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diff --git a/CarpetExtra/SpaceTimeToy/test/spacetimetoy_periodic_coarse/phi.yl b/CarpetExtra/SpaceTimeToy/test/spacetimetoy_periodic_coarse/phi.yl
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+# SPACETIMETOY::phi y (phi)
+#
+# 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 -0.142314838273291
+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 -0.998467688471524
+1 0 0 0 0 9 1 16 -0.946645972224922
+1 0 0 0 0 9 2 16 -0.818132629229041
+1 0 0 0 0 9 3 16 -0.623339046235111
+1 0 0 0 0 9 4 16 -0.378046240855262
+1 0 0 0 0 9 5 16 -0.102126377368883
+1 0 0 0 0 9 6 16 0.182067157842969
+1 0 0 0 0 9 7 16 0.451510694721464
+1 0 0 0 0 9 8 16 0.684375520351121
+1 0 0 0 0 9 9 16 0.861796311459868
+1 0 0 0 0 9 10 16 0.969399490714147
+1 0 0 0 0 9 11 16 0.998467688471524
+1 0 0 0 0 9 12 16 0.946645972224925
+1 0 0 0 0 9 13 16 0.818132629229036
+1 0 0 0 0 9 14 16 0.623339046235104
+1 0 0 0 0 9 15 16 0.378046240855253
+1 0 0 0 0 9 16 16 0.102126377368874
+1 0 0 0 0 9 17 16 -0.182067157842979
+1 0 0 0 0 9 18 16 -0.451510694721473
+1 0 0 0 0 9 19 16 -0.684375520351128
+1 0 0 0 0 9 20 16 -0.861796311459873
+1 0 0 0 0 9 21 16 -0.969399490714149
+1 0 0 0 0 9 22 16 -0.998467688471524
+1 0 0 0 0 9 23 16 -0.946645972224922
+1 0 0 0 0 9 24 16 -0.818132629229041
+1 0 0 0 0 9 25 16 -0.623339046235111
+
+
+# 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 -0.933556336551482
+2 0 0 0 0 9 1 16 -0.795047905556765
+2 0 0 0 0 9 2 16 -0.592129421585802
+2 0 0 0 0 9 3 16 -0.341240133407217
+2 0 0 0 0 9 4 16 -0.0627055990531928
+2 0 0 0 0 9 5 16 0.220908970011565
+2 0 0 0 0 9 6 16 0.486626808122216
+2 0 0 0 0 9 7 16 0.712921036319869
+2 0 0 0 0 9 8 16 0.881458642059544
+2 0 0 0 0 9 9 16 0.978585710855947
+2 0 0 0 0 9 10 16 0.996433585232115
+2 0 0 0 0 9 11 16 0.933556336551486
+2 0 0 0 0 9 12 16 0.795047905556768
+2 0 0 0 0 9 13 16 0.592129421585796
+2 0 0 0 0 9 14 16 0.341240133407208
+2 0 0 0 0 9 15 16 0.062705599053183
+2 0 0 0 0 9 16 16 -0.220908970011574
+2 0 0 0 0 9 17 16 -0.486626808122225
+2 0 0 0 0 9 18 16 -0.712921036319876
+2 0 0 0 0 9 19 16 -0.881458642059548
+2 0 0 0 0 9 20 16 -0.978585710855949
+2 0 0 0 0 9 21 16 -0.996433585232114
+2 0 0 0 0 9 22 16 -0.933556336551482
+2 0 0 0 0 9 23 16 -0.795047905556765
+2 0 0 0 0 9 24 16 -0.592129421585802
+2 0 0 0 0 9 25 16 -0.341240133407217
+
+
+# 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 -0.771793469714844
+3 0 0 0 0 9 1 16 -0.561234706264647
+3 0 0 0 0 9 2 16 -0.305208044704207
+3 0 0 0 0 9 3 16 -0.0244552425039632
+3 0 0 0 0 9 4 16 0.258278778003027
+3 0 0 0 0 9 5 16 0.52008858795925
+3 0 0 0 0 9 6 16 0.739763913604945
+3 0 0 0 0 9 7 16 0.899507966515762
+3 0 0 0 0 9 8 16 0.986379233559332
+3 0 0 0 0 9 9 16 0.993339921323102
+3 0 0 0 0 9 10 16 0.919826116281255
+3 0 0 0 0 9 11 16 0.77179346971485
+3 0 0 0 0 9 12 16 0.561234706264648
+3 0 0 0 0 9 13 16 0.305208044704202
+3 0 0 0 0 9 14 16 0.0244552425039541
+3 0 0 0 0 9 15 16 -0.258278778003037
+3 0 0 0 0 9 16 16 -0.520088587959259
+3 0 0 0 0 9 17 16 -0.739763913604951
+3 0 0 0 0 9 18 16 -0.899507966515767
+3 0 0 0 0 9 19 16 -0.986379233559334
+3 0 0 0 0 9 20 16 -0.993339921323101
+3 0 0 0 0 9 21 16 -0.919826116281251
+3 0 0 0 0 9 22 16 -0.771793469714844
+3 0 0 0 0 9 23 16 -0.561234706264647
+3 0 0 0 0 9 24 16 -0.305208044704207
+3 0 0 0 0 9 25 16 -0.0244552425039632
+
+
+# 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 -0.530260638273941
+4 0 0 0 0 9 1 16 -0.269736091609724
+4 0 0 0 0 9 2 16 0.012640869014411
+4 0 0 0 0 9 3 16 0.29399374160914
+4 0 0 0 0 9 4 16 0.551528989706803
+4 0 0 0 0 9 5 16 0.764382639127621
+4 0 0 0 0 9 6 16 0.915310553084914
+4 0 0 0 0 9 7 16 0.992085449592727
+4 0 0 0 0 9 8 16 0.988487483133888
+4 0 0 0 0 9 9 16 0.904808139552962
+4 0 0 0 0 9 10 16 0.747826621606656
+4 0 0 0 0 9 11 16 0.530260638273946
+4 0 0 0 0 9 12 16 0.269736091609723
+4 0 0 0 0 9 13 16 -0.0126408690144145
+4 0 0 0 0 9 14 16 -0.293993741609147
+4 0 0 0 0 9 15 16 -0.551528989706811
+4 0 0 0 0 9 16 16 -0.764382639127627
+4 0 0 0 0 9 17 16 -0.915310553084918
+4 0 0 0 0 9 18 16 -0.992085449592728
+4 0 0 0 0 9 19 16 -0.988487483133887
+4 0 0 0 0 9 20 16 -0.904808139552958
+4 0 0 0 0 9 21 16 -0.74782662160665
+4 0 0 0 0 9 22 16 -0.530260638273941
+4 0 0 0 0 9 23 16 -0.269736091609724
+4 0 0 0 0 9 24 16 0.012640869014411
+4 0 0 0 0 9 25 16 0.29399374160914
+
+
+# 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 -0.234283142691294
+5 0 0 0 0 9 1 16 0.0489905171024299
+5 0 0 0 0 9 2 16 0.328295256558344
+5 0 0 0 0 9 3 16 0.581003466774967
+5 0 0 0 0 9 4 16 0.786642231474147
+5 0 0 0 0 9 5 16 0.928551920920781
+5 0 0 0 0 9 6 16 0.99523585604532
+5 0 0 0 0 9 7 16 0.981291701008607
+5 0 0 0 0 9 8 16 0.887849128322633
+5 0 0 0 0 9 9 16 0.722478299502037
+5 0 0 0 0 9 10 16 0.498576575599677
+5 0 0 0 0 9 11 16 0.234283142691298
+5 0 0 0 0 9 12 16 -0.0489905171024318
+5 0 0 0 0 9 13 16 -0.328295256558346
+5 0 0 0 0 9 14 16 -0.581003466774971
+5 0 0 0 0 9 15 16 -0.786642231474152
+5 0 0 0 0 9 16 16 -0.928551920920784
+5 0 0 0 0 9 17 16 -0.995235856045321
+5 0 0 0 0 9 18 16 -0.981291701008606
+5 0 0 0 0 9 19 16 -0.887849128322629
+5 0 0 0 0 9 20 16 -0.722478299502031
+5 0 0 0 0 9 21 16 -0.49857657559967
+5 0 0 0 0 9 22 16 -0.234283142691294
+5 0 0 0 0 9 23 16 0.0489905171024299
+5 0 0 0 0 9 24 16 0.328295256558344
+5 0 0 0 0 9 25 16 0.581003466774967
+
+
+# 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 0.0852250519308664
+6 0 0 0 0 9 1 16 0.361742081942054
+6 0 0 0 0 9 2 16 0.608952919837298
+6 0 0 0 0 9 3 16 0.806830013749785
+6 0 0 0 0 9 4 16 0.939342538351114
+6 0 0 0 0 9 5 16 0.995755116980417
+6 0 0 0 0 9 6 16 0.971497538015671
+6 0 0 0 0 9 7 16 0.868535006239222
+6 0 0 0 0 9 8 16 0.695208933633843
+6 0 0 0 0 9 9 16 0.465561167792177
+6 0 0 0 0 9 10 16 0.198196404934864
+6 0 0 0 0 9 11 16 -0.0852250519308652
+6 0 0 0 0 9 12 16 -0.361742081942056
+6 0 0 0 0 9 13 16 -0.608952919837299
+6 0 0 0 0 9 14 16 -0.806830013749785
+6 0 0 0 0 9 15 16 -0.939342538351115
+6 0 0 0 0 9 16 16 -0.995755116980418
+6 0 0 0 0 9 17 16 -0.971497538015669
+6 0 0 0 0 9 18 16 -0.868535006239217
+6 0 0 0 0 9 19 16 -0.695208933633836
+6 0 0 0 0 9 20 16 -0.465561167792169
+6 0 0 0 0 9 21 16 -0.198196404934858
+6 0 0 0 0 9 22 16 0.0852250519308664
+6 0 0 0 0 9 23 16 0.361742081942054
+6 0 0 0 0 9 24 16 0.608952919837298
+6 0 0 0 0 9 25 16 0.806830013749785
+
+