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diff --git a/CarpetExtra/SpaceTimeToy/test/spacetimetoy_periodic_coarse/cart3d_x.zl b/CarpetExtra/SpaceTimeToy/test/spacetimetoy_periodic_coarse/cart3d_x.zl
new file mode 100644
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+++ b/CarpetExtra/SpaceTimeToy/test/spacetimetoy_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
+
+