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diff --git a/CarpetExtra/SpaceTimeToy/test/doubletoy_periodic_coarse/vz.zl b/CarpetExtra/SpaceTimeToy/test/doubletoy_periodic_coarse/vz.zl
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+# 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
+
+