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diff --git a/CarpetExtra/SpaceTimeToy/test/doubletoy_periodic_coarse/psi.zl b/CarpetExtra/SpaceTimeToy/test/doubletoy_periodic_coarse/psi.zl
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+# SPACETIMETOY::psi z (psi)
+#
+# 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 -0.467737106301367
+0 0 0 0 0 9 12 1 -1.00000000000001
+0 0 0 0 0 9 12 2 -1.35935380898385
+0 0 0 0 0 9 12 3 -1.48366299505272
+0 0 0 0 0 9 12 4 -1.35143337062181
+0 0 0 0 0 9 12 5 -0.985528639023647
+0 0 0 0 0 9 12 6 -0.449217052491685
+0 0 0 0 0 9 12 7 0.164768243424893
+0 0 0 0 0 9 12 8 0.750263613180807
+0 0 0 0 0 9 12 9 1.20603158828681
+0 0 0 0 0 9 12 10 1.45326574532501
+0 0 0 0 0 9 12 11 1.44921705249169
+0 0 0 0 0 9 12 12 1.19458556555896
+0 0 0 0 0 9 12 13 0.733399381871916
+0 0 0 0 0 9 12 14 0.145401782335002
+0 0 0 0 0 9 12 15 -0.467737106301357
+0 0 0 0 0 9 12 16 -1
+0 0 0 0 0 9 12 17 -1.35935380898385
+0 0 0 0 0 9 12 18 -1.48366299505272
+0 0 0 0 0 9 12 19 -1.35143337062181
+0 0 0 0 0 9 12 20 -0.985528639023655
+0 0 0 0 0 9 12 21 -0.449217052491695
+0 0 0 0 0 9 12 22 0.164768243424882
+0 0 0 0 0 9 12 23 0.750263613180799
+0 0 0 0 0 9 12 24 1.20603158828681
+0 0 0 0 0 9 12 25 1.45326574532501
+0 0 0 0 0 9 12 26 1.44921705249169
+0 0 0 0 0 9 12 27 1.19458556555896
+0 0 0 0 0 9 12 28 0.733399381871925
+0 0 0 0 0 9 12 29 0.145401782335012
+0 0 0 0 0 9 12 30 -0.467737106301347
+0 0 0 0 0 9 12 31 -0.999999999999993
+0 0 0 0 0 9 12 32 -1.35935380898384
+0 0 0 0 0 9 12 33 -1.48366299505272
+
+
+# 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 -0.891204856688904
+1 0 0 0 0 9 12 1 -1.29492434916456
+1 0 0 0 0 9 12 2 -1.47473965765126
+1 0 0 0 0 9 12 3 -1.39955908174087
+1 0 0 0 0 9 12 4 -1.08238202600237
+1 0 0 0 0 9 12 5 -0.57805128483606
+1 0 0 0 0 9 12 6 0.0262297749094682
+1 0 0 0 0 9 12 7 0.625975468283126
+1 0 0 0 0 9 12 8 1.11748431638203
+1 0 0 0 0 9 12 9 1.41576997415218
+1 0 0 0 0 9 12 10 1.46925614152498
+1 0 0 0 0 9 12 11 1.2686945742551
+1 0 0 0 0 9 12 12 0.848764189368141
+1 0 0 0 0 9 12 13 0.28207476535884
+1 0 0 0 0 9 12 14 -0.333387948149798
+1 0 0 0 0 9 12 15 -0.891204856688912
+1 0 0 0 0 9 12 16 -1.29492434916456
+1 0 0 0 0 9 12 17 -1.47473965765126
+1 0 0 0 0 9 12 18 -1.39955908174087
+1 0 0 0 0 9 12 19 -1.08238202600238
+1 0 0 0 0 9 12 20 -0.57805128483607
+1 0 0 0 0 9 12 21 0.0262297749094584
+1 0 0 0 0 9 12 22 0.625975468283116
+1 0 0 0 0 9 12 23 1.11748431638202
+1 0 0 0 0 9 12 24 1.41576997415217
+1 0 0 0 0 9 12 25 1.46925614152498
+1 0 0 0 0 9 12 26 1.2686945742551
+1 0 0 0 0 9 12 27 0.84876418936815
+1 0 0 0 0 9 12 28 0.282074765358851
+1 0 0 0 0 9 12 29 -0.333387948149789
+1 0 0 0 0 9 12 30 -0.891204856688904
+1 0 0 0 0 9 12 31 -1.29492434916456
+1 0 0 0 0 9 12 32 -1.47473965765126
+1 0 0 0 0 9 12 33 -1.39955908174087
+
+
+# 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 -1.22250389615375
+2 0 0 0 0 9 12 1 -1.45563790907232
+2 0 0 0 0 9 12 2 -1.43707890345701
+2 0 0 0 0 9 12 3 -1.17003589998202
+2 0 0 0 0 9 12 4 -0.700683059957679
+2 0 0 0 0 9 12 5 -0.110175753360892
+2 0 0 0 0 9 12 6 0.499381941907292
+2 0 0 0 0 9 12 7 1.02259196267719
+2 0 0 0 0 9 12 8 1.36898654314386
+2 0 0 0 0 9 12 9 1.47867091344866
+2 0 0 0 0 9 12 10 1.33267964951465
+2 0 0 0 0 9 12 11 0.956255967165026
+2 0 0 0 0 9 12 12 0.414486940779835
+2 0 0 0 0 9 12 13 -0.198950643161834
+2 0 0 0 0 9 12 14 -0.777987853490969
+2 0 0 0 0 9 12 15 -1.22250389615375
+2 0 0 0 0 9 12 16 -1.45563790907231
+2 0 0 0 0 9 12 17 -1.43707890345702
+2 0 0 0 0 9 12 18 -1.17003589998203
+2 0 0 0 0 9 12 19 -0.700683059957689
+2 0 0 0 0 9 12 20 -0.110175753360902
+2 0 0 0 0 9 12 21 0.499381941907282
+2 0 0 0 0 9 12 22 1.02259196267718
+2 0 0 0 0 9 12 23 1.36898654314386
+2 0 0 0 0 9 12 24 1.47867091344866
+2 0 0 0 0 9 12 25 1.33267964951465
+2 0 0 0 0 9 12 26 0.956255967165033
+2 0 0 0 0 9 12 27 0.414486940779846
+2 0 0 0 0 9 12 28 -0.198950643161823
+2 0 0 0 0 9 12 29 -0.777987853490961
+2 0 0 0 0 9 12 30 -1.22250389615375
+2 0 0 0 0 9 12 31 -1.45563790907232
+2 0 0 0 0 9 12 32 -1.43707890345701
+2 0 0 0 0 9 12 33 -1.17003589998202
+
+
+# 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 -1.42713883695848
+3 0 0 0 0 9 12 1 -1.46532163785484
+3 0 0 0 0 9 12 2 -1.25013701553691
+3 0 0 0 0 9 12 3 -0.818792346094417
+3 0 0 0 0 9 12 4 -0.245871041517253
+3 0 0 0 0 9 12 5 0.369563599806532
+3 0 0 0 0 9 12 6 0.921097337343864
+3 0 0 0 0 9 12 7 1.31336497734783
+3 0 0 0 0 9 12 8 1.47853988122212
+3 0 0 0 0 9 12 9 1.38806180751996
+3 0 0 0 0 9 12 10 1.05757523715195
+3 0 0 0 0 9 12 11 0.544224300510972
+3 0 0 0 0 9 12 12 -0.0632279618109142
+3 0 0 0 0 9 12 13 -0.659747535127692
+3 0 0 0 0 9 12 14 -1.1421907660027
+3 0 0 0 0 9 12 15 -1.42713883695848
+3 0 0 0 0 9 12 16 -1.46532163785483
+3 0 0 0 0 9 12 17 -1.25013701553692
+3 0 0 0 0 9 12 18 -0.818792346094426
+3 0 0 0 0 9 12 19 -0.245871041517264
+3 0 0 0 0 9 12 20 0.369563599806523
+3 0 0 0 0 9 12 21 0.921097337343856
+3 0 0 0 0 9 12 22 1.31336497734783
+3 0 0 0 0 9 12 23 1.47853988122212
+3 0 0 0 0 9 12 24 1.38806180751996
+3 0 0 0 0 9 12 25 1.05757523715196
+3 0 0 0 0 9 12 26 0.544224300510981
+3 0 0 0 0 9 12 27 -0.0632279618109034
+3 0 0 0 0 9 12 28 -0.659747535127682
+3 0 0 0 0 9 12 29 -1.14219076600269
+3 0 0 0 0 9 12 30 -1.42713883695848
+3 0 0 0 0 9 12 31 -1.46532163785484
+3 0 0 0 0 9 12 32 -1.25013701553691
+3 0 0 0 0 9 12 33 -0.818792346094417
+
+
+# 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 -1.48373556270965
+4 0 0 0 0 9 12 1 -1.32282470582352
+4 0 0 0 0 9 12 2 -0.933185439815312
+4 0 0 0 0 9 12 3 -0.382189933539474
+4 0 0 0 0 9 12 4 0.234889684331885
+4 0 0 0 0 9 12 5 0.811354741876469
+4 0 0 0 0 9 12 6 1.24752919362418
+4 0 0 0 0 9 12 7 1.46799451434735
+4 0 0 0 0 9 12 8 1.43463024722837
+4 0 0 0 0 9 12 9 1.15320537715697
+4 0 0 0 0 9 12 10 0.672380820833179
+4 0 0 0 0 9 12 11 0.0752955121993341
+4 0 0 0 0 9 12 12 -0.53480907453203
+4 0 0 0 0 9 12 13 -1.05244031368889
+4 0 0 0 0 9 12 14 -1.38809506148885
+4 0 0 0 0 9 12 15 -1.48373556270965
+4 0 0 0 0 9 12 16 -1.32282470582352
+4 0 0 0 0 9 12 17 -0.933185439815324
+4 0 0 0 0 9 12 18 -0.382189933539486
+4 0 0 0 0 9 12 19 0.234889684331873
+4 0 0 0 0 9 12 20 0.811354741876461
+4 0 0 0 0 9 12 21 1.24752919362418
+4 0 0 0 0 9 12 22 1.46799451434735
+4 0 0 0 0 9 12 23 1.43463024722838
+4 0 0 0 0 9 12 24 1.15320537715698
+4 0 0 0 0 9 12 25 0.672380820833188
+4 0 0 0 0 9 12 26 0.0752955121993443
+4 0 0 0 0 9 12 27 -0.53480907453202
+4 0 0 0 0 9 12 28 -1.05244031368888
+4 0 0 0 0 9 12 29 -1.38809506148885
+4 0 0 0 0 9 12 30 -1.48373556270965
+4 0 0 0 0 9 12 31 -1.32282470582352
+4 0 0 0 0 9 12 32 -0.933185439815312
+4 0 0 0 0 9 12 33 -0.382189933539474
+
+
+# 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 -1.38627402673396
+5 0 0 0 0 9 12 1 -1.04279969755804
+5 0 0 0 0 9 12 2 -0.519015827136482
+5 0 0 0 0 9 12 3 0.0945105949077293
+5 0 0 0 0 9 12 4 0.691695276490592
+5 0 0 0 0 9 12 5 1.16927956091392
+5 0 0 0 0 9 12 6 1.4446847866839
+5 0 0 0 0 9 12 7 1.47029088828697
+5 0 0 0 0 9 12 8 1.24167033813184
+5 0 0 0 0 9 12 9 0.798353706292817
+5 0 0 0 0 9 12 10 0.216994465820037
+5 0 0 0 0 9 12 11 -0.401885089125863
+5 0 0 0 0 9 12 12 -0.951275061150483
+5 0 0 0 0 9 12 13 -1.33618093303956
+5 0 0 0 0 9 12 14 -1.4900489827834
+5 0 0 0 0 9 12 15 -1.38627402673395
+5 0 0 0 0 9 12 16 -1.04279969755804
+5 0 0 0 0 9 12 17 -0.519015827136492
+5 0 0 0 0 9 12 18 0.0945105949077168
+5 0 0 0 0 9 12 19 0.691695276490581
+5 0 0 0 0 9 12 20 1.16927956091391
+5 0 0 0 0 9 12 21 1.44468478668389
+5 0 0 0 0 9 12 22 1.47029088828697
+5 0 0 0 0 9 12 23 1.24167033813184
+5 0 0 0 0 9 12 24 0.798353706292825
+5 0 0 0 0 9 12 25 0.216994465820046
+5 0 0 0 0 9 12 26 -0.401885089125852
+5 0 0 0 0 9 12 27 -0.951275061150475
+5 0 0 0 0 9 12 28 -1.33618093303956
+5 0 0 0 0 9 12 29 -1.4900489827834
+5 0 0 0 0 9 12 30 -1.38627402673396
+5 0 0 0 0 9 12 31 -1.04279969755804
+5 0 0 0 0 9 12 32 -0.519015827136482
+5 0 0 0 0 9 12 33 0.0945105949077293
+
+
+# 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 -1.1447287897228
+6 0 0 0 0 9 12 1 -0.654196820819541
+6 0 0 0 0 9 12 2 -0.0505482784050511
+6 0 0 0 0 9 12 3 0.561840520562367
+6 0 0 0 0 9 12 4 1.07708198936366
+6 0 0 0 0 9 12 5 1.40608619722129
+6 0 0 0 0 9 12 6 1.49196532768727
+6 0 0 0 0 9 12 7 1.31987009891663
+6 0 0 0 0 9 12 8 0.919557339399893
+6 0 0 0 0 9 12 9 0.360244761984743
+6 0 0 0 0 9 12 10 -0.261357407498489
+6 0 0 0 0 9 12 11 -0.837768506867725
+6 0 0 0 0 9 12 12 -1.26932182051158
+6 0 0 0 0 9 12 13 -1.48139785996226
+6 0 0 0 0 9 12 14 -1.4373267513484
+6 0 0 0 0 9 12 15 -1.1447287897228
+6 0 0 0 0 9 12 16 -0.654196820819547
+6 0 0 0 0 9 12 17 -0.0505482784050582
+6 0 0 0 0 9 12 18 0.561840520562357
+6 0 0 0 0 9 12 19 1.07708198936365
+6 0 0 0 0 9 12 20 1.40608619722128
+6 0 0 0 0 9 12 21 1.49196532768727
+6 0 0 0 0 9 12 22 1.31987009891664
+6 0 0 0 0 9 12 23 0.919557339399901
+6 0 0 0 0 9 12 24 0.360244761984753
+6 0 0 0 0 9 12 25 -0.261357407498479
+6 0 0 0 0 9 12 26 -0.837768506867716
+6 0 0 0 0 9 12 27 -1.26932182051157
+6 0 0 0 0 9 12 28 -1.48139785996226
+6 0 0 0 0 9 12 29 -1.4373267513484
+6 0 0 0 0 9 12 30 -1.1447287897228
+6 0 0 0 0 9 12 31 -0.654196820819541
+6 0 0 0 0 9 12 32 -0.0505482784050511
+6 0 0 0 0 9 12 33 0.561840520562367
+
+