5 0 0 0 0 9 12 18 1.2
+5 0 0 0 0 9 12 19 1.8
+5 0 0 0 0 9 12 20 2.4
+5 0 0 0 0 9 12 21 3
+5 0 0 0 0 9 12 22 3.6
+5 0 0 0 0 9 12 23 4.2
+5 0 0 0 0 9 12 24 4.8
+5 0 0 0 0 9 12 25 5.4
+5 0 0 0 0 9 12 26 6
+5 0 0 0 0 9 12 27 6.6
+5 0 0 0 0 9 12 28 7.2
+5 0 0 0 0 9 12 29 7.8
+5 0 0 0 0 9 12 30 8.4
+5 0 0 0 0 9 12 31 9
+5 0 0 0 0 9 12 32 9.6
+5 0 0 0 0 9 12 33 10.2
+
+
+# iteration 6
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+6 0 0 0 0 9 12 0 9.6
+6 0 0 0 0 9 12 1 9
+6 0 0 0 0 9 12 2 8.4
+6 0 0 0 0 9 12 3 7.8
+6 0 0 0 0 9 12 4 7.2
+6 0 0 0 0 9 12 5 6.6
+6 0 0 0 0 9 12 6 6
+6 0 0 0 0 9 12 7 5.4
+6 0 0 0 0 9 12 8 4.8
+6 0 0 0 0 9 12 9 4.2
+6 0 0 0 0 9 12 10 3.6
+6 0 0 0 0 9 12 11 3
+6 0 0 0 0 9 12 12 2.4
+6 0 0 0 0 9 12 13 1.8
+6 0 0 0 0 9 12 14 1.2
+6 0 0 0 0 9 12 15 0.6
+6 0 0 0 0 9 12 16 6.2803698347351e-16
+6 0 0 0 0 9 12 17 0.6
+6 0 0 0 0 9 12 18 1.2
+6 0 0 0 0 9 12 19 1.8
+6 0 0 0 0 9 12 20 2.4
+6 0 0 0 0 9 12 21 3
+6 0 0 0 0 9 12 22 3.6
+6 0 0 0 0 9 12 23 4.2
+6 0 0 0 0 9 12 24 4.8
+6 0 0 0 0 9 12 25 5.4
+6 0 0 0 0 9 12 26 6
+6 0 0 0 0 9 12 27 6.6
+6 0 0 0 0 9 12 28 7.2
+6 0 0 0 0 9 12 29 7.8
+6 0 0 0 0 9 12 30 8.4
+6 0 0 0 0 9 12 31 9
+6 0 0 0 0 9 12 32 9.6
+6 0 0 0 0 9 12 33 10.2
+
+
diff --git a/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/u.xl b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/u.xl
new file mode 100644
index 000000000..9b6c76b91
--- /dev/null
+++ b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/u.xl
@@ -0,0 +1,170 @@
+# HYDROTOY::u x (u)
+#
+# iteration 0
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+0 0 0 0 0 0 12 16 -0.80901699437495
+0 0 0 0 0 1 12 16 -0.978147600733806
+0 0 0 0 0 2 12 16 -0.978147600733805
+0 0 0 0 0 3 12 16 -0.809016994374946
+0 0 0 0 0 4 12 16 -0.499999999999998
+0 0 0 0 0 5 12 16 -0.104528463267652
+0 0 0 0 0 6 12 16 0.309016994374949
+0 0 0 0 0 7 12 16 0.669130606358859
+0 0 0 0 0 8 12 16 0.913545457642601
+0 0 0 0 0 9 12 16 1
+0 0 0 0 0 10 12 16 0.913545457642601
+0 0 0 0 0 11 12 16 0.669130606358859
+0 0 0 0 0 12 12 16 0.309016994374949
+0 0 0 0 0 13 12 16 -0.104528463267652
+0 0 0 0 0 14 12 16 -0.499999999999998
+0 0 0 0 0 15 12 16 -0.809016994374946
+0 0 0 0 0 16 12 16 -0.978147600733805
+0 0 0 0 0 17 12 16 -0.978147600733806
+0 0 0 0 0 18 12 16 -0.809016994374949
+
+
+# iteration 1
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+1 0 0 0 0 0 12 16 -0.955765485796519
+1 0 0 0 0 1 12 16 -0.994570500607911
+1 0 0 0 0 2 12 16 -0.861405240474848
+1 0 0 0 0 3 12 16 -0.579295188642749
+1 0 0 0 0 4 12 16 -0.197019735962746
+1 0 0 0 0 5 12 16 0.219322218933327
+1 0 0 0 0 6 12 16 0.597741369696019
+1 0 0 0 0 7 12 16 0.872805607328403
+1 0 0 0 0 8 12 16 0.99695382626369
+1 0 0 0 0 9 12 16 0.948719671596806
+1 0 0 0 0 10 12 16 0.736443266863195
+1 0 0 0 0 11 12 16 0.396829130911893
+1 0 0 0 0 12 12 16 -0.0114003668535526
+1 0 0 0 0 13 12 16 -0.417658637620938
+1 0 0 0 0 14 12 16 -0.751699935634057
+1 0 0 0 0 15 12 16 -0.955765485796519
+1 0 0 0 0 16 12 16 -0.994570500607911
+1 0 0 0 0 17 12 16 -0.861405240474848
+1 0 0 0 0 18 12 16 -0.579295188642749
+
+
+# iteration 2
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+2 0 0 0 0 0 12 16 -1.00236259183865
+2 0 0 0 0 1 12 16 -0.906417389262528
+2 0 0 0 0 2 12 16 -0.653744385539442
+2 0 0 0 0 3 12 16 -0.288033038475295
+2 0 0 0 0 4 12 16 0.127481837639237
+2 0 0 0 0 5 12 16 0.520953945889808
+2 0 0 0 0 6 12 16 0.824348384178011
+2 0 0 0 0 7 12 16 0.985205497871871
+2 0 0 0 0 8 12 16 0.975711630672718
+2 0 0 0 0 9 12 16 0.797508358468364
+2 0 0 0 0 10 12 16 0.481408645948843
+2 0 0 0 0 11 12 16 0.0820690050845183
+2 0 0 0 0 12 12 16 -0.331461112332425
+2 0 0 0 0 13 12 16 -0.68767859219742
+2 0 0 0 0 14 12 16 -0.924990196107598
+2 0 0 0 0 15 12 16 -1.00236259183865
+2 0 0 0 0 16 12 16 -0.906417389262528
+2 0 0 0 0 17 12 16 -0.653744385539442
+2 0 0 0 0 18 12 16 -0.288033038475295
+
+
+# iteration 3
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+3 0 0 0 0 0 12 16 -0.94364338228954
+3 0 0 0 0 1 12 16 -0.722686120855475
+3 0 0 0 0 2 12 16 -0.376769863728199
+3 0 0 0 0 3 12 16 0.0342933256844357
+3 0 0 0 0 4 12 16 0.439426887541149
+3 0 0 0 0 5 12 16 0.768579548474049
+3 0 0 0 0 6 12 16 0.964837823149789
+3 0 0 0 0 7 12 16 0.994266872926481
+3 0 0 0 0 8 12 16 0.851778147743211
+3 0 0 0 0 9 12 16 0.562009242653596
+3 0 0 0 0 10 12 16 0.175063833815491
+3 0 0 0 0 11 12 16 -0.242151702294314
+3 0 0 0 0 12 12 16 -0.617497009198279
+3 0 0 0 0 13 12 16 -0.886071473427644
+3 0 0 0 0 14 12 16 -1.00143613019474
+3 0 0 0 0 15 12 16 -0.94364338228954
+3 0 0 0 0 16 12 16 -0.722686120855475
+3 0 0 0 0 17 12 16 -0.376769863728199
+3 0 0 0 0 18 12 16 0.0342933256844357
+
+
+# iteration 4
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+4 0 0 0 0 0 12 16 -0.785507602738876
+4 0 0 0 0 1 12 16 -0.462452108726221
+4 0 0 0 0 2 12 16 -0.0594344438692843
+4 0 0 0 0 3 12 16 0.35385997627762
+4 0 0 0 0 4 12 16 0.705968791809162
+4 0 0 0 0 5 12 16 0.936009189711769
+4 0 0 0 0 6 12 16 1.00420509533667
+4 0 0 0 0 7 12 16 0.89876481706098
+4 0 0 0 0 8 12 16 0.637919936893408
+4 0 0 0 0 9 12 16 0.266772904316276
+4 0 0 0 0 10 12 16 -0.150501586972893
+4 0 0 0 0 11 12 16 -0.541752986610453
+4 0 0 0 0 12 12 16 -0.839330373191693
+4 0 0 0 0 13 12 16 -0.991779913171026
+4 0 0 0 0 14 12 16 -0.972741696125436
+4 0 0 0 0 15 12 16 -0.785507602738876
+4 0 0 0 0 16 12 16 -0.462452108726221
+4 0 0 0 0 17 12 16 -0.0594344438692843
+4 0 0 0 0 18 12 16 0.35385997627762
+
+
+# iteration 5
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+5 0 0 0 0 0 12 16 -0.544328174867942
+5 0 0 0 0 1 12 16 -0.152888277069066
+5 0 0 0 0 2 12 16 0.264987392781447
+5 0 0 0 0 3 12 16 0.637044335085157
+5 0 0 0 0 4 12 16 0.898950524486546
+5 0 0 0 0 5 12 16 1.00542000149508
+5 0 0 0 0 6 12 16 0.938043226291145
+5 0 0 0 0 7 12 16 0.708470255406295
+5 0 0 0 0 8 12 16 0.356396341111483
+5 0 0 0 0 9 12 16 -0.0573017383206181
+5 0 0 0 0 10 12 16 -0.461091826627135
+5 0 0 0 0 11 12 16 -0.785154949222079
+5 0 0 0 0 12 12 16 -0.97345764818774
+5 0 0 0 0 13 12 16 -0.993440676196639
+5 0 0 0 0 14 12 16 -0.841648786165927
+5 0 0 0 0 15 12 16 -0.544328174867942
+5 0 0 0 0 16 12 16 -0.152888277069066
+5 0 0 0 0 17 12 16 0.264987392781447
+5 0 0 0 0 18 12 16 0.637044335085157
+
+
+# iteration 6
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+6 0 0 0 0 0 12 16 -0.245256464451885
+6 0 0 0 0 1 12 16 0.173571974101471
+6 0 0 0 0 2 12 16 0.562388241480802
+6 0 0 0 0 3 12 16 0.853962472771321
+6 0 0 0 0 4 12 16 0.997878834514167
+6 0 0 0 0 5 12 16 0.969252880324897
+6 0 0 0 0 6 12 16 0.773034297741468
+6 0 0 0 0 7 12 16 0.443151062282416
+6 0 0 0 0 8 12 16 0.0366429822537203
+6 0 0 0 0 9 12 16 -0.376201002297687
+6 0 0 0 0 10 12 16 -0.723996415873011
+6 0 0 0 0 11 12 16 -0.946606271842939
+6 0 0 0 0 12 12 16 -1.00553930376322
+6 0 0 0 0 13 12 16 -0.890605455025042
+6 0 0 0 0 14 12 16 -0.621677832216481
+6 0 0 0 0 15 12 16 -0.245256464451885
+6 0 0 0 0 16 12 16 0.173571974101471
+6 0 0 0 0 17 12 16 0.562388241480802
+6 0 0 0 0 18 12 16 0.853962472771321
+
+
diff --git a/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/u.yl b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/u.yl
new file mode 100644
index 000000000..50f79e875
--- /dev/null
+++ b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/u.yl
@@ -0,0 +1,219 @@
+# HYDROTOY::u y (u)
+#
+# iteration 0
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+0 0 0 0 0 9 0 16 -0.959492973614494
+0 0 0 0 0 9 1 16 -1
+0 0 0 0 0 9 2 16 -0.9594929736145
+0 0 0 0 0 9 3 16 -0.841253532831185
+0 0 0 0 0 9 4 16 -0.65486073394529
+0 0 0 0 0 9 5 16 -0.415415013001892
+0 0 0 0 0 9 6 16 -0.14231483827329
+0 0 0 0 0 9 7 16 0.142314838273281
+0 0 0 0 0 9 8 16 0.415415013001883
+0 0 0 0 0 9 9 16 0.654860733945283
+0 0 0 0 0 9 10 16 0.84125353283118
+0 0 0 0 0 9 11 16 0.959492973614497
+0 0 0 0 0 9 12 16 1
+0 0 0 0 0 9 13 16 0.959492973614497
+0 0 0 0 0 9 14 16 0.84125353283118
+0 0 0 0 0 9 15 16 0.654860733945283
+0 0 0 0 0 9 16 16 0.415415013001883
+0 0 0 0 0 9 17 16 0.142314838273281
+0 0 0 0 0 9 18 16 -0.142314838273291
+0 0 0 0 0 9 19 16 -0.415415013001892
+0 0 0 0 0 9 20 16 -0.65486073394529
+0 0 0 0 0 9 21 16 -0.841253532831186
+0 0 0 0 0 9 22 16 -0.9594929736145
+0 0 0 0 0 9 23 16 -1
+0 0 0 0 0 9 24 16 -0.959492973614494
+0 0 0 0 0 9 25 16 -0.841253532831175
+
+
+# iteration 1
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+1 0 0 0 0 9 0 16 -1.00051323460778
+1 0 0 0 0 9 1 16 -0.948719671596804
+1 0 0 0 0 9 2 16 -0.820066483046201
+1 0 0 0 0 9 3 16 -0.624976385162354
+1 0 0 0 0 9 4 16 -0.379254417430333
+1 0 0 0 0 9 5 16 -0.102807512310972
+1 0 0 0 0 9 6 16 0.181968246036004
+1 0 0 0 0 9 7 16 0.452002019295973
+1 0 0 0 0 9 8 16 0.685417277112096
+1 0 0 0 0 9 9 16 0.863304103470101
+1 0 0 0 0 9 10 16 0.971251165632154
+1 0 0 0 0 9 11 16 1.00051323460778
+1 0 0 0 0 9 12 16 0.948719671596806
+1 0 0 0 0 9 13 16 0.820066483046195
+1 0 0 0 0 9 14 16 0.624976385162347
+1 0 0 0 0 9 15 16 0.379254417430324
+1 0 0 0 0 9 16 16 0.102807512310963
+1 0 0 0 0 9 17 16 -0.181968246036014
+1 0 0 0 0 9 18 16 -0.452002019295981
+1 0 0 0 0 9 19 16 -0.685417277112103
+1 0 0 0 0 9 20 16 -0.863304103470106
+1 0 0 0 0 9 21 16 -0.971251165632156
+1 0 0 0 0 9 22 16 -1.00051323460778
+1 0 0 0 0 9 23 16 -0.948719671596804
+1 0 0 0 0 9 24 16 -0.820066483046201
+1 0 0 0 0 9 25 16 -0.624976385162354
+
+
+# iteration 2
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+2 0 0 0 0 9 0 16 -0.936397049231443
+2 0 0 0 0 9 1 16 -0.79750835846836
+2 0 0 0 0 9 2 16 -0.594010283467016
+2 0 0 0 0 9 3 16 -0.342389028014344
+2 0 0 0 0 9 4 16 -0.0630294497779055
+2 0 0 0 0 9 5 16 0.221436399628968
+2 0 0 0 0 9 6 16 0.487962788870879
+2 0 0 0 0 9 7 16 0.714957334984917
+2 0 0 0 0 9 8 16 0.884030289833469
+2 0 0 0 0 9 9 16 0.981484368130286
+2 0 0 0 0 9 10 16 0.999424420033478
+2 0 0 0 0 9 11 16 0.936397049231446
+2 0 0 0 0 9 12 16 0.797508358468364
+2 0 0 0 0 9 13 16 0.594010283467008
+2 0 0 0 0 9 14 16 0.342389028014335
+2 0 0 0 0 9 15 16 0.0630294497778957
+2 0 0 0 0 9 16 16 -0.221436399628977
+2 0 0 0 0 9 17 16 -0.487962788870887
+2 0 0 0 0 9 18 16 -0.714957334984924
+2 0 0 0 0 9 19 16 -0.884030289833474
+2 0 0 0 0 9 20 16 -0.981484368130287
+2 0 0 0 0 9 21 16 -0.999424420033477
+2 0 0 0 0 9 22 16 -0.936397049231443
+2 0 0 0 0 9 23 16 -0.79750835846836
+2 0 0 0 0 9 24 16 -0.594010283467016
+2 0 0 0 0 9 25 16 -0.342389028014344
+
+
+# iteration 3
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+3 0 0 0 0 9 0 16 -0.773612345734507
+3 0 0 0 0 9 1 16 -0.562009242653593
+3 0 0 0 0 9 2 16 -0.30487549313056
+3 0 0 0 0 9 3 16 -0.0230425443184478
+3 0 0 0 0 9 4 16 0.260657174395054
+3 0 0 0 0 9 5 16 0.523239999026976
+3 0 0 0 0 9 6 16 0.743433030765824
+3 0 0 0 0 9 7 16 0.903397539718502
+3 0 0 0 0 9 8 16 0.990174152715228
+3 0 0 0 0 9 9 16 0.996732744651397
+3 0 0 0 0 9 10 16 0.922541977413788
+3 0 0 0 0 9 11 16 0.773612345734511
+3 0 0 0 0 9 12 16 0.562009242653596
+3 0 0 0 0 9 13 16 0.30487549313055
+3 0 0 0 0 9 14 16 0.0230425443184395
+3 0 0 0 0 9 15 16 -0.260657174395064
+3 0 0 0 0 9 16 16 -0.523239999026984
+3 0 0 0 0 9 17 16 -0.743433030765831
+3 0 0 0 0 9 18 16 -0.903397539718506
+3 0 0 0 0 9 19 16 -0.99017415271523
+3 0 0 0 0 9 20 16 -0.996732744651396
+3 0 0 0 0 9 21 16 -0.922541977413785
+3 0 0 0 0 9 22 16 -0.773612345734507
+3 0 0 0 0 9 23 16 -0.562009242653593
+3 0 0 0 0 9 24 16 -0.30487549313056
+3 0 0 0 0 9 25 16 -0.0230425443184478
+
+
+# iteration 4
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+4 0 0 0 0 9 0 16 -0.529023034768285
+4 0 0 0 0 9 1 16 -0.266772904316274
+4 0 0 0 0 9 2 16 0.0170895802838814
+4 0 0 0 0 9 3 16 0.299567568725097
+4 0 0 0 0 9 4 16 0.55777637434513
+4 0 0 0 0 9 5 16 0.77079745533955
+4 0 0 0 0 9 6 16 0.921373110611335
+4 0 0 0 0 9 7 16 0.997304596078268
+4 0 0 0 0 9 8 16 0.992440394369748
+4 0 0 0 0 9 9 16 0.907174574179681
+4 0 0 0 0 9 10 16 0.748414865164506
+4 0 0 0 0 9 11 16 0.529023034768289
+4 0 0 0 0 9 12 16 0.266772904316276
+4 0 0 0 0 9 13 16 -0.0170895802838905
+4 0 0 0 0 9 14 16 -0.299567568725103
+4 0 0 0 0 9 15 16 -0.557776374345138
+4 0 0 0 0 9 16 16 -0.770797455339557
+4 0 0 0 0 9 17 16 -0.921373110611339
+4 0 0 0 0 9 18 16 -0.997304596078268
+4 0 0 0 0 9 19 16 -0.992440394369747
+4 0 0 0 0 9 20 16 -0.907174574179677
+4 0 0 0 0 9 21 16 -0.7484148651645
+4 0 0 0 0 9 22 16 -0.529023034768285
+4 0 0 0 0 9 23 16 -0.266772904316274
+4 0 0 0 0 9 24 16 0.0170895802838814
+4 0 0 0 0 9 25 16 0.299567568725097
+
+
+# iteration 5
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+5 0 0 0 0 9 0 16 -0.228142427103317
+5 0 0 0 0 9 1 16 0.0573017383206182
+5 0 0 0 0 9 2 16 0.338103657692372
+5 0 0 0 0 9 3 16 0.591514429497776
+5 0 0 0 0 9 4 16 0.797004220097029
+5 0 0 0 0 9 5 16 0.937925468750632
+5 0 0 0 0 9 6 16 1.0028615739836
+5 0 0 0 0 9 7 16 0.986551798739849
+5 0 0 0 0 9 8 16 0.890317464011655
+5 0 0 0 0 9 9 16 0.721954903271074
+5 0 0 0 0 9 10 16 0.495103849898604
+5 0 0 0 0 9 11 16 0.22814242710332
+5 0 0 0 0 9 12 16 -0.0573017383206181
+5 0 0 0 0 9 13 16 -0.338103657692379
+5 0 0 0 0 9 14 16 -0.591514429497779
+5 0 0 0 0 9 15 16 -0.797004220097035
+5 0 0 0 0 9 16 16 -0.937925468750636
+5 0 0 0 0 9 17 16 -1.0028615739836
+5 0 0 0 0 9 18 16 -0.986551798739846
+5 0 0 0 0 9 19 16 -0.890317464011651
+5 0 0 0 0 9 20 16 -0.721954903271068
+5 0 0 0 0 9 21 16 -0.495103849898596
+5 0 0 0 0 9 22 16 -0.228142427103317
+5 0 0 0 0 9 23 16 0.0573017383206182
+5 0 0 0 0 9 24 16 0.338103657692372
+5 0 0 0 0 9 25 16 0.591514429497776
+
+
+# iteration 6
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+6 0 0 0 0 9 0 16 0.0975277748355794
+6 0 0 0 0 9 1 16 0.376201002297685
+6 0 0 0 0 9 2 16 0.624396661907141
+6 0 0 0 0 9 3 16 0.822007417398816
+6 0 0 0 0 9 4 16 0.953024020599179
+6 0 0 0 0 9 5 16 1.00683228550269
+6 0 0 0 0 9 6 16 0.979072986496933
+6 0 0 0 0 9 7 16 0.871995016896448
+6 0 0 0 0 9 8 16 0.69427319698106
+6 0 0 0 0 9 9 16 0.460305491647954
+6 0 0 0 0 9 10 16 0.189046572923696
+6 0 0 0 0 9 11 16 -0.0975277748355793
+6 0 0 0 0 9 12 16 -0.376201002297687
+6 0 0 0 0 9 13 16 -0.624396661907144
+6 0 0 0 0 9 14 16 -0.822007417398816
+6 0 0 0 0 9 15 16 -0.953024020599182
+6 0 0 0 0 9 16 16 -1.00683228550269
+6 0 0 0 0 9 17 16 -0.979072986496931
+6 0 0 0 0 9 18 16 -0.871995016896444
+6 0 0 0 0 9 19 16 -0.694273196981054
+6 0 0 0 0 9 20 16 -0.460305491647947
+6 0 0 0 0 9 21 16 -0.189046572923689
+6 0 0 0 0 9 22 16 0.0975277748355794
+6 0 0 0 0 9 23 16 0.376201002297685
+6 0 0 0 0 9 24 16 0.624396661907141
+6 0 0 0 0 9 25 16 0.822007417398816
+
+
diff --git a/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/u.zl b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/u.zl
new file mode 100644
index 000000000..57a1edbb4
--- /dev/null
+++ b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/u.zl
@@ -0,0 +1,275 @@
+# HYDROTOY::u z (u)
+#
+# iteration 0
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+0 0 0 0 0 9 12 0 0.913545457642604
+0 0 0 0 0 9 12 1 1
+0 0 0 0 0 9 12 2 0.913545457642598
+0 0 0 0 0 9 12 3 0.669130606358854
+0 0 0 0 0 9 12 4 0.309016994374941
+0 0 0 0 0 9 12 5 -0.104528463267659
+0 0 0 0 0 9 12 6 -0.500000000000004
+0 0 0 0 0 9 12 7 -0.80901699437495
+0 0 0 0 0 9 12 8 -0.978147600733806
+0 0 0 0 0 9 12 9 -0.978147600733805
+0 0 0 0 0 9 12 10 -0.809016994374946
+0 0 0 0 0 9 12 11 -0.499999999999998
+0 0 0 0 0 9 12 12 -0.104528463267652
+0 0 0 0 0 9 12 13 0.309016994374949
+0 0 0 0 0 9 12 14 0.669130606358859
+0 0 0 0 0 9 12 15 0.913545457642601
+0 0 0 0 0 9 12 16 1
+0 0 0 0 0 9 12 17 0.913545457642601
+0 0 0 0 0 9 12 18 0.669130606358859
+0 0 0 0 0 9 12 19 0.309016994374949
+0 0 0 0 0 9 12 20 -0.104528463267652
+0 0 0 0 0 9 12 21 -0.499999999999998
+0 0 0 0 0 9 12 22 -0.809016994374946
+0 0 0 0 0 9 12 23 -0.978147600733805
+0 0 0 0 0 9 12 24 -0.978147600733806
+0 0 0 0 0 9 12 25 -0.80901699437495
+0 0 0 0 0 9 12 26 -0.500000000000004
+0 0 0 0 0 9 12 27 -0.104528463267659
+0 0 0 0 0 9 12 28 0.309016994374942
+0 0 0 0 0 9 12 29 0.669130606358854
+0 0 0 0 0 9 12 30 0.913545457642598
+0 0 0 0 0 9 12 31 1
+0 0 0 0 0 9 12 32 0.913545457642604
+0 0 0 0 0 9 12 33 0.669130606358864
+
+
+# iteration 1
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+1 0 0 0 0 9 12 0 0.996953826263689
+1 0 0 0 0 9 12 1 0.948719671596808
+1 0 0 0 0 9 12 2 0.73644326686319
+1 0 0 0 0 9 12 3 0.396829130911887
+1 0 0 0 0 9 12 4 -0.0114003668535601
+1 0 0 0 0 9 12 5 -0.417658637620944
+1 0 0 0 0 9 12 6 -0.751699935634062
+1 0 0 0 0 9 12 7 -0.955765485796521
+1 0 0 0 0 9 12 8 -0.99457050060791
+1 0 0 0 0 9 12 9 -0.861405240474847
+1 0 0 0 0 9 12 10 -0.579295188642748
+1 0 0 0 0 9 12 11 -0.197019735962745
+1 0 0 0 0 9 12 12 0.219322218933327
+1 0 0 0 0 9 12 13 0.597741369696019
+1 0 0 0 0 9 12 14 0.872805607328403
+1 0 0 0 0 9 12 15 0.99695382626369
+1 0 0 0 0 9 12 16 0.948719671596806
+1 0 0 0 0 9 12 17 0.736443266863195
+1 0 0 0 0 9 12 18 0.396829130911893
+1 0 0 0 0 9 12 19 -0.0114003668535524
+1 0 0 0 0 9 12 20 -0.417658637620938
+1 0 0 0 0 9 12 21 -0.751699935634057
+1 0 0 0 0 9 12 22 -0.955765485796519
+1 0 0 0 0 9 12 23 -0.994570500607911
+1 0 0 0 0 9 12 24 -0.861405240474851
+1 0 0 0 0 9 12 25 -0.579295188642754
+1 0 0 0 0 9 12 26 -0.197019735962752
+1 0 0 0 0 9 12 27 0.21932221893332
+1 0 0 0 0 9 12 28 0.597741369696014
+1 0 0 0 0 9 12 29 0.8728056073284
+1 0 0 0 0 9 12 30 0.996953826263689
+1 0 0 0 0 9 12 31 0.948719671596808
+1 0 0 0 0 9 12 32 0.73644326686319
+1 0 0 0 0 9 12 33 0.396829130911887
+
+
+# iteration 2
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+2 0 0 0 0 9 12 0 0.97571163067272
+2 0 0 0 0 9 12 1 0.797508358468365
+2 0 0 0 0 9 12 2 0.481408645948837
+2 0 0 0 0 9 12 3 0.0820690050845114
+2 0 0 0 0 9 12 4 -0.331461112332432
+2 0 0 0 0 9 12 5 -0.687678592197425
+2 0 0 0 0 9 12 6 -0.924990196107601
+2 0 0 0 0 9 12 7 -1.00236259183865
+2 0 0 0 0 9 12 8 -0.906417389262526
+2 0 0 0 0 9 12 9 -0.653744385539442
+2 0 0 0 0 9 12 10 -0.288033038475295
+2 0 0 0 0 9 12 11 0.127481837639237
+2 0 0 0 0 9 12 12 0.520953945889809
+2 0 0 0 0 9 12 13 0.824348384178011
+2 0 0 0 0 9 12 14 0.985205497871871
+2 0 0 0 0 9 12 15 0.975711630672718
+2 0 0 0 0 9 12 16 0.797508358468364
+2 0 0 0 0 9 12 17 0.481408645948843
+2 0 0 0 0 9 12 18 0.0820690050845184
+2 0 0 0 0 9 12 19 -0.331461112332425
+2 0 0 0 0 9 12 20 -0.68767859219742
+2 0 0 0 0 9 12 21 -0.924990196107598
+2 0 0 0 0 9 12 22 -1.00236259183865
+2 0 0 0 0 9 12 23 -0.906417389262529
+2 0 0 0 0 9 12 24 -0.653744385539447
+2 0 0 0 0 9 12 25 -0.288033038475302
+2 0 0 0 0 9 12 26 0.12748183763923
+2 0 0 0 0 9 12 27 0.520953945889802
+2 0 0 0 0 9 12 28 0.824348384178007
+2 0 0 0 0 9 12 29 0.985205497871869
+2 0 0 0 0 9 12 30 0.97571163067272
+2 0 0 0 0 9 12 31 0.797508358468365
+2 0 0 0 0 9 12 32 0.481408645948837
+2 0 0 0 0 9 12 33 0.0820690050845114
+
+
+# iteration 3
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+3 0 0 0 0 9 12 0 0.851778147743213
+3 0 0 0 0 9 12 1 0.562009242653597
+3 0 0 0 0 9 12 2 0.175063833815484
+3 0 0 0 0 9 12 3 -0.24215170229432
+3 0 0 0 0 9 12 4 -0.617497009198284
+3 0 0 0 0 9 12 5 -0.886071473427647
+3 0 0 0 0 9 12 6 -1.00143613019474
+3 0 0 0 0 9 12 7 -0.943643382289538
+3 0 0 0 0 9 12 8 -0.722686120855472
+3 0 0 0 0 9 12 9 -0.376769863728199
+3 0 0 0 0 9 12 10 0.0342933256844365
+3 0 0 0 0 9 12 11 0.439426887541149
+3 0 0 0 0 9 12 12 0.76857954847405
+3 0 0 0 0 9 12 13 0.964837823149789
+3 0 0 0 0 9 12 14 0.994266872926481
+3 0 0 0 0 9 12 15 0.851778147743211
+3 0 0 0 0 9 12 16 0.562009242653596
+3 0 0 0 0 9 12 17 0.175063833815491
+3 0 0 0 0 9 12 18 -0.242151702294313
+3 0 0 0 0 9 12 19 -0.617497009198278
+3 0 0 0 0 9 12 20 -0.886071473427644
+3 0 0 0 0 9 12 21 -1.00143613019474
+3 0 0 0 0 9 12 22 -0.94364338228954
+3 0 0 0 0 9 12 23 -0.722686120855477
+3 0 0 0 0 9 12 24 -0.376769863728206
+3 0 0 0 0 9 12 25 0.034293325684429
+3 0 0 0 0 9 12 26 0.439426887541143
+3 0 0 0 0 9 12 27 0.768579548474045
+3 0 0 0 0 9 12 28 0.964837823149787
+3 0 0 0 0 9 12 29 0.994266872926482
+3 0 0 0 0 9 12 30 0.851778147743213
+3 0 0 0 0 9 12 31 0.562009242653597
+3 0 0 0 0 9 12 32 0.175063833815484
+3 0 0 0 0 9 12 33 -0.24215170229432
+
+
+# iteration 4
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+4 0 0 0 0 9 12 0 0.63791993689341
+4 0 0 0 0 9 12 1 0.266772904316275
+4 0 0 0 0 9 12 2 -0.1505015869729
+4 0 0 0 0 9 12 3 -0.541752986610458
+4 0 0 0 0 9 12 4 -0.839330373191696
+4 0 0 0 0 9 12 5 -0.991779913171028
+4 0 0 0 0 9 12 6 -0.972741696125435
+4 0 0 0 0 9 12 7 -0.785507602738873
+4 0 0 0 0 9 12 8 -0.462452108726218
+4 0 0 0 0 9 12 9 -0.0594344438692841
+4 0 0 0 0 9 12 10 0.353859976277621
+4 0 0 0 0 9 12 11 0.705968791809162
+4 0 0 0 0 9 12 12 0.936009189711769
+4 0 0 0 0 9 12 13 1.00420509533667
+4 0 0 0 0 9 12 14 0.89876481706098
+4 0 0 0 0 9 12 15 0.637919936893408
+4 0 0 0 0 9 12 16 0.266772904316276
+4 0 0 0 0 9 12 17 -0.150501586972892
+4 0 0 0 0 9 12 18 -0.541752986610453
+4 0 0 0 0 9 12 19 -0.839330373191692
+4 0 0 0 0 9 12 20 -0.991779913171026
+4 0 0 0 0 9 12 21 -0.972741696125436
+4 0 0 0 0 9 12 22 -0.785507602738877
+4 0 0 0 0 9 12 23 -0.462452108726224
+4 0 0 0 0 9 12 24 -0.0594344438692912
+4 0 0 0 0 9 12 25 0.353859976277614
+4 0 0 0 0 9 12 26 0.705968791809157
+4 0 0 0 0 9 12 27 0.936009189711766
+4 0 0 0 0 9 12 28 1.00420509533667
+4 0 0 0 0 9 12 29 0.898764817060982
+4 0 0 0 0 9 12 30 0.63791993689341
+4 0 0 0 0 9 12 31 0.266772904316275
+4 0 0 0 0 9 12 32 -0.1505015869729
+4 0 0 0 0 9 12 33 -0.541752986610458
+
+
+# iteration 5
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+5 0 0 0 0 9 12 0 0.356396341111483
+5 0 0 0 0 9 12 1 -0.0573017383206205
+5 0 0 0 0 9 12 2 -0.461091826627141
+5 0 0 0 0 9 12 3 -0.785154949222081
+5 0 0 0 0 9 12 4 -0.973457648187742
+5 0 0 0 0 9 12 5 -0.993440676196638
+5 0 0 0 0 9 12 6 -0.841648786165924
+5 0 0 0 0 9 12 7 -0.544328174867939
+5 0 0 0 0 9 12 8 -0.152888277069062
+5 0 0 0 0 9 12 9 0.264987392781448
+5 0 0 0 0 9 12 10 0.637044335085158
+5 0 0 0 0 9 12 11 0.898950524486546
+5 0 0 0 0 9 12 12 1.00542000149508
+5 0 0 0 0 9 12 13 0.938043226291145
+5 0 0 0 0 9 12 14 0.708470255406295
+5 0 0 0 0 9 12 15 0.356396341111483
+5 0 0 0 0 9 12 16 -0.0573017383206181
+5 0 0 0 0 9 12 17 -0.461091826627135
+5 0 0 0 0 9 12 18 -0.785154949222079
+5 0 0 0 0 9 12 19 -0.97345764818774
+5 0 0 0 0 9 12 20 -0.993440676196639
+5 0 0 0 0 9 12 21 -0.841648786165928
+5 0 0 0 0 9 12 22 -0.544328174867945
+5 0 0 0 0 9 12 23 -0.15288827706907
+5 0 0 0 0 9 12 24 0.264987392781441
+5 0 0 0 0 9 12 25 0.637044335085152
+5 0 0 0 0 9 12 26 0.898950524486543
+5 0 0 0 0 9 12 27 1.00542000149508
+5 0 0 0 0 9 12 28 0.938043226291147
+5 0 0 0 0 9 12 29 0.708470255406299
+5 0 0 0 0 9 12 30 0.356396341111483
+5 0 0 0 0 9 12 31 -0.0573017383206205
+5 0 0 0 0 9 12 32 -0.461091826627141
+5 0 0 0 0 9 12 33 -0.785154949222081
+
+
+# iteration 6
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+6 0 0 0 0 9 12 0 0.036642982253719
+6 0 0 0 0 9 12 1 -0.37620100229769
+6 0 0 0 0 9 12 2 -0.723996415873014
+6 0 0 0 0 9 12 3 -0.946606271842938
+6 0 0 0 0 9 12 4 -1.00553930376322
+6 0 0 0 0 9 12 5 -0.890605455025039
+6 0 0 0 0 9 12 6 -0.621677832216476
+6 0 0 0 0 9 12 7 -0.245256464451882
+6 0 0 0 0 9 12 8 0.173571974101474
+6 0 0 0 0 9 12 9 0.562388241480803
+6 0 0 0 0 9 12 10 0.853962472771322
+6 0 0 0 0 9 12 11 0.997878834514167
+6 0 0 0 0 9 12 12 0.969252880324898
+6 0 0 0 0 9 12 13 0.773034297741468
+6 0 0 0 0 9 12 14 0.443151062282416
+6 0 0 0 0 9 12 15 0.0366429822537202
+6 0 0 0 0 9 12 16 -0.376201002297687
+6 0 0 0 0 9 12 17 -0.723996415873011
+6 0 0 0 0 9 12 18 -0.946606271842939
+6 0 0 0 0 9 12 19 -1.00553930376322
+6 0 0 0 0 9 12 20 -0.890605455025042
+6 0 0 0 0 9 12 21 -0.621677832216482
+6 0 0 0 0 9 12 22 -0.245256464451889
+6 0 0 0 0 9 12 23 0.173571974101467
+6 0 0 0 0 9 12 24 0.562388241480797
+6 0 0 0 0 9 12 25 0.853962472771319
+6 0 0 0 0 9 12 26 0.997878834514166
+6 0 0 0 0 9 12 27 0.969252880324899
+6 0 0 0 0 9 12 28 0.773034297741472
+6 0 0 0 0 9 12 29 0.44315106228242
+6 0 0 0 0 9 12 30 0.036642982253719
+6 0 0 0 0 9 12 31 -0.37620100229769
+6 0 0 0 0 9 12 32 -0.723996415873014
+6 0 0 0 0 9 12 33 -0.946606271842938
+
+
diff --git a/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/vx.xl b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/vx.xl
new file mode 100644
index 000000000..dc98ae343
--- /dev/null
+++ b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/vx.xl
@@ -0,0 +1,170 @@
+# HYDROTOY::vx x (vx)
+#
+# iteration 0
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+0 0 0 0 0 0 12 16 -0.515299953858482
+0 0 0 0 0 1 12 16 -0.62302697845592
+0 0 0 0 0 2 12 16 -0.62302697845592
+0 0 0 0 0 3 12 16 -0.51529995385848
+0 0 0 0 0 4 12 16 -0.318472885885792
+0 0 0 0 0 5 12 16 -0.0665789627081124
+0 0 0 0 0 6 12 16 0.196827067972688
+0 0 0 0 0 7 12 16 0.426199910483233
+0 0 0 0 0 8 12 16 0.581878916566594
+0 0 0 0 0 9 12 16 0.636945771771587
+0 0 0 0 0 10 12 16 0.581878916566594
+0 0 0 0 0 11 12 16 0.426199910483233
+0 0 0 0 0 12 12 16 0.196827067972688
+0 0 0 0 0 13 12 16 -0.0665789627081126
+0 0 0 0 0 14 12 16 -0.318472885885792
+0 0 0 0 0 15 12 16 -0.51529995385848
+0 0 0 0 0 16 12 16 -0.62302697845592
+0 0 0 0 0 17 12 16 -0.62302697845592
+0 0 0 0 0 18 12 16 -0.515299953858482
+
+
+# iteration 1
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+1 0 0 0 0 0 12 16 -0.608492170320791
+1 0 0 0 0 1 12 16 -0.633457407715208
+1 0 0 0 0 2 12 16 -0.548892104535778
+1 0 0 0 0 3 12 16 -0.369418369953888
+1 0 0 0 0 4 12 16 -0.126068843146438
+1 0 0 0 0 5 12 16 0.139079131940516
+1 0 0 0 0 6 12 16 0.380179061620706
+1 0 0 0 0 7 12 16 0.555542577728329
+1 0 0 0 0 8 12 16 0.634847735200848
+1 0 0 0 0 9 12 16 0.604381951846525
+1 0 0 0 0 10 12 16 0.469413038380277
+1 0 0 0 0 11 12 16 0.253278346094503
+1 0 0 0 0 12 12 16 -0.00665047319254958
+1 0 0 0 0 13 12 16 -0.265429365246958
+1 0 0 0 0 14 12 16 -0.478313108700085
+1 0 0 0 0 15 12 16 -0.608492170320791
+1 0 0 0 0 16 12 16 -0.633457407715208
+1 0 0 0 0 17 12 16 -0.548892104535778
+1 0 0 0 0 18 12 16 -0.369418369953888
+
+
+# iteration 2
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+2 0 0 0 0 0 12 16 -0.638086200378305
+2 0 0 0 0 1 12 16 -0.57748024821656
+2 0 0 0 0 2 12 16 -0.417022714894814
+2 0 0 0 0 3 12 16 -0.184458165635327
+2 0 0 0 0 4 12 16 0.0800008762123354
+2 0 0 0 0 5 12 16 0.330627039777741
+2 0 0 0 0 6 12 16 0.524084784513214
+2 0 0 0 0 7 12 16 0.626923508845556
+2 0 0 0 0 8 12 16 0.621361463077223
+2 0 0 0 0 9 12 16 0.508360375451159
+2 0 0 0 0 10 12 16 0.307459160600565
+2 0 0 0 0 11 12 16 0.0533954637033468
+2 0 0 0 0 12 12 16 -0.209900793950739
+2 0 0 0 0 13 12 16 -0.436903297441893
+2 0 0 0 0 14 12 16 -0.588361251663493
+2 0 0 0 0 15 12 16 -0.638086200378305
+2 0 0 0 0 16 12 16 -0.57748024821656
+2 0 0 0 0 17 12 16 -0.417022714894814
+2 0 0 0 0 18 12 16 -0.184458165635327
+
+
+# iteration 3
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+3 0 0 0 0 0 12 16 -0.600801795900965
+3 0 0 0 0 1 12 16 -0.460809125595697
+3 0 0 0 0 2 12 16 -0.241138371155451
+3 0 0 0 0 3 12 16 0.0202273983308999
+3 0 0 0 0 4 12 16 0.278095666885694
+3 0 0 0 0 5 12 16 0.487878668216131
+3 0 0 0 0 6 12 16 0.613303015573443
+3 0 0 0 0 7 12 16 0.632681699855125
+3 0 0 0 0 8 12 16 0.542663970499055
+3 0 0 0 0 9 12 16 0.358814710696295
+3 0 0 0 0 10 12 16 0.112923127684834
+3 0 0 0 0 11 12 16 -0.152493889977744
+3 0 0 0 0 12 12 16 -0.391543328699671
+3 0 0 0 0 13 12 16 -0.562891368829953
+3 0 0 0 0 14 12 16 -0.636910377581988
+3 0 0 0 0 15 12 16 -0.600801795900965
+3 0 0 0 0 16 12 16 -0.460809125595697
+3 0 0 0 0 17 12 16 -0.241138371155451
+3 0 0 0 0 18 12 16 0.0202273983308999
+
+
+# iteration 4
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+4 0 0 0 0 0 12 16 -0.50038504730599
+4 0 0 0 0 1 12 16 -0.295557108392468
+4 0 0 0 0 2 12 16 -0.0396246603858525
+4 0 0 0 0 3 12 16 0.223159251380213
+4 0 0 0 0 4 12 16 0.447356901244488
+4 0 0 0 0 5 12 16 0.594202478773731
+4 0 0 0 0 6 12 16 0.638305049562943
+4 0 0 0 0 7 12 16 0.572038878463393
+4 0 0 0 0 8 12 16 0.406861988467459
+4 0 0 0 0 9 12 16 0.171334964440373
+4 0 0 0 0 10 12 16 -0.0938174314677396
+4 0 0 0 0 11 12 16 -0.342747941170472
+4 0 0 0 0 12 12 16 -0.532414218077537
+4 0 0 0 0 13 12 16 -0.630021239847671
+4 0 0 0 0 14 12 16 -0.618691865684861
+4 0 0 0 0 15 12 16 -0.50038504730599
+4 0 0 0 0 16 12 16 -0.295557108392468
+4 0 0 0 0 17 12 16 -0.0396246603858525
+4 0 0 0 0 18 12 16 0.223159251380213
+
+
+# iteration 5
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+5 0 0 0 0 0 12 16 -0.34723280804116
+5 0 0 0 0 1 12 16 -0.0989793588236481
+5 0 0 0 0 2 12 16 0.166388520733717
+5 0 0 0 0 3 12 16 0.402986313463963
+5 0 0 0 0 4 12 16 0.569904111580568
+5 0 0 0 0 5 12 16 0.638280311388575
+5 0 0 0 0 6 12 16 0.596292046762909
+5 0 0 0 0 7 12 16 0.451199470108754
+5 0 0 0 0 8 12 16 0.228090406054292
+5 0 0 0 0 9 12 16 -0.0344575613432429
+5 0 0 0 0 10 12 16 -0.291047503347414
+5 0 0 0 0 11 12 16 -0.497312687939257
+5 0 0 0 0 12 12 16 -0.617587990842467
+5 0 0 0 0 13 12 16 -0.631076719518255
+5 0 0 0 0 14 12 16 -0.535446550237324
+5 0 0 0 0 15 12 16 -0.34723280804116
+5 0 0 0 0 16 12 16 -0.0989793588236481
+5 0 0 0 0 17 12 16 0.166388520733717
+5 0 0 0 0 18 12 16 0.402986313463963
+
+
+# iteration 6
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+6 0 0 0 0 0 12 16 -0.157316535477104
+6 0 0 0 0 1 12 16 0.108328421385471
+6 0 0 0 0 2 12 16 0.355242410057684
+6 0 0 0 0 3 12 16 0.540731758754941
+6 0 0 0 0 4 12 16 0.632723673969661
+6 0 0 0 0 5 12 16 0.615311917840902
+6 0 0 0 0 6 12 16 0.491507141184166
+6 0 0 0 0 7 12 16 0.282716314614489
+6 0 0 0 0 8 12 16 0.0250412688508799
+6 0 0 0 0 9 12 16 -0.236963639789832
+6 0 0 0 0 10 12 16 -0.457995382363797
+6 0 0 0 0 11 12 16 -0.599835562569634
+6 0 0 0 0 12 12 16 -0.637958724672169
+6 0 0 0 0 13 12 16 -0.56577302760582
+6 0 0 0 0 14 12 16 -0.395760034179828
+6 0 0 0 0 15 12 16 -0.157316535477104
+6 0 0 0 0 16 12 16 0.108328421385471
+6 0 0 0 0 17 12 16 0.355242410057684
+6 0 0 0 0 18 12 16 0.540731758754941
+
+
diff --git a/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/vx.yl b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/vx.yl
new file mode 100644
index 000000000..8dd2b03f5
--- /dev/null
+++ b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/vx.yl
@@ -0,0 +1,219 @@
+# HYDROTOY::vx y (vx)
+#
+# iteration 0
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+0 0 0 0 0 9 0 16 -0.611144992588299
+0 0 0 0 0 9 1 16 -0.636945771771587
+0 0 0 0 0 9 2 16 -0.611144992588303
+0 0 0 0 0 9 3 16 -0.535832880724733
+0 0 0 0 0 9 4 16 -0.417110775585691
+0 0 0 0 0 9 5 16 -0.264596836061994
+0 0 0 0 0 9 6 16 -0.0906468344985295
+0 0 0 0 0 9 7 16 0.0906468344985235
+0 0 0 0 0 9 8 16 0.264596836061988
+0 0 0 0 0 9 9 16 0.417110775585686
+0 0 0 0 0 9 10 16 0.53583288072473
+0 0 0 0 0 9 11 16 0.611144992588301
+0 0 0 0 0 9 12 16 0.636945771771587
+0 0 0 0 0 9 13 16 0.611144992588301
+0 0 0 0 0 9 14 16 0.53583288072473
+0 0 0 0 0 9 15 16 0.417110775585686
+0 0 0 0 0 9 16 16 0.264596836061988
+0 0 0 0 0 9 17 16 0.0906468344985234
+0 0 0 0 0 9 18 16 -0.0906468344985296
+0 0 0 0 0 9 19 16 -0.264596836061994
+0 0 0 0 0 9 20 16 -0.417110775585691
+0 0 0 0 0 9 21 16 -0.535832880724734
+0 0 0 0 0 9 22 16 -0.611144992588303
+0 0 0 0 0 9 23 16 -0.636945771771587
+0 0 0 0 0 9 24 16 -0.611144992588299
+0 0 0 0 0 9 25 16 -0.535832880724727
+
+
+# iteration 1
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+1 0 0 0 0 9 0 16 -0.637195713383579
+1 0 0 0 0 9 1 16 -0.604381951846523
+1 0 0 0 0 9 2 16 -0.522604758968737
+1 0 0 0 0 9 3 16 -0.398489236569475
+1 0 0 0 0 9 4 16 -0.242090486130096
+1 0 0 0 0 9 5 16 -0.0660790042720144
+1 0 0 0 0 9 6 16 0.115285805525215
+1 0 0 0 0 9 7 16 0.287310844989877
+1 0 0 0 0 9 8 16 0.436059668496847
+1 0 0 0 0 9 9 16 0.549481531008906
+1 0 0 0 0 9 10 16 0.618387667771117
+1 0 0 0 0 9 11 16 0.637195713383579
+1 0 0 0 0 9 12 16 0.604381951846525
+1 0 0 0 0 9 13 16 0.522604758968734
+1 0 0 0 0 9 14 16 0.39848923656947
+1 0 0 0 0 9 15 16 0.24209048613009
+1 0 0 0 0 9 16 16 0.0660790042720083
+1 0 0 0 0 9 17 16 -0.115285805525221
+1 0 0 0 0 9 18 16 -0.287310844989883
+1 0 0 0 0 9 19 16 -0.436059668496852
+1 0 0 0 0 9 20 16 -0.54948153100891
+1 0 0 0 0 9 21 16 -0.618387667771118
+1 0 0 0 0 9 22 16 -0.637195713383579
+1 0 0 0 0 9 23 16 -0.604381951846523
+1 0 0 0 0 9 24 16 -0.522604758968737
+1 0 0 0 0 9 25 16 -0.398489236569475
+
+
+# iteration 2
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+2 0 0 0 0 9 0 16 -0.59648290094983
+2 0 0 0 0 9 1 16 -0.508360375451156
+2 0 0 0 0 9 2 16 -0.379053515669004
+2 0 0 0 0 9 3 16 -0.2190379943654
+2 0 0 0 0 9 4 16 -0.0412773174274225
+2 0 0 0 0 9 5 16 0.139827402282866
+2 0 0 0 0 9 6 16 0.309604137445777
+2 0 0 0 0 9 7 16 0.454298586679535
+2 0 0 0 0 9 8 16 0.562188466238243
+2 0 0 0 0 9 9 16 0.624533179725876
+2 0 0 0 0 9 10 16 0.636281929233952
+2 0 0 0 0 9 11 16 0.596482900949832
+2 0 0 0 0 9 12 16 0.508360375451159
+2 0 0 0 0 9 13 16 0.379053515668998
+2 0 0 0 0 9 14 16 0.219037994365394
+2 0 0 0 0 9 15 16 0.0412773174274162
+2 0 0 0 0 9 16 16 -0.139827402282872
+2 0 0 0 0 9 17 16 -0.309604137445783
+2 0 0 0 0 9 18 16 -0.454298586679539
+2 0 0 0 0 9 19 16 -0.562188466238246
+2 0 0 0 0 9 20 16 -0.624533179725877
+2 0 0 0 0 9 21 16 -0.636281929233952
+2 0 0 0 0 9 22 16 -0.59648290094983
+2 0 0 0 0 9 23 16 -0.508360375451156
+2 0 0 0 0 9 24 16 -0.379053515669004
+2 0 0 0 0 9 25 16 -0.2190379943654
+
+
+# iteration 3
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+3 0 0 0 0 9 0 16 -0.493113583217527
+3 0 0 0 0 9 1 16 -0.358814710696291
+3 0 0 0 0 9 2 16 -0.195446804267703
+3 0 0 0 0 9 3 16 -0.0162449601242362
+3 0 0 0 0 9 4 16 0.164272954075997
+3 0 0 0 0 9 5 16 0.331482450505869
+3 0 0 0 0 9 6 16 0.471837210197796
+3 0 0 0 0 9 7 16 0.573966525243435
+3 0 0 0 0 9 8 16 0.629596485924211
+3 0 0 0 0 9 9 16 0.634220283669883
+3 0 0 0 0 9 10 16 0.587463325885882
+3 0 0 0 0 9 11 16 0.493113583217531
+3 0 0 0 0 9 12 16 0.358814710696295
+3 0 0 0 0 9 13 16 0.195446804267697
+3 0 0 0 0 9 14 16 0.0162449601242304
+3 0 0 0 0 9 15 16 -0.164272954076003
+3 0 0 0 0 9 16 16 -0.331482450505874
+3 0 0 0 0 9 17 16 -0.4718372101978
+3 0 0 0 0 9 18 16 -0.573966525243437
+3 0 0 0 0 9 19 16 -0.629596485924212
+3 0 0 0 0 9 20 16 -0.634220283669883
+3 0 0 0 0 9 21 16 -0.587463325885879
+3 0 0 0 0 9 22 16 -0.493113583217527
+3 0 0 0 0 9 23 16 -0.358814710696291
+3 0 0 0 0 9 24 16 -0.195446804267703
+3 0 0 0 0 9 25 16 -0.0162449601242362
+
+
+# iteration 4
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+4 0 0 0 0 9 0 16 -0.337796446653127
+4 0 0 0 0 9 1 16 -0.17133496444037
+4 0 0 0 0 9 2 16 0.00900705762306821
+4 0 0 0 0 9 3 16 0.188619381444931
+4 0 0 0 0 9 4 16 0.352950884744777
+4 0 0 0 0 9 5 16 0.488688406442338
+4 0 0 0 0 9 6 16 0.584835299791801
+4 0 0 0 0 9 7 16 0.633602315301583
+4 0 0 0 0 9 8 16 0.631038639403692
+4 0 0 0 0 9 9 16 0.577351965872606
+4 0 0 0 0 9 10 16 0.476891669710873
+4 0 0 0 0 9 11 16 0.337796446653131
+4 0 0 0 0 9 12 16 0.171334964440373
+4 0 0 0 0 9 13 16 -0.00900705762307509
+4 0 0 0 0 9 14 16 -0.188619381444936
+4 0 0 0 0 9 15 16 -0.352950884744783
+4 0 0 0 0 9 16 16 -0.488688406442342
+4 0 0 0 0 9 17 16 -0.584835299791803
+4 0 0 0 0 9 18 16 -0.633602315301584
+4 0 0 0 0 9 19 16 -0.631038639403691
+4 0 0 0 0 9 20 16 -0.577351965872604
+4 0 0 0 0 9 21 16 -0.476891669710869
+4 0 0 0 0 9 22 16 -0.337796446653127
+4 0 0 0 0 9 23 16 -0.17133496444037
+4 0 0 0 0 9 24 16 0.00900705762306821
+4 0 0 0 0 9 25 16 0.188619381444931
+
+
+# iteration 5
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+5 0 0 0 0 9 0 16 -0.146732746204847
+5 0 0 0 0 9 1 16 0.0344575613432452
+5 0 0 0 0 9 2 16 0.212856322198309
+5 0 0 0 0 9 3 16 0.374010729734168
+5 0 0 0 0 9 4 16 0.504865012274416
+5 0 0 0 0 9 5 16 0.594818134068033
+5 0 0 0 0 9 6 16 0.63658262815911
+5 0 0 0 0 9 7 16 0.6267749836194
+5 0 0 0 0 9 8 16 0.566189757481202
+5 0 0 0 0 9 9 16 0.459735204452018
+5 0 0 0 0 9 10 16 0.31603563930867
+5 0 0 0 0 9 11 16 0.146732746204851
+5 0 0 0 0 9 12 16 -0.0344575613432429
+5 0 0 0 0 9 13 16 -0.212856322198315
+5 0 0 0 0 9 14 16 -0.374010729734171
+5 0 0 0 0 9 15 16 -0.50486501227442
+5 0 0 0 0 9 16 16 -0.594818134068035
+5 0 0 0 0 9 17 16 -0.63658262815911
+5 0 0 0 0 9 18 16 -0.626774983619399
+5 0 0 0 0 9 19 16 -0.566189757481199
+5 0 0 0 0 9 20 16 -0.459735204452014
+5 0 0 0 0 9 21 16 -0.316035639308665
+5 0 0 0 0 9 22 16 -0.146732746204847
+5 0 0 0 0 9 23 16 0.0344575613432452
+5 0 0 0 0 9 24 16 0.212856322198309
+5 0 0 0 0 9 25 16 0.374010729734168
+
+
+# iteration 6
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+6 0 0 0 0 9 0 16 0.0600734663797312
+6 0 0 0 0 9 1 16 0.236963639789833
+6 0 0 0 0 9 2 16 0.394656428381187
+6 0 0 0 0 9 3 16 0.520376500257261
+6 0 0 0 0 9 4 16 0.603938762880696
+6 0 0 0 0 9 5 16 0.638573498697662
+6 0 0 0 0 9 6 16 0.621474807392969
+6 0 0 0 0 9 7 16 0.554027923246292
+6 0 0 0 0 9 8 16 0.441696991689129
+6 0 0 0 0 9 9 16 0.293582396738469
+6 0 0 0 0 9 10 16 0.121683502005799
+6 0 0 0 0 9 11 16 -0.0600734663797285
+6 0 0 0 0 9 12 16 -0.236963639789832
+6 0 0 0 0 9 13 16 -0.394656428381192
+6 0 0 0 0 9 14 16 -0.520376500257262
+6 0 0 0 0 9 15 16 -0.603938762880698
+6 0 0 0 0 9 16 16 -0.638573498697663
+6 0 0 0 0 9 17 16 -0.621474807392968
+6 0 0 0 0 9 18 16 -0.554027923246289
+6 0 0 0 0 9 19 16 -0.441696991689125
+6 0 0 0 0 9 20 16 -0.293582396738464
+6 0 0 0 0 9 21 16 -0.121683502005794
+6 0 0 0 0 9 22 16 0.0600734663797312
+6 0 0 0 0 9 23 16 0.236963639789833
+6 0 0 0 0 9 24 16 0.394656428381187
+6 0 0 0 0 9 25 16 0.520376500257261
+
+
diff --git a/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/vx.zl b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/vx.zl
new file mode 100644
index 000000000..7f168ca87
--- /dev/null
+++ b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/vx.zl
@@ -0,0 +1,275 @@
+# HYDROTOY::vx z (vx)
+#
+# iteration 0
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+0 0 0 0 0 9 12 0 0.581878916566596
+0 0 0 0 0 9 12 1 0.636945771771587
+0 0 0 0 0 9 12 2 0.581878916566593
+0 0 0 0 0 9 12 3 0.42619991048323
+0 0 0 0 0 9 12 4 0.196827067972683
+0 0 0 0 0 9 12 5 -0.0665789627081168
+0 0 0 0 0 9 12 6 -0.318472885885796
+0 0 0 0 0 9 12 7 -0.515299953858482
+0 0 0 0 0 9 12 8 -0.62302697845592
+0 0 0 0 0 9 12 9 -0.62302697845592
+0 0 0 0 0 9 12 10 -0.515299953858479
+0 0 0 0 0 9 12 11 -0.318472885885792
+0 0 0 0 0 9 12 12 -0.0665789627081123
+0 0 0 0 0 9 12 13 0.196827067972688
+0 0 0 0 0 9 12 14 0.426199910483233
+0 0 0 0 0 9 12 15 0.581878916566594
+0 0 0 0 0 9 12 16 0.636945771771587
+0 0 0 0 0 9 12 17 0.581878916566594
+0 0 0 0 0 9 12 18 0.426199910483233
+0 0 0 0 0 9 12 19 0.196827067972688
+0 0 0 0 0 9 12 20 -0.0665789627081124
+0 0 0 0 0 9 12 21 -0.318472885885792
+0 0 0 0 0 9 12 22 -0.515299953858479
+0 0 0 0 0 9 12 23 -0.62302697845592
+0 0 0 0 0 9 12 24 -0.62302697845592
+0 0 0 0 0 9 12 25 -0.515299953858482
+0 0 0 0 0 9 12 26 -0.318472885885796
+0 0 0 0 0 9 12 27 -0.0665789627081168
+0 0 0 0 0 9 12 28 0.196827067972684
+0 0 0 0 0 9 12 29 0.42619991048323
+0 0 0 0 0 9 12 30 0.581878916566593
+0 0 0 0 0 9 12 31 0.636945771771587
+0 0 0 0 0 9 12 32 0.581878916566596
+0 0 0 0 0 9 12 33 0.426199910483237
+
+
+# iteration 1
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+1 0 0 0 0 9 12 0 0.634847735200847
+1 0 0 0 0 9 12 1 0.604381951846527
+1 0 0 0 0 9 12 2 0.469413038380274
+1 0 0 0 0 9 12 3 0.253278346094499
+1 0 0 0 0 9 12 4 -0.00665047319255442
+1 0 0 0 0 9 12 5 -0.265429365246962
+1 0 0 0 0 9 12 6 -0.478313108700088
+1 0 0 0 0 9 12 7 -0.608492170320792
+1 0 0 0 0 9 12 8 -0.633457407715207
+1 0 0 0 0 9 12 9 -0.548892104535778
+1 0 0 0 0 9 12 10 -0.369418369953887
+1 0 0 0 0 9 12 11 -0.126068843146438
+1 0 0 0 0 9 12 12 0.139079131940516
+1 0 0 0 0 9 12 13 0.380179061620706
+1 0 0 0 0 9 12 14 0.555542577728329
+1 0 0 0 0 9 12 15 0.634847735200848
+1 0 0 0 0 9 12 16 0.604381951846525
+1 0 0 0 0 9 12 17 0.469413038380277
+1 0 0 0 0 9 12 18 0.253278346094503
+1 0 0 0 0 9 12 19 -0.00665047319254941
+1 0 0 0 0 9 12 20 -0.265429365246958
+1 0 0 0 0 9 12 21 -0.478313108700085
+1 0 0 0 0 9 12 22 -0.608492170320791
+1 0 0 0 0 9 12 23 -0.633457407715208
+1 0 0 0 0 9 12 24 -0.54889210453578
+1 0 0 0 0 9 12 25 -0.369418369953891
+1 0 0 0 0 9 12 26 -0.126068843146442
+1 0 0 0 0 9 12 27 0.139079131940511
+1 0 0 0 0 9 12 28 0.380179061620702
+1 0 0 0 0 9 12 29 0.555542577728327
+1 0 0 0 0 9 12 30 0.634847735200847
+1 0 0 0 0 9 12 31 0.604381951846527
+1 0 0 0 0 9 12 32 0.469413038380274
+1 0 0 0 0 9 12 33 0.253278346094499
+
+
+# iteration 2
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+2 0 0 0 0 9 12 0 0.621361463077224
+2 0 0 0 0 9 12 1 0.508360375451162
+2 0 0 0 0 9 12 2 0.307459160600561
+2 0 0 0 0 9 12 3 0.0533954637033426
+2 0 0 0 0 9 12 4 -0.209900793950744
+2 0 0 0 0 9 12 5 -0.436903297441897
+2 0 0 0 0 9 12 6 -0.588361251663495
+2 0 0 0 0 9 12 7 -0.638086200378305
+2 0 0 0 0 9 12 8 -0.577480248216559
+2 0 0 0 0 9 12 9 -0.417022714894814
+2 0 0 0 0 9 12 10 -0.184458165635327
+2 0 0 0 0 9 12 11 0.0800008762123356
+2 0 0 0 0 9 12 12 0.330627039777741
+2 0 0 0 0 9 12 13 0.524084784513215
+2 0 0 0 0 9 12 14 0.626923508845556
+2 0 0 0 0 9 12 15 0.621361463077223
+2 0 0 0 0 9 12 16 0.508360375451159
+2 0 0 0 0 9 12 17 0.307459160600565
+2 0 0 0 0 9 12 18 0.0533954637033469
+2 0 0 0 0 9 12 19 -0.209900793950739
+2 0 0 0 0 9 12 20 -0.436903297441893
+2 0 0 0 0 9 12 21 -0.588361251663493
+2 0 0 0 0 9 12 22 -0.638086200378305
+2 0 0 0 0 9 12 23 -0.577480248216561
+2 0 0 0 0 9 12 24 -0.417022714894818
+2 0 0 0 0 9 12 25 -0.184458165635331
+2 0 0 0 0 9 12 26 0.080000876212331
+2 0 0 0 0 9 12 27 0.330627039777737
+2 0 0 0 0 9 12 28 0.524084784513212
+2 0 0 0 0 9 12 29 0.626923508845555
+2 0 0 0 0 9 12 30 0.621361463077224
+2 0 0 0 0 9 12 31 0.508360375451162
+2 0 0 0 0 9 12 32 0.307459160600561
+2 0 0 0 0 9 12 33 0.0533954637033426
+
+
+# iteration 3
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+3 0 0 0 0 9 12 0 0.542663970499057
+3 0 0 0 0 9 12 1 0.358814710696298
+3 0 0 0 0 9 12 2 0.112923127684829
+3 0 0 0 0 9 12 3 -0.152493889977748
+3 0 0 0 0 9 12 4 -0.391543328699675
+3 0 0 0 0 9 12 5 -0.562891368829955
+3 0 0 0 0 9 12 6 -0.636910377581988
+3 0 0 0 0 9 12 7 -0.600801795900964
+3 0 0 0 0 9 12 8 -0.460809125595696
+3 0 0 0 0 9 12 9 -0.241138371155451
+3 0 0 0 0 9 12 10 0.0202273983309004
+3 0 0 0 0 9 12 11 0.278095666885694
+3 0 0 0 0 9 12 12 0.487878668216131
+3 0 0 0 0 9 12 13 0.613303015573443
+3 0 0 0 0 9 12 14 0.632681699855125
+3 0 0 0 0 9 12 15 0.542663970499055
+3 0 0 0 0 9 12 16 0.358814710696295
+3 0 0 0 0 9 12 17 0.112923127684834
+3 0 0 0 0 9 12 18 -0.152493889977744
+3 0 0 0 0 9 12 19 -0.391543328699671
+3 0 0 0 0 9 12 20 -0.562891368829953
+3 0 0 0 0 9 12 21 -0.636910377581988
+3 0 0 0 0 9 12 22 -0.600801795900965
+3 0 0 0 0 9 12 23 -0.460809125595699
+3 0 0 0 0 9 12 24 -0.241138371155455
+3 0 0 0 0 9 12 25 0.0202273983308956
+3 0 0 0 0 9 12 26 0.27809566688569
+3 0 0 0 0 9 12 27 0.487878668216128
+3 0 0 0 0 9 12 28 0.613303015573441
+3 0 0 0 0 9 12 29 0.632681699855126
+3 0 0 0 0 9 12 30 0.542663970499057
+3 0 0 0 0 9 12 31 0.358814710696298
+3 0 0 0 0 9 12 32 0.112923127684829
+3 0 0 0 0 9 12 33 -0.152493889977748
+
+
+# iteration 4
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+4 0 0 0 0 9 12 0 0.406861988467461
+4 0 0 0 0 9 12 1 0.171334964440375
+4 0 0 0 0 9 12 2 -0.0938174314677452
+4 0 0 0 0 9 12 3 -0.342747941170475
+4 0 0 0 0 9 12 4 -0.53241421807754
+4 0 0 0 0 9 12 5 -0.630021239847671
+4 0 0 0 0 9 12 6 -0.61869186568486
+4 0 0 0 0 9 12 7 -0.500385047305989
+4 0 0 0 0 9 12 8 -0.295557108392468
+4 0 0 0 0 9 12 9 -0.0396246603858536
+4 0 0 0 0 9 12 10 0.223159251380214
+4 0 0 0 0 9 12 11 0.447356901244488
+4 0 0 0 0 9 12 12 0.594202478773731
+4 0 0 0 0 9 12 13 0.638305049562943
+4 0 0 0 0 9 12 14 0.572038878463393
+4 0 0 0 0 9 12 15 0.406861988467459
+4 0 0 0 0 9 12 16 0.171334964440373
+4 0 0 0 0 9 12 17 -0.0938174314677396
+4 0 0 0 0 9 12 18 -0.342747941170472
+4 0 0 0 0 9 12 19 -0.532414218077537
+4 0 0 0 0 9 12 20 -0.630021239847671
+4 0 0 0 0 9 12 21 -0.618691865684861
+4 0 0 0 0 9 12 22 -0.500385047305992
+4 0 0 0 0 9 12 23 -0.295557108392472
+4 0 0 0 0 9 12 24 -0.0396246603858582
+4 0 0 0 0 9 12 25 0.223159251380209
+4 0 0 0 0 9 12 26 0.447356901244485
+4 0 0 0 0 9 12 27 0.594202478773729
+4 0 0 0 0 9 12 28 0.638305049562943
+4 0 0 0 0 9 12 29 0.572038878463395
+4 0 0 0 0 9 12 30 0.406861988467461
+4 0 0 0 0 9 12 31 0.171334964440375
+4 0 0 0 0 9 12 32 -0.0938174314677452
+4 0 0 0 0 9 12 33 -0.342747941170475
+
+
+# iteration 5
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+5 0 0 0 0 9 12 0 0.228090406054295
+5 0 0 0 0 9 12 1 -0.0344575613432415
+5 0 0 0 0 9 12 2 -0.29104750334742
+5 0 0 0 0 9 12 3 -0.497312687939259
+5 0 0 0 0 9 12 4 -0.617587990842469
+5 0 0 0 0 9 12 5 -0.631076719518255
+5 0 0 0 0 9 12 6 -0.535446550237322
+5 0 0 0 0 9 12 7 -0.347232808041159
+5 0 0 0 0 9 12 8 -0.0989793588236489
+5 0 0 0 0 9 12 9 0.166388520733715
+5 0 0 0 0 9 12 10 0.402986313463964
+5 0 0 0 0 9 12 11 0.569904111580567
+5 0 0 0 0 9 12 12 0.638280311388576
+5 0 0 0 0 9 12 13 0.596292046762908
+5 0 0 0 0 9 12 14 0.451199470108754
+5 0 0 0 0 9 12 15 0.228090406054293
+5 0 0 0 0 9 12 16 -0.0344575613432429
+5 0 0 0 0 9 12 17 -0.291047503347414
+5 0 0 0 0 9 12 18 -0.497312687939257
+5 0 0 0 0 9 12 19 -0.617587990842467
+5 0 0 0 0 9 12 20 -0.631076719518255
+5 0 0 0 0 9 12 21 -0.535446550237325
+5 0 0 0 0 9 12 22 -0.347232808041163
+5 0 0 0 0 9 12 23 -0.0989793588236532
+5 0 0 0 0 9 12 24 0.166388520733711
+5 0 0 0 0 9 12 25 0.40298631346396
+5 0 0 0 0 9 12 26 0.569904111580566
+5 0 0 0 0 9 12 27 0.638280311388575
+5 0 0 0 0 9 12 28 0.59629204676291
+5 0 0 0 0 9 12 29 0.451199470108757
+5 0 0 0 0 9 12 30 0.228090406054295
+5 0 0 0 0 9 12 31 -0.0344575613432415
+5 0 0 0 0 9 12 32 -0.29104750334742
+5 0 0 0 0 9 12 33 -0.497312687939259
+
+
+# iteration 6
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+6 0 0 0 0 9 12 0 0.025041268850882
+6 0 0 0 0 9 12 1 -0.236963639789831
+6 0 0 0 0 9 12 2 -0.457995382363801
+6 0 0 0 0 9 12 3 -0.599835562569633
+6 0 0 0 0 9 12 4 -0.63795872467217
+6 0 0 0 0 9 12 5 -0.565773027605818
+6 0 0 0 0 9 12 6 -0.395760034179826
+6 0 0 0 0 9 12 7 -0.157316535477102
+6 0 0 0 0 9 12 8 0.10832842138547
+6 0 0 0 0 9 12 9 0.355242410057682
+6 0 0 0 0 9 12 10 0.540731758754941
+6 0 0 0 0 9 12 11 0.63272367396966
+6 0 0 0 0 9 12 12 0.615311917840902
+6 0 0 0 0 9 12 13 0.491507141184166
+6 0 0 0 0 9 12 14 0.282716314614489
+6 0 0 0 0 9 12 15 0.02504126885088
+6 0 0 0 0 9 12 16 -0.236963639789832
+6 0 0 0 0 9 12 17 -0.457995382363797
+6 0 0 0 0 9 12 18 -0.599835562569634
+6 0 0 0 0 9 12 19 -0.637958724672169
+6 0 0 0 0 9 12 20 -0.565773027605821
+6 0 0 0 0 9 12 21 -0.395760034179829
+6 0 0 0 0 9 12 22 -0.157316535477107
+6 0 0 0 0 9 12 23 0.108328421385466
+6 0 0 0 0 9 12 24 0.355242410057678
+6 0 0 0 0 9 12 25 0.540731758754938
+6 0 0 0 0 9 12 26 0.63272367396966
+6 0 0 0 0 9 12 27 0.615311917840903
+6 0 0 0 0 9 12 28 0.491507141184169
+6 0 0 0 0 9 12 29 0.282716314614493
+6 0 0 0 0 9 12 30 0.025041268850882
+6 0 0 0 0 9 12 31 -0.236963639789831
+6 0 0 0 0 9 12 32 -0.457995382363801
+6 0 0 0 0 9 12 33 -0.599835562569633
+
+
diff --git a/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/vy.xl b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/vy.xl
new file mode 100644
index 000000000..b803ef4f4
--- /dev/null
+++ b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/vy.xl
@@ -0,0 +1,170 @@
+# HYDROTOY::vy x (vy)
+#
+# iteration 0
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+0 0 0 0 0 0 12 16 -0.351340877630785
+0 0 0 0 0 1 12 16 -0.424791121674493
+0 0 0 0 0 2 12 16 -0.424791121674492
+0 0 0 0 0 3 12 16 -0.351340877630783
+0 0 0 0 0 4 12 16 -0.217140604013041
+0 0 0 0 0 5 12 16 -0.045394747300986
+0 0 0 0 0 6 12 16 0.134200273617742
+0 0 0 0 0 7 12 16 0.290590848056751
+0 0 0 0 0 8 12 16 0.39673562493177
+0 0 0 0 0 9 12 16 0.434281208026084
+0 0 0 0 0 10 12 16 0.39673562493177
+0 0 0 0 0 11 12 16 0.290590848056751
+0 0 0 0 0 12 12 16 0.134200273617742
+0 0 0 0 0 13 12 16 -0.045394747300986
+0 0 0 0 0 14 12 16 -0.217140604013041
+0 0 0 0 0 15 12 16 -0.351340877630783
+0 0 0 0 0 16 12 16 -0.424791121674492
+0 0 0 0 0 17 12 16 -0.424791121674493
+0 0 0 0 0 18 12 16 -0.351340877630785
+
+
+# iteration 1
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+1 0 0 0 0 0 12 16 -0.415891937557671
+1 0 0 0 0 1 12 16 -0.432015923162627
+1 0 0 0 0 2 12 16 -0.373440430911314
+1 0 0 0 0 3 12 16 -0.250293695555626
+1 0 0 0 0 4 12 16 -0.0838689063915308
+1 0 0 0 0 5 12 16 0.0970575786127553
+1 0 0 0 0 6 12 16 0.261201926534475
+1 0 0 0 0 7 12 16 0.380182088413377
+1 0 0 0 0 8 12 16 0.433425313359762
+1 0 0 0 0 9 12 16 0.411725364080886
+1 0 0 0 0 10 12 16 0.318834358944916
+1 0 0 0 0 11 12 16 0.170813996628152
+1 0 0 0 0 12 12 16 -0.00674165750206195
+1 0 0 0 0 13 12 16 -0.183131617804134
+1 0 0 0 0 14 12 16 -0.327856457689353
+1 0 0 0 0 15 12 16 -0.415891937557671
+1 0 0 0 0 16 12 16 -0.432015923162627
+1 0 0 0 0 17 12 16 -0.373440430911314
+1 0 0 0 0 18 12 16 -0.250293695555626
+
+
+# iteration 2
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+2 0 0 0 0 0 12 16 -0.436390709668035
+2 0 0 0 0 1 12 16 -0.393242459943245
+2 0 0 0 0 2 12 16 -0.282099016398671
+2 0 0 0 0 3 12 16 -0.122178090129659
+2 0 0 0 0 4 12 16 0.0588685378758739
+2 0 0 0 0 5 12 16 0.229736260878792
+2 0 0 0 0 6 12 16 0.360880497287357
+2 0 0 0 0 7 12 16 0.429625217218545
+2 0 0 0 0 8 12 16 0.424083834070078
+2 0 0 0 0 9 12 16 0.345214503330211
+2 0 0 0 0 10 12 16 0.206654448789244
+2 0 0 0 0 11 12 16 0.0323619626558881
+2 0 0 0 0 12 12 16 -0.147526200819872
+2 0 0 0 0 13 12 16 -0.301905743940417
+2 0 0 0 0 14 12 16 -0.404083041206084
+2 0 0 0 0 15 12 16 -0.436390709668035
+2 0 0 0 0 16 12 16 -0.393242459943245
+2 0 0 0 0 17 12 16 -0.282099016398671
+2 0 0 0 0 18 12 16 -0.122178090129659
+
+
+# iteration 3
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+3 0 0 0 0 0 12 16 -0.410565078310416
+3 0 0 0 0 1 12 16 -0.31242836501202
+3 0 0 0 0 2 12 16 -0.160269949080453
+3 0 0 0 0 3 12 16 0.019600597053901
+3 0 0 0 0 4 12 16 0.196082021891802
+3 0 0 0 0 5 12 16 0.338659083795364
+3 0 0 0 0 6 12 16 0.422678913489517
+3 0 0 0 0 7 12 16 0.433613719123954
+3 0 0 0 0 8 12 16 0.369572773464887
+3 0 0 0 0 9 12 16 0.241629337810498
+3 0 0 0 0 10 12 16 0.0719059945150529
+3 0 0 0 0 11 12 16 -0.110250548477497
+3 0 0 0 0 12 12 16 -0.273343770043499
+3 0 0 0 0 13 12 16 -0.389173370518787
+3 0 0 0 0 14 12 16 -0.437711359702299
+3 0 0 0 0 15 12 16 -0.410565078310416
+3 0 0 0 0 16 12 16 -0.31242836501202
+3 0 0 0 0 17 12 16 -0.160269949080453
+3 0 0 0 0 18 12 16 0.019600597053901
+
+
+# iteration 4
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+4 0 0 0 0 0 12 16 -0.341009832150574
+4 0 0 0 0 1 12 16 -0.197963946518029
+4 0 0 0 0 2 12 16 -0.02068829608652
+4 0 0 0 0 3 12 16 0.160164548685615
+4 0 0 0 0 4 12 16 0.313323487940762
+4 0 0 0 0 5 12 16 0.412305949676424
+4 0 0 0 0 6 12 16 0.43999696703107
+4 0 0 0 0 7 12 16 0.391608511539087
+4 0 0 0 0 8 12 16 0.275507386750355
+4 0 0 0 0 9 12 16 0.111768531886454
+4 0 0 0 0 10 12 16 -0.0712961175258505
+4 0 0 0 0 11 12 16 -0.242033020513042
+4 0 0 0 0 12 12 16 -0.370920215452565
+4 0 0 0 0 13 12 16 -0.43567193543597
+4 0 0 0 0 14 12 16 -0.425092019827216
+4 0 0 0 0 15 12 16 -0.341009832150574
+4 0 0 0 0 16 12 16 -0.197963946518029
+4 0 0 0 0 17 12 16 -0.02068829608652
+4 0 0 0 0 18 12 16 0.160164548685615
+
+
+# iteration 5
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+5 0 0 0 0 0 12 16 -0.234926515860751
+5 0 0 0 0 1 12 16 -0.0618012649721795
+5 0 0 0 0 2 12 16 0.12200998607695
+5 0 0 0 0 3 12 16 0.284724602107445
+5 0 0 0 0 4 12 16 0.398207747791759
+5 0 0 0 0 5 12 16 0.442837156279058
+5 0 0 0 0 6 12 16 0.410895997396441
+5 0 0 0 0 7 12 16 0.307907187691032
+5 0 0 0 0 8 12 16 0.151678427984859
+5 0 0 0 0 9 12 16 -0.0307769098751558
+5 0 0 0 0 10 12 16 -0.207910640418307
+5 0 0 0 0 11 12 16 -0.349094732424262
+5 0 0 0 0 12 12 16 -0.42991717376798
+5 0 0 0 0 13 12 16 -0.436403030092304
+5 0 0 0 0 14 12 16 -0.367430837916603
+5 0 0 0 0 15 12 16 -0.234926515860751
+5 0 0 0 0 16 12 16 -0.0618012649721795
+5 0 0 0 0 17 12 16 0.12200998607695
+5 0 0 0 0 18 12 16 0.284724602107445
+
+
+# iteration 6
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+6 0 0 0 0 0 12 16 -0.103378011524754
+6 0 0 0 0 1 12 16 0.0817937416880688
+6 0 0 0 0 2 12 16 0.25282261389021
+6 0 0 0 0 3 12 16 0.38013615932939
+6 0 0 0 0 4 12 16 0.441720709391928
+6 0 0 0 0 5 12 16 0.426927735893935
+6 0 0 0 0 6 12 16 0.338315078343162
+6 0 0 0 0 7 12 16 0.191204670250857
+6 0 0 0 0 8 12 16 0.011033237632282
+6 0 0 0 0 9 12 16 -0.171045942006732
+6 0 0 0 0 10 12 16 -0.323549724369182
+6 0 0 0 0 11 12 16 -0.420108820031231
+6 0 0 0 0 12 12 16 -0.444027284141066
+6 0 0 0 0 13 12 16 -0.391169396961672
+6 0 0 0 0 14 12 16 -0.270674767385196
+6 0 0 0 0 15 12 16 -0.103378011524754
+6 0 0 0 0 16 12 16 0.0817937416880688
+6 0 0 0 0 17 12 16 0.25282261389021
+6 0 0 0 0 18 12 16 0.38013615932939
+
+
diff --git a/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/vy.yl b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/vy.yl
new file mode 100644
index 000000000..f963029e8
--- /dev/null
+++ b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/vy.yl
@@ -0,0 +1,219 @@
+# HYDROTOY::vy y (vy)
+#
+# iteration 0
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+0 0 0 0 0 9 0 16 -0.416689767673842
+0 0 0 0 0 9 1 16 -0.434281208026084
+0 0 0 0 0 9 2 16 -0.416689767673844
+0 0 0 0 0 9 3 16 -0.365340600494138
+0 0 0 0 0 9 4 16 -0.284393710626609
+0 0 0 0 0 9 5 16 -0.180406933678633
+0 0 0 0 0 9 6 16 -0.0618046598853613
+0 0 0 0 0 9 7 16 0.0618046598853572
+0 0 0 0 0 9 8 16 0.180406933678629
+0 0 0 0 0 9 9 16 0.284393710626606
+0 0 0 0 0 9 10 16 0.365340600494136
+0 0 0 0 0 9 11 16 0.416689767673843
+0 0 0 0 0 9 12 16 0.434281208026084
+0 0 0 0 0 9 13 16 0.416689767673843
+0 0 0 0 0 9 14 16 0.365340600494136
+0 0 0 0 0 9 15 16 0.284393710626605
+0 0 0 0 0 9 16 16 0.180406933678629
+0 0 0 0 0 9 17 16 0.0618046598853571
+0 0 0 0 0 9 18 16 -0.0618046598853614
+0 0 0 0 0 9 19 16 -0.180406933678633
+0 0 0 0 0 9 20 16 -0.284393710626609
+0 0 0 0 0 9 21 16 -0.365340600494138
+0 0 0 0 0 9 22 16 -0.416689767673844
+0 0 0 0 0 9 23 16 -0.434281208026084
+0 0 0 0 0 9 24 16 -0.416689767673842
+0 0 0 0 0 9 25 16 -0.365340600494133
+
+
+# iteration 1
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+1 0 0 0 0 9 0 16 -0.434734210686685
+1 0 0 0 0 9 1 16 -0.411725364080886
+1 0 0 0 0 9 2 16 -0.355360977102279
+1 0 0 0 0 9 3 16 -0.270207357171949
+1 0 0 0 0 9 4 16 -0.163163144148577
+1 0 0 0 0 9 5 16 -0.0429004235548697
+1 0 0 0 0 9 6 16 0.0808378342166104
+1 0 0 0 0 9 7 16 0.198027091420972
+1 0 0 0 0 9 8 16 0.299173371390867
+1 0 0 0 0 9 9 16 0.376082404063222
+1 0 0 0 0 9 10 16 0.422523477006552
+1 0 0 0 0 9 11 16 0.434734210686685
+1 0 0 0 0 9 12 16 0.411725364080886
+1 0 0 0 0 9 13 16 0.355360977102275
+1 0 0 0 0 9 14 16 0.270207357171945
+1 0 0 0 0 9 15 16 0.163163144148573
+1 0 0 0 0 9 16 16 0.0429004235548656
+1 0 0 0 0 9 17 16 -0.0808378342166146
+1 0 0 0 0 9 18 16 -0.198027091420976
+1 0 0 0 0 9 19 16 -0.29917337139087
+1 0 0 0 0 9 20 16 -0.376082404063224
+1 0 0 0 0 9 21 16 -0.422523477006553
+1 0 0 0 0 9 22 16 -0.434734210686685
+1 0 0 0 0 9 23 16 -0.411725364080886
+1 0 0 0 0 9 24 16 -0.355360977102279
+1 0 0 0 0 9 25 16 -0.270207357171949
+
+
+# iteration 2
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+2 0 0 0 0 9 0 16 -0.406533838434933
+2 0 0 0 0 9 1 16 -0.345214503330214
+2 0 0 0 0 9 2 16 -0.255927942235384
+2 0 0 0 0 9 3 16 -0.145907621322717
+2 0 0 0 0 9 4 16 -0.0240667326765224
+2 0 0 0 0 9 5 16 0.0997238995207541
+2 0 0 0 0 9 6 16 0.215435494459725
+2 0 0 0 0 9 7 16 0.313693786881789
+2 0 0 0 0 9 8 16 0.386538474299475
+2 0 0 0 0 9 9 16 0.428068113362239
+2 0 0 0 0 9 10 16 0.43491821969949
+2 0 0 0 0 9 11 16 0.406533838434934
+2 0 0 0 0 9 12 16 0.345214503330211
+2 0 0 0 0 9 13 16 0.255927942235378
+2 0 0 0 0 9 14 16 0.145907621322713
+2 0 0 0 0 9 15 16 0.0240667326765182
+2 0 0 0 0 9 16 16 -0.099723899520758
+2 0 0 0 0 9 17 16 -0.215435494459729
+2 0 0 0 0 9 18 16 -0.313693786881792
+2 0 0 0 0 9 19 16 -0.386538474299477
+2 0 0 0 0 9 20 16 -0.42806811336224
+2 0 0 0 0 9 21 16 -0.434918219699489
+2 0 0 0 0 9 22 16 -0.406533838434933
+2 0 0 0 0 9 23 16 -0.345214503330214
+2 0 0 0 0 9 24 16 -0.255927942235384
+2 0 0 0 0 9 25 16 -0.145907621322717
+
+
+# iteration 3
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+3 0 0 0 0 9 0 16 -0.334933448650902
+3 0 0 0 0 9 1 16 -0.241629337810503
+3 0 0 0 0 9 2 16 -0.128749855045699
+3 0 0 0 0 9 3 16 -0.00543982472995432
+3 0 0 0 0 9 4 16 0.118310907833522
+3 0 0 0 0 9 5 16 0.232476794266388
+3 0 0 0 0 9 6 16 0.327808793420523
+3 0 0 0 0 9 7 16 0.396583673685688
+3 0 0 0 0 9 8 16 0.433229703282761
+3 0 0 0 0 9 9 16 0.434778038836117
+3 0 0 0 0 9 10 16 0.40110324340753
+3 0 0 0 0 9 11 16 0.334933448650904
+3 0 0 0 0 9 12 16 0.241629337810498
+3 0 0 0 0 9 13 16 0.12874985504569
+3 0 0 0 0 9 14 16 0.00543982472995024
+3 0 0 0 0 9 15 16 -0.118310907833526
+3 0 0 0 0 9 16 16 -0.232476794266392
+3 0 0 0 0 9 17 16 -0.327808793420526
+3 0 0 0 0 9 18 16 -0.396583673685689
+3 0 0 0 0 9 19 16 -0.433229703282761
+3 0 0 0 0 9 20 16 -0.434778038836117
+3 0 0 0 0 9 21 16 -0.401103243407529
+3 0 0 0 0 9 22 16 -0.334933448650902
+3 0 0 0 0 9 23 16 -0.241629337810503
+3 0 0 0 0 9 24 16 -0.128749855045699
+3 0 0 0 0 9 25 16 -0.00543982472995432
+
+
+# iteration 4
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+4 0 0 0 0 9 0 16 -0.227350582070024
+4 0 0 0 0 9 1 16 -0.111768531886463
+4 0 0 0 0 9 2 16 0.012868340037492
+4 0 0 0 0 9 3 16 0.136462695582585
+4 0 0 0 0 9 4 16 0.249001655106467
+4 0 0 0 0 9 5 16 0.341367981403489
+4 0 0 0 0 9 6 16 0.406078704040755
+4 0 0 0 0 9 7 16 0.437891345119682
+4 0 0 0 0 9 8 16 0.434228633657117
+4 0 0 0 0 9 9 16 0.395387300752772
+4 0 0 0 0 9 10 16 0.324514040200256
+4 0 0 0 0 9 11 16 0.227350582070025
+4 0 0 0 0 9 12 16 0.111768531886454
+4 0 0 0 0 9 13 16 -0.0128683400375039
+4 0 0 0 0 9 14 16 -0.136462695582588
+4 0 0 0 0 9 15 16 -0.249001655106472
+4 0 0 0 0 9 16 16 -0.341367981403491
+4 0 0 0 0 9 17 16 -0.406078704040756
+4 0 0 0 0 9 18 16 -0.437891345119682
+4 0 0 0 0 9 19 16 -0.434228633657116
+4 0 0 0 0 9 20 16 -0.39538730075277
+4 0 0 0 0 9 21 16 -0.324514040200255
+4 0 0 0 0 9 22 16 -0.227350582070024
+4 0 0 0 0 9 23 16 -0.111768531886463
+4 0 0 0 0 9 24 16 0.012868340037492
+4 0 0 0 0 9 25 16 0.136462695582585
+
+
+# iteration 5
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+5 0 0 0 0 9 0 16 -0.0950072936959622
+5 0 0 0 0 9 1 16 0.030776909875144
+5 0 0 0 0 9 2 16 0.154067751245506
+5 0 0 0 0 9 3 16 0.264876939686164
+5 0 0 0 0 9 4 16 0.354227373757255
+5 0 0 0 0 9 5 16 0.414880412677843
+5 0 0 0 0 9 6 16 0.44192230795209
+5 0 0 0 0 9 7 16 0.433162286049222
+5 0 0 0 0 9 8 16 0.389310031845953
+5 0 0 0 0 9 9 16 0.313918194178434
+5 0 0 0 0 9 10 16 0.213094571361964
+5 0 0 0 0 9 11 16 0.0950072936959618
+5 0 0 0 0 9 12 16 -0.0307769098751558
+5 0 0 0 0 9 13 16 -0.154067751245519
+5 0 0 0 0 9 14 16 -0.264876939686168
+5 0 0 0 0 9 15 16 -0.354227373757259
+5 0 0 0 0 9 16 16 -0.414880412677845
+5 0 0 0 0 9 17 16 -0.44192230795209
+5 0 0 0 0 9 18 16 -0.433162286049221
+5 0 0 0 0 9 19 16 -0.389310031845951
+5 0 0 0 0 9 20 16 -0.313918194178431
+5 0 0 0 0 9 21 16 -0.213094571361964
+5 0 0 0 0 9 22 16 -0.0950072936959622
+5 0 0 0 0 9 23 16 0.030776909875144
+5 0 0 0 0 9 24 16 0.154067751245506
+5 0 0 0 0 9 25 16 0.264876939686164
+
+
+# iteration 6
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+6 0 0 0 0 9 0 16 0.0482402942310665
+6 0 0 0 0 9 1 16 0.171045942006719
+6 0 0 0 0 9 2 16 0.279994464810382
+6 0 0 0 0 9 3 16 0.366259501266316
+6 0 0 0 0 9 4 16 0.422852371158769
+6 0 0 0 0 9 5 16 0.445188256739823
+6 0 0 0 0 9 6 16 0.431457637396323
+6 0 0 0 0 9 7 16 0.382772886248344
+6 0 0 0 0 9 8 16 0.303078152294531
+6 0 0 0 0 9 9 16 0.198829828916991
+6 0 0 0 0 9 10 16 0.0784734952871189
+6 0 0 0 0 9 11 16 -0.0482402942310689
+6 0 0 0 0 9 12 16 -0.171045942006732
+6 0 0 0 0 9 13 16 -0.279994464810395
+6 0 0 0 0 9 14 16 -0.36625950126632
+6 0 0 0 0 9 15 16 -0.422852371158772
+6 0 0 0 0 9 16 16 -0.445188256739823
+6 0 0 0 0 9 17 16 -0.431457637396322
+6 0 0 0 0 9 18 16 -0.382772886248342
+6 0 0 0 0 9 19 16 -0.303078152294529
+6 0 0 0 0 9 20 16 -0.198829828916988
+6 0 0 0 0 9 21 16 -0.0784734952871194
+6 0 0 0 0 9 22 16 0.0482402942310665
+6 0 0 0 0 9 23 16 0.171045942006719
+6 0 0 0 0 9 24 16 0.279994464810382
+6 0 0 0 0 9 25 16 0.366259501266316
+
+
diff --git a/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/vy.zl b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/vy.zl
new file mode 100644
index 000000000..b3578a6e9
--- /dev/null
+++ b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/vy.zl
@@ -0,0 +1,275 @@
+# HYDROTOY::vy z (vy)
+#
+# iteration 0
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+0 0 0 0 0 9 12 0 0.396735624931772
+0 0 0 0 0 9 12 1 0.434281208026084
+0 0 0 0 0 9 12 2 0.396735624931769
+0 0 0 0 0 9 12 3 0.290590848056749
+0 0 0 0 0 9 12 4 0.134200273617739
+0 0 0 0 0 9 12 5 -0.0453947473009889
+0 0 0 0 0 9 12 6 -0.217140604013044
+0 0 0 0 0 9 12 7 -0.351340877630785
+0 0 0 0 0 9 12 8 -0.424791121674493
+0 0 0 0 0 9 12 9 -0.424791121674492
+0 0 0 0 0 9 12 10 -0.351340877630783
+0 0 0 0 0 9 12 11 -0.217140604013041
+0 0 0 0 0 9 12 12 -0.0453947473009859
+0 0 0 0 0 9 12 13 0.134200273617742
+0 0 0 0 0 9 12 14 0.290590848056751
+0 0 0 0 0 9 12 15 0.39673562493177
+0 0 0 0 0 9 12 16 0.434281208026084
+0 0 0 0 0 9 12 17 0.39673562493177
+0 0 0 0 0 9 12 18 0.290590848056751
+0 0 0 0 0 9 12 19 0.134200273617742
+0 0 0 0 0 9 12 20 -0.045394747300986
+0 0 0 0 0 9 12 21 -0.217140604013041
+0 0 0 0 0 9 12 22 -0.351340877630783
+0 0 0 0 0 9 12 23 -0.424791121674492
+0 0 0 0 0 9 12 24 -0.424791121674493
+0 0 0 0 0 9 12 25 -0.351340877630785
+0 0 0 0 0 9 12 26 -0.217140604013044
+0 0 0 0 0 9 12 27 -0.0453947473009889
+0 0 0 0 0 9 12 28 0.134200273617739
+0 0 0 0 0 9 12 29 0.290590848056749
+0 0 0 0 0 9 12 30 0.396735624931769
+0 0 0 0 0 9 12 31 0.434281208026084
+0 0 0 0 0 9 12 32 0.396735624931772
+0 0 0 0 0 9 12 33 0.290590848056754
+
+
+# iteration 1
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+1 0 0 0 0 9 12 0 0.433425313359762
+1 0 0 0 0 9 12 1 0.411725364080886
+1 0 0 0 0 9 12 2 0.318834358944915
+1 0 0 0 0 9 12 3 0.17081399662815
+1 0 0 0 0 9 12 4 -0.00674165750206535
+1 0 0 0 0 9 12 5 -0.183131617804137
+1 0 0 0 0 9 12 6 -0.327856457689355
+1 0 0 0 0 9 12 7 -0.415891937557671
+1 0 0 0 0 9 12 8 -0.432015923162627
+1 0 0 0 0 9 12 9 -0.373440430911314
+1 0 0 0 0 9 12 10 -0.250293695555626
+1 0 0 0 0 9 12 11 -0.0838689063915307
+1 0 0 0 0 9 12 12 0.0970575786127554
+1 0 0 0 0 9 12 13 0.261201926534475
+1 0 0 0 0 9 12 14 0.380182088413377
+1 0 0 0 0 9 12 15 0.433425313359762
+1 0 0 0 0 9 12 16 0.411725364080886
+1 0 0 0 0 9 12 17 0.318834358944916
+1 0 0 0 0 9 12 18 0.170813996628152
+1 0 0 0 0 9 12 19 -0.00674165750206186
+1 0 0 0 0 9 12 20 -0.183131617804134
+1 0 0 0 0 9 12 21 -0.327856457689353
+1 0 0 0 0 9 12 22 -0.415891937557671
+1 0 0 0 0 9 12 23 -0.432015923162627
+1 0 0 0 0 9 12 24 -0.373440430911315
+1 0 0 0 0 9 12 25 -0.250293695555629
+1 0 0 0 0 9 12 26 -0.0838689063915337
+1 0 0 0 0 9 12 27 0.0970575786127523
+1 0 0 0 0 9 12 28 0.261201926534473
+1 0 0 0 0 9 12 29 0.380182088413376
+1 0 0 0 0 9 12 30 0.433425313359762
+1 0 0 0 0 9 12 31 0.411725364080886
+1 0 0 0 0 9 12 32 0.318834358944915
+1 0 0 0 0 9 12 33 0.17081399662815
+
+
+# iteration 2
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+2 0 0 0 0 9 12 0 0.424083834070079
+2 0 0 0 0 9 12 1 0.345214503330213
+2 0 0 0 0 9 12 2 0.206654448789242
+2 0 0 0 0 9 12 3 0.0323619626558851
+2 0 0 0 0 9 12 4 -0.147526200819875
+2 0 0 0 0 9 12 5 -0.301905743940419
+2 0 0 0 0 9 12 6 -0.404083041206085
+2 0 0 0 0 9 12 7 -0.436390709668035
+2 0 0 0 0 9 12 8 -0.393242459943244
+2 0 0 0 0 9 12 9 -0.282099016398671
+2 0 0 0 0 9 12 10 -0.122178090129659
+2 0 0 0 0 9 12 11 0.058868537875874
+2 0 0 0 0 9 12 12 0.229736260878792
+2 0 0 0 0 9 12 13 0.360880497287357
+2 0 0 0 0 9 12 14 0.429625217218545
+2 0 0 0 0 9 12 15 0.424083834070078
+2 0 0 0 0 9 12 16 0.345214503330211
+2 0 0 0 0 9 12 17 0.206654448789244
+2 0 0 0 0 9 12 18 0.0323619626558882
+2 0 0 0 0 9 12 19 -0.147526200819872
+2 0 0 0 0 9 12 20 -0.301905743940417
+2 0 0 0 0 9 12 21 -0.404083041206084
+2 0 0 0 0 9 12 22 -0.436390709668035
+2 0 0 0 0 9 12 23 -0.393242459943245
+2 0 0 0 0 9 12 24 -0.282099016398674
+2 0 0 0 0 9 12 25 -0.122178090129662
+2 0 0 0 0 9 12 26 0.0588685378758712
+2 0 0 0 0 9 12 27 0.229736260878789
+2 0 0 0 0 9 12 28 0.360880497287356
+2 0 0 0 0 9 12 29 0.429625217218544
+2 0 0 0 0 9 12 30 0.424083834070079
+2 0 0 0 0 9 12 31 0.345214503330213
+2 0 0 0 0 9 12 32 0.206654448789242
+2 0 0 0 0 9 12 33 0.0323619626558851
+
+
+# iteration 3
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+3 0 0 0 0 9 12 0 0.369572773464889
+3 0 0 0 0 9 12 1 0.2416293378105
+3 0 0 0 0 9 12 2 0.0719059945150494
+3 0 0 0 0 9 12 3 -0.1102505484775
+3 0 0 0 0 9 12 4 -0.273343770043502
+3 0 0 0 0 9 12 5 -0.389173370518788
+3 0 0 0 0 9 12 6 -0.437711359702299
+3 0 0 0 0 9 12 7 -0.410565078310415
+3 0 0 0 0 9 12 8 -0.312428365012018
+3 0 0 0 0 9 12 9 -0.160269949080453
+3 0 0 0 0 9 12 10 0.0196005970539014
+3 0 0 0 0 9 12 11 0.196082021891802
+3 0 0 0 0 9 12 12 0.338659083795364
+3 0 0 0 0 9 12 13 0.422678913489517
+3 0 0 0 0 9 12 14 0.433613719123953
+3 0 0 0 0 9 12 15 0.369572773464887
+3 0 0 0 0 9 12 16 0.241629337810498
+3 0 0 0 0 9 12 17 0.0719059945150529
+3 0 0 0 0 9 12 18 -0.110250548477497
+3 0 0 0 0 9 12 19 -0.273343770043499
+3 0 0 0 0 9 12 20 -0.389173370518787
+3 0 0 0 0 9 12 21 -0.437711359702299
+3 0 0 0 0 9 12 22 -0.410565078310416
+3 0 0 0 0 9 12 23 -0.312428365012021
+3 0 0 0 0 9 12 24 -0.160269949080456
+3 0 0 0 0 9 12 25 0.019600597053898
+3 0 0 0 0 9 12 26 0.196082021891799
+3 0 0 0 0 9 12 27 0.338659083795362
+3 0 0 0 0 9 12 28 0.422678913489517
+3 0 0 0 0 9 12 29 0.433613719123954
+3 0 0 0 0 9 12 30 0.369572773464889
+3 0 0 0 0 9 12 31 0.2416293378105
+3 0 0 0 0 9 12 32 0.0719059945150494
+3 0 0 0 0 9 12 33 -0.1102505484775
+
+
+# iteration 4
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+4 0 0 0 0 9 12 0 0.275507386750357
+4 0 0 0 0 9 12 1 0.111768531886456
+4 0 0 0 0 9 12 2 -0.0712961175258543
+4 0 0 0 0 9 12 3 -0.242033020513044
+4 0 0 0 0 9 12 4 -0.370920215452567
+4 0 0 0 0 9 12 5 -0.43567193543597
+4 0 0 0 0 9 12 6 -0.425092019827216
+4 0 0 0 0 9 12 7 -0.341009832150572
+4 0 0 0 0 9 12 8 -0.197963946518027
+4 0 0 0 0 9 12 9 -0.0206882960865204
+4 0 0 0 0 9 12 10 0.160164548685615
+4 0 0 0 0 9 12 11 0.313323487940762
+4 0 0 0 0 9 12 12 0.412305949676424
+4 0 0 0 0 9 12 13 0.43999696703107
+4 0 0 0 0 9 12 14 0.391608511539087
+4 0 0 0 0 9 12 15 0.275507386750355
+4 0 0 0 0 9 12 16 0.111768531886454
+4 0 0 0 0 9 12 17 -0.0712961175258505
+4 0 0 0 0 9 12 18 -0.242033020513042
+4 0 0 0 0 9 12 19 -0.370920215452565
+4 0 0 0 0 9 12 20 -0.43567193543597
+4 0 0 0 0 9 12 21 -0.425092019827216
+4 0 0 0 0 9 12 22 -0.341009832150574
+4 0 0 0 0 9 12 23 -0.19796394651803
+4 0 0 0 0 9 12 24 -0.0206882960865234
+4 0 0 0 0 9 12 25 0.160164548685612
+4 0 0 0 0 9 12 26 0.31332348794076
+4 0 0 0 0 9 12 27 0.412305949676423
+4 0 0 0 0 9 12 28 0.439996967031071
+4 0 0 0 0 9 12 29 0.391608511539088
+4 0 0 0 0 9 12 30 0.275507386750357
+4 0 0 0 0 9 12 31 0.111768531886456
+4 0 0 0 0 9 12 32 -0.0712961175258543
+4 0 0 0 0 9 12 33 -0.242033020513044
+
+
+# iteration 5
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+5 0 0 0 0 9 12 0 0.15167842798486
+5 0 0 0 0 9 12 1 -0.0307769098751551
+5 0 0 0 0 9 12 2 -0.207910640418311
+5 0 0 0 0 9 12 3 -0.349094732424263
+5 0 0 0 0 9 12 4 -0.429917173767981
+5 0 0 0 0 9 12 5 -0.436403030092303
+5 0 0 0 0 9 12 6 -0.367430837916602
+5 0 0 0 0 9 12 7 -0.234926515860749
+5 0 0 0 0 9 12 8 -0.0618012649721778
+5 0 0 0 0 9 12 9 0.122009986076949
+5 0 0 0 0 9 12 10 0.284724602107446
+5 0 0 0 0 9 12 11 0.398207747791759
+5 0 0 0 0 9 12 12 0.442837156279058
+5 0 0 0 0 9 12 13 0.410895997396441
+5 0 0 0 0 9 12 14 0.307907187691032
+5 0 0 0 0 9 12 15 0.151678427984859
+5 0 0 0 0 9 12 16 -0.0307769098751558
+5 0 0 0 0 9 12 17 -0.207910640418307
+5 0 0 0 0 9 12 18 -0.349094732424262
+5 0 0 0 0 9 12 19 -0.42991717376798
+5 0 0 0 0 9 12 20 -0.436403030092304
+5 0 0 0 0 9 12 21 -0.367430837916603
+5 0 0 0 0 9 12 22 -0.234926515860751
+5 0 0 0 0 9 12 23 -0.061801264972181
+5 0 0 0 0 9 12 24 0.122009986076946
+5 0 0 0 0 9 12 25 0.284724602107443
+5 0 0 0 0 9 12 26 0.398207747791758
+5 0 0 0 0 9 12 27 0.442837156279058
+5 0 0 0 0 9 12 28 0.410895997396442
+5 0 0 0 0 9 12 29 0.307907187691033
+5 0 0 0 0 9 12 30 0.15167842798486
+5 0 0 0 0 9 12 31 -0.0307769098751551
+5 0 0 0 0 9 12 32 -0.207910640418311
+5 0 0 0 0 9 12 33 -0.349094732424263
+
+
+# iteration 6
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+6 0 0 0 0 9 12 0 0.0110332376322835
+6 0 0 0 0 9 12 1 -0.171045942006732
+6 0 0 0 0 9 12 2 -0.323549724369184
+6 0 0 0 0 9 12 3 -0.42010882003123
+6 0 0 0 0 9 12 4 -0.444027284141066
+6 0 0 0 0 9 12 5 -0.391169396961671
+6 0 0 0 0 9 12 6 -0.270674767385194
+6 0 0 0 0 9 12 7 -0.103378011524753
+6 0 0 0 0 9 12 8 0.0817937416880701
+6 0 0 0 0 9 12 9 0.25282261389021
+6 0 0 0 0 9 12 10 0.380136159329391
+6 0 0 0 0 9 12 11 0.441720709391928
+6 0 0 0 0 9 12 12 0.426927735893936
+6 0 0 0 0 9 12 13 0.338315078343162
+6 0 0 0 0 9 12 14 0.191204670250857
+6 0 0 0 0 9 12 15 0.011033237632282
+6 0 0 0 0 9 12 16 -0.171045942006732
+6 0 0 0 0 9 12 17 -0.323549724369182
+6 0 0 0 0 9 12 18 -0.420108820031231
+6 0 0 0 0 9 12 19 -0.444027284141066
+6 0 0 0 0 9 12 20 -0.391169396961673
+6 0 0 0 0 9 12 21 -0.270674767385196
+6 0 0 0 0 9 12 22 -0.103378011524755
+6 0 0 0 0 9 12 23 0.081793741688067
+6 0 0 0 0 9 12 24 0.252822613890207
+6 0 0 0 0 9 12 25 0.380136159329389
+6 0 0 0 0 9 12 26 0.441720709391927
+6 0 0 0 0 9 12 27 0.426927735893936
+6 0 0 0 0 9 12 28 0.338315078343164
+6 0 0 0 0 9 12 29 0.191204670250859
+6 0 0 0 0 9 12 30 0.0110332376322835
+6 0 0 0 0 9 12 31 -0.171045942006732
+6 0 0 0 0 9 12 32 -0.323549724369184
+6 0 0 0 0 9 12 33 -0.42010882003123
+
+
diff --git a/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/vz.xl b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/vz.xl
new file mode 100644
index 000000000..0d957fb62
--- /dev/null
+++ b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/vz.xl
@@ -0,0 +1,170 @@
+# HYDROTOY::vz x (vz)
+#
+# iteration 0
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+0 0 0 0 0 0 12 16 -0.515299953858482
+0 0 0 0 0 1 12 16 -0.62302697845592
+0 0 0 0 0 2 12 16 -0.62302697845592
+0 0 0 0 0 3 12 16 -0.51529995385848
+0 0 0 0 0 4 12 16 -0.318472885885792
+0 0 0 0 0 5 12 16 -0.0665789627081124
+0 0 0 0 0 6 12 16 0.196827067972688
+0 0 0 0 0 7 12 16 0.426199910483233
+0 0 0 0 0 8 12 16 0.581878916566594
+0 0 0 0 0 9 12 16 0.636945771771587
+0 0 0 0 0 10 12 16 0.581878916566594
+0 0 0 0 0 11 12 16 0.426199910483233
+0 0 0 0 0 12 12 16 0.196827067972688
+0 0 0 0 0 13 12 16 -0.0665789627081126
+0 0 0 0 0 14 12 16 -0.318472885885792
+0 0 0 0 0 15 12 16 -0.51529995385848
+0 0 0 0 0 16 12 16 -0.62302697845592
+0 0 0 0 0 17 12 16 -0.62302697845592
+0 0 0 0 0 18 12 16 -0.515299953858482
+
+
+# iteration 1
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+1 0 0 0 0 0 12 16 -0.608492170320791
+1 0 0 0 0 1 12 16 -0.633457407715208
+1 0 0 0 0 2 12 16 -0.548892104535778
+1 0 0 0 0 3 12 16 -0.369418369953888
+1 0 0 0 0 4 12 16 -0.126068843146438
+1 0 0 0 0 5 12 16 0.139079131940516
+1 0 0 0 0 6 12 16 0.380179061620706
+1 0 0 0 0 7 12 16 0.555542577728329
+1 0 0 0 0 8 12 16 0.634847735200848
+1 0 0 0 0 9 12 16 0.604381951846525
+1 0 0 0 0 10 12 16 0.469413038380277
+1 0 0 0 0 11 12 16 0.253278346094503
+1 0 0 0 0 12 12 16 -0.00665047319254958
+1 0 0 0 0 13 12 16 -0.265429365246958
+1 0 0 0 0 14 12 16 -0.478313108700085
+1 0 0 0 0 15 12 16 -0.608492170320791
+1 0 0 0 0 16 12 16 -0.633457407715208
+1 0 0 0 0 17 12 16 -0.548892104535778
+1 0 0 0 0 18 12 16 -0.369418369953888
+
+
+# iteration 2
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+2 0 0 0 0 0 12 16 -0.638086200378305
+2 0 0 0 0 1 12 16 -0.577480248216561
+2 0 0 0 0 2 12 16 -0.417022714894814
+2 0 0 0 0 3 12 16 -0.184458165635327
+2 0 0 0 0 4 12 16 0.0800008762123353
+2 0 0 0 0 5 12 16 0.330627039777741
+2 0 0 0 0 6 12 16 0.524084784513215
+2 0 0 0 0 7 12 16 0.626923508845556
+2 0 0 0 0 8 12 16 0.621361463077223
+2 0 0 0 0 9 12 16 0.508360375451159
+2 0 0 0 0 10 12 16 0.307459160600565
+2 0 0 0 0 11 12 16 0.0533954637033468
+2 0 0 0 0 12 12 16 -0.209900793950739
+2 0 0 0 0 13 12 16 -0.436903297441893
+2 0 0 0 0 14 12 16 -0.588361251663493
+2 0 0 0 0 15 12 16 -0.638086200378305
+2 0 0 0 0 16 12 16 -0.577480248216561
+2 0 0 0 0 17 12 16 -0.417022714894814
+2 0 0 0 0 18 12 16 -0.184458165635327
+
+
+# iteration 3
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+3 0 0 0 0 0 12 16 -0.600801795900965
+3 0 0 0 0 1 12 16 -0.460809125595699
+3 0 0 0 0 2 12 16 -0.241138371155451
+3 0 0 0 0 3 12 16 0.0202273983308998
+3 0 0 0 0 4 12 16 0.278095666885694
+3 0 0 0 0 5 12 16 0.487878668216132
+3 0 0 0 0 6 12 16 0.613303015573443
+3 0 0 0 0 7 12 16 0.632681699855125
+3 0 0 0 0 8 12 16 0.542663970499055
+3 0 0 0 0 9 12 16 0.358814710696295
+3 0 0 0 0 10 12 16 0.112923127684834
+3 0 0 0 0 11 12 16 -0.152493889977744
+3 0 0 0 0 12 12 16 -0.391543328699671
+3 0 0 0 0 13 12 16 -0.562891368829953
+3 0 0 0 0 14 12 16 -0.636910377581988
+3 0 0 0 0 15 12 16 -0.600801795900965
+3 0 0 0 0 16 12 16 -0.460809125595699
+3 0 0 0 0 17 12 16 -0.241138371155451
+3 0 0 0 0 18 12 16 0.0202273983308998
+
+
+# iteration 4
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+4 0 0 0 0 0 12 16 -0.500385047305991
+4 0 0 0 0 1 12 16 -0.295557108392471
+4 0 0 0 0 2 12 16 -0.0396246603858532
+4 0 0 0 0 3 12 16 0.223159251380213
+4 0 0 0 0 4 12 16 0.447356901244488
+4 0 0 0 0 5 12 16 0.594202478773731
+4 0 0 0 0 6 12 16 0.638305049562943
+4 0 0 0 0 7 12 16 0.572038878463393
+4 0 0 0 0 8 12 16 0.406861988467459
+4 0 0 0 0 9 12 16 0.171334964440373
+4 0 0 0 0 10 12 16 -0.0938174314677397
+4 0 0 0 0 11 12 16 -0.342747941170472
+4 0 0 0 0 12 12 16 -0.532414218077537
+4 0 0 0 0 13 12 16 -0.63002123984767
+4 0 0 0 0 14 12 16 -0.618691865684861
+4 0 0 0 0 15 12 16 -0.500385047305991
+4 0 0 0 0 16 12 16 -0.295557108392471
+4 0 0 0 0 17 12 16 -0.0396246603858532
+4 0 0 0 0 18 12 16 0.223159251380213
+
+
+# iteration 5
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+5 0 0 0 0 0 12 16 -0.347232808041161
+5 0 0 0 0 1 12 16 -0.0989793588236514
+5 0 0 0 0 2 12 16 0.166388520733716
+5 0 0 0 0 3 12 16 0.402986313463963
+5 0 0 0 0 4 12 16 0.569904111580568
+5 0 0 0 0 5 12 16 0.638280311388576
+5 0 0 0 0 6 12 16 0.596292046762909
+5 0 0 0 0 7 12 16 0.451199470108754
+5 0 0 0 0 8 12 16 0.228090406054292
+5 0 0 0 0 9 12 16 -0.0344575613432431
+5 0 0 0 0 10 12 16 -0.291047503347414
+5 0 0 0 0 11 12 16 -0.497312687939257
+5 0 0 0 0 12 12 16 -0.617587990842467
+5 0 0 0 0 13 12 16 -0.631076719518255
+5 0 0 0 0 14 12 16 -0.535446550237325
+5 0 0 0 0 15 12 16 -0.347232808041161
+5 0 0 0 0 16 12 16 -0.0989793588236514
+5 0 0 0 0 17 12 16 0.166388520733716
+5 0 0 0 0 18 12 16 0.402986313463963
+
+
+# iteration 6
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+6 0 0 0 0 0 12 16 -0.157316535477105
+6 0 0 0 0 1 12 16 0.108328421385468
+6 0 0 0 0 2 12 16 0.355242410057682
+6 0 0 0 0 3 12 16 0.54073175875494
+6 0 0 0 0 4 12 16 0.63272367396966
+6 0 0 0 0 5 12 16 0.615311917840902
+6 0 0 0 0 6 12 16 0.491507141184166
+6 0 0 0 0 7 12 16 0.282716314614489
+6 0 0 0 0 8 12 16 0.02504126885088
+6 0 0 0 0 9 12 16 -0.236963639789832
+6 0 0 0 0 10 12 16 -0.457995382363797
+6 0 0 0 0 11 12 16 -0.599835562569634
+6 0 0 0 0 12 12 16 -0.637958724672169
+6 0 0 0 0 13 12 16 -0.565773027605821
+6 0 0 0 0 14 12 16 -0.395760034179829
+6 0 0 0 0 15 12 16 -0.157316535477105
+6 0 0 0 0 16 12 16 0.108328421385468
+6 0 0 0 0 17 12 16 0.355242410057682
+6 0 0 0 0 18 12 16 0.54073175875494
+
+
diff --git a/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/vz.yl b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/vz.yl
new file mode 100644
index 000000000..743e0cba1
--- /dev/null
+++ b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/vz.yl
@@ -0,0 +1,219 @@
+# HYDROTOY::vz y (vz)
+#
+# iteration 0
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+0 0 0 0 0 9 0 16 -0.611144992588299
+0 0 0 0 0 9 1 16 -0.636945771771587
+0 0 0 0 0 9 2 16 -0.611144992588303
+0 0 0 0 0 9 3 16 -0.535832880724733
+0 0 0 0 0 9 4 16 -0.417110775585691
+0 0 0 0 0 9 5 16 -0.264596836061994
+0 0 0 0 0 9 6 16 -0.0906468344985295
+0 0 0 0 0 9 7 16 0.0906468344985235
+0 0 0 0 0 9 8 16 0.264596836061988
+0 0 0 0 0 9 9 16 0.417110775585686
+0 0 0 0 0 9 10 16 0.53583288072473
+0 0 0 0 0 9 11 16 0.611144992588301
+0 0 0 0 0 9 12 16 0.636945771771587
+0 0 0 0 0 9 13 16 0.611144992588301
+0 0 0 0 0 9 14 16 0.53583288072473
+0 0 0 0 0 9 15 16 0.417110775585686
+0 0 0 0 0 9 16 16 0.264596836061988
+0 0 0 0 0 9 17 16 0.0906468344985234
+0 0 0 0 0 9 18 16 -0.0906468344985296
+0 0 0 0 0 9 19 16 -0.264596836061994
+0 0 0 0 0 9 20 16 -0.417110775585691
+0 0 0 0 0 9 21 16 -0.535832880724734
+0 0 0 0 0 9 22 16 -0.611144992588303
+0 0 0 0 0 9 23 16 -0.636945771771587
+0 0 0 0 0 9 24 16 -0.611144992588299
+0 0 0 0 0 9 25 16 -0.535832880724727
+
+
+# iteration 1
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+1 0 0 0 0 9 0 16 -0.637195713383579
+1 0 0 0 0 9 1 16 -0.604381951846523
+1 0 0 0 0 9 2 16 -0.522604758968737
+1 0 0 0 0 9 3 16 -0.398489236569475
+1 0 0 0 0 9 4 16 -0.242090486130096
+1 0 0 0 0 9 5 16 -0.0660790042720144
+1 0 0 0 0 9 6 16 0.115285805525215
+1 0 0 0 0 9 7 16 0.287310844989877
+1 0 0 0 0 9 8 16 0.436059668496847
+1 0 0 0 0 9 9 16 0.549481531008906
+1 0 0 0 0 9 10 16 0.618387667771117
+1 0 0 0 0 9 11 16 0.637195713383579
+1 0 0 0 0 9 12 16 0.604381951846525
+1 0 0 0 0 9 13 16 0.522604758968734
+1 0 0 0 0 9 14 16 0.39848923656947
+1 0 0 0 0 9 15 16 0.24209048613009
+1 0 0 0 0 9 16 16 0.0660790042720084
+1 0 0 0 0 9 17 16 -0.115285805525221
+1 0 0 0 0 9 18 16 -0.287310844989883
+1 0 0 0 0 9 19 16 -0.436059668496852
+1 0 0 0 0 9 20 16 -0.54948153100891
+1 0 0 0 0 9 21 16 -0.618387667771118
+1 0 0 0 0 9 22 16 -0.637195713383579
+1 0 0 0 0 9 23 16 -0.604381951846523
+1 0 0 0 0 9 24 16 -0.522604758968737
+1 0 0 0 0 9 25 16 -0.398489236569475
+
+
+# iteration 2
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+2 0 0 0 0 9 0 16 -0.59648290094983
+2 0 0 0 0 9 1 16 -0.508360375451156
+2 0 0 0 0 9 2 16 -0.379053515669004
+2 0 0 0 0 9 3 16 -0.2190379943654
+2 0 0 0 0 9 4 16 -0.0412773174274224
+2 0 0 0 0 9 5 16 0.139827402282866
+2 0 0 0 0 9 6 16 0.309604137445777
+2 0 0 0 0 9 7 16 0.454298586679535
+2 0 0 0 0 9 8 16 0.562188466238243
+2 0 0 0 0 9 9 16 0.624533179725876
+2 0 0 0 0 9 10 16 0.636281929233952
+2 0 0 0 0 9 11 16 0.596482900949832
+2 0 0 0 0 9 12 16 0.508360375451159
+2 0 0 0 0 9 13 16 0.379053515668998
+2 0 0 0 0 9 14 16 0.219037994365394
+2 0 0 0 0 9 15 16 0.0412773174274162
+2 0 0 0 0 9 16 16 -0.139827402282872
+2 0 0 0 0 9 17 16 -0.309604137445783
+2 0 0 0 0 9 18 16 -0.454298586679539
+2 0 0 0 0 9 19 16 -0.562188466238246
+2 0 0 0 0 9 20 16 -0.624533179725877
+2 0 0 0 0 9 21 16 -0.636281929233952
+2 0 0 0 0 9 22 16 -0.59648290094983
+2 0 0 0 0 9 23 16 -0.508360375451156
+2 0 0 0 0 9 24 16 -0.379053515669004
+2 0 0 0 0 9 25 16 -0.2190379943654
+
+
+# iteration 3
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+3 0 0 0 0 9 0 16 -0.493113583217527
+3 0 0 0 0 9 1 16 -0.358814710696291
+3 0 0 0 0 9 2 16 -0.195446804267703
+3 0 0 0 0 9 3 16 -0.0162449601242363
+3 0 0 0 0 9 4 16 0.164272954075997
+3 0 0 0 0 9 5 16 0.331482450505869
+3 0 0 0 0 9 6 16 0.471837210197796
+3 0 0 0 0 9 7 16 0.573966525243434
+3 0 0 0 0 9 8 16 0.629596485924211
+3 0 0 0 0 9 9 16 0.634220283669883
+3 0 0 0 0 9 10 16 0.587463325885882
+3 0 0 0 0 9 11 16 0.493113583217531
+3 0 0 0 0 9 12 16 0.358814710696295
+3 0 0 0 0 9 13 16 0.195446804267697
+3 0 0 0 0 9 14 16 0.0162449601242305
+3 0 0 0 0 9 15 16 -0.164272954076003
+3 0 0 0 0 9 16 16 -0.331482450505874
+3 0 0 0 0 9 17 16 -0.4718372101978
+3 0 0 0 0 9 18 16 -0.573966525243437
+3 0 0 0 0 9 19 16 -0.629596485924212
+3 0 0 0 0 9 20 16 -0.634220283669883
+3 0 0 0 0 9 21 16 -0.587463325885879
+3 0 0 0 0 9 22 16 -0.493113583217527
+3 0 0 0 0 9 23 16 -0.358814710696291
+3 0 0 0 0 9 24 16 -0.195446804267703
+3 0 0 0 0 9 25 16 -0.0162449601242363
+
+
+# iteration 4
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+4 0 0 0 0 9 0 16 -0.337796446653127
+4 0 0 0 0 9 1 16 -0.17133496444037
+4 0 0 0 0 9 2 16 0.00900705762306818
+4 0 0 0 0 9 3 16 0.188619381444931
+4 0 0 0 0 9 4 16 0.352950884744777
+4 0 0 0 0 9 5 16 0.488688406442338
+4 0 0 0 0 9 6 16 0.5848352997918
+4 0 0 0 0 9 7 16 0.633602315301583
+4 0 0 0 0 9 8 16 0.631038639403692
+4 0 0 0 0 9 9 16 0.577351965872606
+4 0 0 0 0 9 10 16 0.476891669710873
+4 0 0 0 0 9 11 16 0.337796446653131
+4 0 0 0 0 9 12 16 0.171334964440373
+4 0 0 0 0 9 13 16 -0.00900705762307519
+4 0 0 0 0 9 14 16 -0.188619381444936
+4 0 0 0 0 9 15 16 -0.352950884744783
+4 0 0 0 0 9 16 16 -0.488688406442342
+4 0 0 0 0 9 17 16 -0.584835299791803
+4 0 0 0 0 9 18 16 -0.633602315301584
+4 0 0 0 0 9 19 16 -0.631038639403691
+4 0 0 0 0 9 20 16 -0.577351965872604
+4 0 0 0 0 9 21 16 -0.476891669710869
+4 0 0 0 0 9 22 16 -0.337796446653127
+4 0 0 0 0 9 23 16 -0.17133496444037
+4 0 0 0 0 9 24 16 0.00900705762306818
+4 0 0 0 0 9 25 16 0.188619381444931
+
+
+# iteration 5
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+5 0 0 0 0 9 0 16 -0.146732746204847
+5 0 0 0 0 9 1 16 0.0344575613432452
+5 0 0 0 0 9 2 16 0.212856322198309
+5 0 0 0 0 9 3 16 0.374010729734168
+5 0 0 0 0 9 4 16 0.504865012274416
+5 0 0 0 0 9 5 16 0.594818134068033
+5 0 0 0 0 9 6 16 0.63658262815911
+5 0 0 0 0 9 7 16 0.6267749836194
+5 0 0 0 0 9 8 16 0.566189757481202
+5 0 0 0 0 9 9 16 0.459735204452018
+5 0 0 0 0 9 10 16 0.31603563930867
+5 0 0 0 0 9 11 16 0.146732746204851
+5 0 0 0 0 9 12 16 -0.0344575613432431
+5 0 0 0 0 9 13 16 -0.212856322198315
+5 0 0 0 0 9 14 16 -0.374010729734171
+5 0 0 0 0 9 15 16 -0.50486501227442
+5 0 0 0 0 9 16 16 -0.594818134068035
+5 0 0 0 0 9 17 16 -0.63658262815911
+5 0 0 0 0 9 18 16 -0.626774983619399
+5 0 0 0 0 9 19 16 -0.566189757481199
+5 0 0 0 0 9 20 16 -0.459735204452014
+5 0 0 0 0 9 21 16 -0.316035639308665
+5 0 0 0 0 9 22 16 -0.146732746204847
+5 0 0 0 0 9 23 16 0.0344575613432452
+5 0 0 0 0 9 24 16 0.212856322198309
+5 0 0 0 0 9 25 16 0.374010729734168
+
+
+# iteration 6
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+6 0 0 0 0 9 0 16 0.0600734663797312
+6 0 0 0 0 9 1 16 0.236963639789833
+6 0 0 0 0 9 2 16 0.394656428381188
+6 0 0 0 0 9 3 16 0.520376500257262
+6 0 0 0 0 9 4 16 0.603938762880696
+6 0 0 0 0 9 5 16 0.638573498697662
+6 0 0 0 0 9 6 16 0.621474807392969
+6 0 0 0 0 9 7 16 0.554027923246292
+6 0 0 0 0 9 8 16 0.441696991689129
+6 0 0 0 0 9 9 16 0.293582396738469
+6 0 0 0 0 9 10 16 0.121683502005799
+6 0 0 0 0 9 11 16 -0.0600734663797284
+6 0 0 0 0 9 12 16 -0.236963639789832
+6 0 0 0 0 9 13 16 -0.394656428381192
+6 0 0 0 0 9 14 16 -0.520376500257262
+6 0 0 0 0 9 15 16 -0.603938762880698
+6 0 0 0 0 9 16 16 -0.638573498697662
+6 0 0 0 0 9 17 16 -0.621474807392968
+6 0 0 0 0 9 18 16 -0.554027923246289
+6 0 0 0 0 9 19 16 -0.441696991689125
+6 0 0 0 0 9 20 16 -0.293582396738463
+6 0 0 0 0 9 21 16 -0.121683502005794
+6 0 0 0 0 9 22 16 0.0600734663797312
+6 0 0 0 0 9 23 16 0.236963639789833
+6 0 0 0 0 9 24 16 0.394656428381188
+6 0 0 0 0 9 25 16 0.520376500257262
+
+
diff --git a/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/vz.zl b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/vz.zl
new file mode 100644
index 000000000..fc23c9e27
--- /dev/null
+++ b/CarpetExtra/HydroToy/test/hydrotoy_periodic_coarse/vz.zl
@@ -0,0 +1,275 @@
+# HYDROTOY::vz z (vz)
+#
+# iteration 0
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+0 0 0 0 0 9 12 0 0.581878916566596
+0 0 0 0 0 9 12 1 0.636945771771587
+0 0 0 0 0 9 12 2 0.581878916566593
+0 0 0 0 0 9 12 3 0.42619991048323
+0 0 0 0 0 9 12 4 0.196827067972683
+0 0 0 0 0 9 12 5 -0.0665789627081168
+0 0 0 0 0 9 12 6 -0.318472885885796
+0 0 0 0 0 9 12 7 -0.515299953858482
+0 0 0 0 0 9 12 8 -0.62302697845592
+0 0 0 0 0 9 12 9 -0.62302697845592
+0 0 0 0 0 9 12 10 -0.515299953858479
+0 0 0 0 0 9 12 11 -0.318472885885792
+0 0 0 0 0 9 12 12 -0.0665789627081123
+0 0 0 0 0 9 12 13 0.196827067972688
+0 0 0 0 0 9 12 14 0.426199910483233
+0 0 0 0 0 9 12 15 0.581878916566594
+0 0 0 0 0 9 12 16 0.636945771771587
+0 0 0 0 0 9 12 17 0.581878916566594
+0 0 0 0 0 9 12 18 0.426199910483233
+0 0 0 0 0 9 12 19 0.196827067972688
+0 0 0 0 0 9 12 20 -0.0665789627081124
+0 0 0 0 0 9 12 21 -0.318472885885792
+0 0 0 0 0 9 12 22 -0.515299953858479
+0 0 0 0 0 9 12 23 -0.62302697845592
+0 0 0 0 0 9 12 24 -0.62302697845592
+0 0 0 0 0 9 12 25 -0.515299953858482
+0 0 0 0 0 9 12 26 -0.318472885885796
+0 0 0 0 0 9 12 27 -0.0665789627081168
+0 0 0 0 0 9 12 28 0.196827067972684
+0 0 0 0 0 9 12 29 0.42619991048323
+0 0 0 0 0 9 12 30 0.581878916566593
+0 0 0 0 0 9 12 31 0.636945771771587
+0 0 0 0 0 9 12 32 0.581878916566596
+0 0 0 0 0 9 12 33 0.426199910483237
+
+
+# iteration 1
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+1 0 0 0 0 9 12 0 0.634847735200847
+1 0 0 0 0 9 12 1 0.604381951846525
+1 0 0 0 0 9 12 2 0.469413038380274
+1 0 0 0 0 9 12 3 0.253278346094499
+1 0 0 0 0 9 12 4 -0.00665047319255438
+1 0 0 0 0 9 12 5 -0.265429365246962
+1 0 0 0 0 9 12 6 -0.478313108700088
+1 0 0 0 0 9 12 7 -0.608492170320792
+1 0 0 0 0 9 12 8 -0.633457407715207
+1 0 0 0 0 9 12 9 -0.548892104535778
+1 0 0 0 0 9 12 10 -0.369418369953887
+1 0 0 0 0 9 12 11 -0.126068843146438
+1 0 0 0 0 9 12 12 0.139079131940516
+1 0 0 0 0 9 12 13 0.380179061620706
+1 0 0 0 0 9 12 14 0.555542577728329
+1 0 0 0 0 9 12 15 0.634847735200848
+1 0 0 0 0 9 12 16 0.604381951846525
+1 0 0 0 0 9 12 17 0.469413038380277
+1 0 0 0 0 9 12 18 0.253278346094503
+1 0 0 0 0 9 12 19 -0.00665047319254942
+1 0 0 0 0 9 12 20 -0.265429365246958
+1 0 0 0 0 9 12 21 -0.478313108700085
+1 0 0 0 0 9 12 22 -0.608492170320791
+1 0 0 0 0 9 12 23 -0.633457407715208
+1 0 0 0 0 9 12 24 -0.54889210453578
+1 0 0 0 0 9 12 25 -0.369418369953891
+1 0 0 0 0 9 12 26 -0.126068843146442
+1 0 0 0 0 9 12 27 0.139079131940511
+1 0 0 0 0 9 12 28 0.380179061620702
+1 0 0 0 0 9 12 29 0.555542577728327
+1 0 0 0 0 9 12 30 0.634847735200847
+1 0 0 0 0 9 12 31 0.604381951846525
+1 0 0 0 0 9 12 32 0.469413038380274
+1 0 0 0 0 9 12 33 0.253278346094499
+
+
+# iteration 2
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+2 0 0 0 0 9 12 0 0.621361463077223
+2 0 0 0 0 9 12 1 0.508360375451158
+2 0 0 0 0 9 12 2 0.307459160600559
+2 0 0 0 0 9 12 3 0.0533954637033422
+2 0 0 0 0 9 12 4 -0.209900793950744
+2 0 0 0 0 9 12 5 -0.436903297441896
+2 0 0 0 0 9 12 6 -0.588361251663495
+2 0 0 0 0 9 12 7 -0.638086200378305
+2 0 0 0 0 9 12 8 -0.577480248216559
+2 0 0 0 0 9 12 9 -0.417022714894814
+2 0 0 0 0 9 12 10 -0.184458165635327
+2 0 0 0 0 9 12 11 0.0800008762123356
+2 0 0 0 0 9 12 12 0.330627039777741
+2 0 0 0 0 9 12 13 0.524084784513215
+2 0 0 0 0 9 12 14 0.626923508845556
+2 0 0 0 0 9 12 15 0.621361463077223
+2 0 0 0 0 9 12 16 0.508360375451159
+2 0 0 0 0 9 12 17 0.307459160600565
+2 0 0 0 0 9 12 18 0.0533954637033469
+2 0 0 0 0 9 12 19 -0.209900793950739
+2 0 0 0 0 9 12 20 -0.436903297441894
+2 0 0 0 0 9 12 21 -0.588361251663493
+2 0 0 0 0 9 12 22 -0.638086200378305
+2 0 0 0 0 9 12 23 -0.577480248216561
+2 0 0 0 0 9 12 24 -0.417022714894818
+2 0 0 0 0 9 12 25 -0.184458165635331
+2 0 0 0 0 9 12 26 0.0800008762123312
+2 0 0 0 0 9 12 27 0.330627039777737
+2 0 0 0 0 9 12 28 0.524084784513212
+2 0 0 0 0 9 12 29 0.626923508845555
+2 0 0 0 0 9 12 30 0.621361463077223
+2 0 0 0 0 9 12 31 0.508360375451158
+2 0 0 0 0 9 12 32 0.307459160600559
+2 0 0 0 0 9 12 33 0.0533954637033422
+
+
+# iteration 3
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+3 0 0 0 0 9 12 0 0.542663970499056
+3 0 0 0 0 9 12 1 0.358814710696292
+3 0 0 0 0 9 12 2 0.112923127684826
+3 0 0 0 0 9 12 3 -0.152493889977748
+3 0 0 0 0 9 12 4 -0.391543328699675
+3 0 0 0 0 9 12 5 -0.562891368829955
+3 0 0 0 0 9 12 6 -0.636910377581988
+3 0 0 0 0 9 12 7 -0.600801795900964
+3 0 0 0 0 9 12 8 -0.460809125595696
+3 0 0 0 0 9 12 9 -0.241138371155451
+3 0 0 0 0 9 12 10 0.0202273983309004
+3 0 0 0 0 9 12 11 0.278095666885694
+3 0 0 0 0 9 12 12 0.487878668216132
+3 0 0 0 0 9 12 13 0.613303015573443
+3 0 0 0 0 9 12 14 0.632681699855125
+3 0 0 0 0 9 12 15 0.542663970499055
+3 0 0 0 0 9 12 16 0.358814710696295
+3 0 0 0 0 9 12 17 0.112923127684834
+3 0 0 0 0 9 12 18 -0.152493889977744
+3 0 0 0 0 9 12 19 -0.391543328699671
+3 0 0 0 0 9 12 20 -0.562891368829953
+3 0 0 0 0 9 12 21 -0.636910377581988
+3 0 0 0 0 9 12 22 -0.600801795900965
+3 0 0 0 0 9 12 23 -0.4608091255957
+3 0 0 0 0 9 12 24 -0.241138371155455
+3 0 0 0 0 9 12 25 0.0202273983308957
+3 0 0 0 0 9 12 26 0.27809566688569
+3 0 0 0 0 9 12 27 0.487878668216129
+3 0 0 0 0 9 12 28 0.613303015573442
+3 0 0 0 0 9 12 29 0.632681699855125
+3 0 0 0 0 9 12 30 0.542663970499056
+3 0 0 0 0 9 12 31 0.358814710696292
+3 0 0 0 0 9 12 32 0.112923127684826
+3 0 0 0 0 9 12 33 -0.152493889977748
+
+
+# iteration 4
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+4 0 0 0 0 9 12 0 0.406861988467459
+4 0 0 0 0 9 12 1 0.171334964440367
+4 0 0 0 0 9 12 2 -0.0938174314677489
+4 0 0 0 0 9 12 3 -0.342747941170476
+4 0 0 0 0 9 12 4 -0.53241421807754
+4 0 0 0 0 9 12 5 -0.630021239847671
+4 0 0 0 0 9 12 6 -0.61869186568486
+4 0 0 0 0 9 12 7 -0.500385047305989
+4 0 0 0 0 9 12 8 -0.295557108392468
+4 0 0 0 0 9 12 9 -0.0396246603858534
+4 0 0 0 0 9 12 10 0.223159251380214
+4 0 0 0 0 9 12 11 0.447356901244488
+4 0 0 0 0 9 12 12 0.594202478773731
+4 0 0 0 0 9 12 13 0.638305049562943
+4 0 0 0 0 9 12 14 0.572038878463393
+4 0 0 0 0 9 12 15 0.406861988467459
+4 0 0 0 0 9 12 16 0.171334964440373
+4 0 0 0 0 9 12 17 -0.0938174314677396
+4 0 0 0 0 9 12 18 -0.342747941170472
+4 0 0 0 0 9 12 19 -0.532414218077537
+4 0 0 0 0 9 12 20 -0.630021239847671
+4 0 0 0 0 9 12 21 -0.618691865684861
+4 0 0 0 0 9 12 22 -0.500385047305991
+4 0 0 0 0 9 12 23 -0.295557108392472
+4 0 0 0 0 9 12 24 -0.0396246603858582
+4 0 0 0 0 9 12 25 0.223159251380209
+4 0 0 0 0 9 12 26 0.447356901244485
+4 0 0 0 0 9 12 27 0.594202478773729
+4 0 0 0 0 9 12 28 0.638305049562943
+4 0 0 0 0 9 12 29 0.572038878463394
+4 0 0 0 0 9 12 30 0.406861988467459
+4 0 0 0 0 9 12 31 0.171334964440367
+4 0 0 0 0 9 12 32 -0.0938174314677489
+4 0 0 0 0 9 12 33 -0.342747941170476
+
+
+# iteration 5
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+5 0 0 0 0 9 12 0 0.228090406054292
+5 0 0 0 0 9 12 1 -0.0344575613432509
+5 0 0 0 0 9 12 2 -0.291047503347424
+5 0 0 0 0 9 12 3 -0.49731268793926
+5 0 0 0 0 9 12 4 -0.61758799084247
+5 0 0 0 0 9 12 5 -0.631076719518254
+5 0 0 0 0 9 12 6 -0.535446550237322
+5 0 0 0 0 9 12 7 -0.347232808041159
+5 0 0 0 0 9 12 8 -0.0989793588236489
+5 0 0 0 0 9 12 9 0.166388520733715
+5 0 0 0 0 9 12 10 0.402986313463964
+5 0 0 0 0 9 12 11 0.569904111580567
+5 0 0 0 0 9 12 12 0.638280311388576
+5 0 0 0 0 9 12 13 0.596292046762908
+5 0 0 0 0 9 12 14 0.451199470108754
+5 0 0 0 0 9 12 15 0.228090406054293
+5 0 0 0 0 9 12 16 -0.0344575613432431
+5 0 0 0 0 9 12 17 -0.291047503347414
+5 0 0 0 0 9 12 18 -0.497312687939257
+5 0 0 0 0 9 12 19 -0.617587990842467
+5 0 0 0 0 9 12 20 -0.631076719518255
+5 0 0 0 0 9 12 21 -0.535446550237325
+5 0 0 0 0 9 12 22 -0.347232808041162
+5 0 0 0 0 9 12 23 -0.0989793588236535
+5 0 0 0 0 9 12 24 0.166388520733711
+5 0 0 0 0 9 12 25 0.40298631346396
+5 0 0 0 0 9 12 26 0.569904111580566
+5 0 0 0 0 9 12 27 0.638280311388575
+5 0 0 0 0 9 12 28 0.59629204676291
+5 0 0 0 0 9 12 29 0.451199470108755
+5 0 0 0 0 9 12 30 0.228090406054292
+5 0 0 0 0 9 12 31 -0.0344575613432509
+5 0 0 0 0 9 12 32 -0.291047503347424
+5 0 0 0 0 9 12 33 -0.49731268793926
+
+
+# iteration 6
+# time level 0   refinement level 0   component 0   multigrid level 0
+# column format: it tl rl c ml x y z data
+6 0 0 0 0 9 12 0 0.0250412688508779
+6 0 0 0 0 9 12 1 -0.236963639789841
+6 0 0 0 0 9 12 2 -0.457995382363806
+6 0 0 0 0 9 12 3 -0.599835562569635
+6 0 0 0 0 9 12 4 -0.637958724672171
+6 0 0 0 0 9 12 5 -0.565773027605818
+6 0 0 0 0 9 12 6 -0.395760034179826
+6 0 0 0 0 9 12 7 -0.157316535477102
+6 0 0 0 0 9 12 8 0.10832842138547
+6 0 0 0 0 9 12 9 0.355242410057682
+6 0 0 0 0 9 12 10 0.540731758754941
+6 0 0 0 0 9 12 11 0.63272367396966
+6 0 0 0 0 9 12 12 0.615311917840902
+6 0 0 0 0 9 12 13 0.491507141184166
+6 0 0 0 0 9 12 14 0.282716314614489
+6 0 0 0 0 9 12 15 0.0250412688508801
+6 0 0 0 0 9 12 16 -0.236963639789832
+6 0 0 0 0 9 12 17 -0.457995382363797
+6 0 0 0 0 9 12 18 -0.599835562569634
+6 0 0 0 0 9 12 19 -0.637958724672169
+6 0 0 0 0 9 12 20 -0.565773027605821
+6 0 0 0 0 9 12 21 -0.39576003417983
+6 0 0 0 0 9 12 22 -0.157316535477107
+6 0 0 0 0 9 12 23 0.108328421385465
+6 0 0 0 0 9 12 24 0.355242410057678
+6 0 0 0 0 9 12 25 0.540731758754939
+6 0 0 0 0 9 12 26 0.63272367396966
+6 0 0 0 0 9 12 27 0.615311917840903
+6 0 0 0 0 9 12 28 0.491507141184168
+6 0 0 0 0 9 12 29 0.282716314614489
+6 0 0 0 0 9 12 30 0.0250412688508779
+6 0 0 0 0 9 12 31 -0.236963639789841
+6 0 0 0 0 9 12 32 -0.457995382363806
+6 0 0 0 0 9 12 33 -0.599835562569635
+
+