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diff --git a/CarpetExtra/WaveToyF77/test/wavetoyf77_periodic_coarse/phi.zl b/CarpetExtra/WaveToyF77/test/wavetoyf77_periodic_coarse/phi.zl
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+# WAVETOY::phi z (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 12 0 0.913545457642598
+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 0.913545457642598
+0 0 0 0 0 9 12 33 0.669130606358854
+
+
+# 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 0.996351822641284
+1 0 0 0 0 9 12 1 0.946867382673999
+1 0 0 0 0 9 12 2 0.733660970222251
+1 0 0 0 0 9 12 3 0.393597910918405
+1 0 0 0 0 9 12 4 -0.0145218029079991
+1 0 0 0 0 9 12 5 -0.420130565085172
+1 0 0 0 0 9 12 6 -0.753094935792757
+1 0 0 0 0 9 12 7 -0.955842350449067
+1 0 0 0 0 9 12 8 -0.993315939157588
+1 0 0 0 0 9 12 9 -0.85903617799375
+1 0 0 0 0 9 12 10 -0.576221257556115
+1 0 0 0 0 9 12 11 -0.193772446881243
+1 0 0 0 0 9 12 12 0.222181380226812
+1 0 0 0 0 9 12 13 0.599718028239179
+1 0 0 0 0 9 12 14 0.873557980901746
+1 0 0 0 0 9 12 15 0.996351822641285
+1 0 0 0 0 9 12 16 0.946867382673999
+1 0 0 0 0 9 12 17 0.733660970222255
+1 0 0 0 0 9 12 18 0.393597910918411
+1 0 0 0 0 9 12 19 -0.014521802907992
+1 0 0 0 0 9 12 20 -0.420130565085165
+1 0 0 0 0 9 12 21 -0.753094935792752
+1 0 0 0 0 9 12 22 -0.955842350449065
+1 0 0 0 0 9 12 23 -0.993315939157588
+1 0 0 0 0 9 12 24 -0.859036177993754
+1 0 0 0 0 9 12 25 -0.576221257556121
+1 0 0 0 0 9 12 26 -0.19377244688125
+1 0 0 0 0 9 12 27 0.222181380226806
+1 0 0 0 0 9 12 28 0.599718028239173
+1 0 0 0 0 9 12 29 0.873557980901742
+1 0 0 0 0 9 12 30 0.996351822641284
+1 0 0 0 0 9 12 31 0.946867382673999
+1 0 0 0 0 9 12 32 0.733660970222251
+1 0 0 0 0 9 12 33 0.393597910918405
+
+
+# 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 0.97283942200207
+2 0 0 0 0 9 12 1 0.792696388078995
+2 0 0 0 0 9 12 2 0.47548894723645
+2 0 0 0 0 9 12 3 0.0760651477352512
+2 0 0 0 0 9 12 4 -0.336511006839545
+2 0 0 0 0 9 12 5 -0.690901351225261
+2 0 0 0 0 9 12 6 -0.925828575342399
+2 0 0 0 0 9 12 7 -1.00067162789428
+2 0 0 0 0 9 12 8 -0.902489465166891
+2 0 0 0 0 9 12 9 -0.648258675052749
+2 0 0 0 0 9 12 10 -0.281938070776809
+2 0 0 0 0 9 12 11 0.133132187263405
+2 0 0 0 0 9 12 12 0.525182680657825
+2 0 0 0 0 9 12 13 0.826424317431636
+2 0 0 0 0 9 12 14 0.984769681892292
+2 0 0 0 0 9 12 15 0.972839422002068
+2 0 0 0 0 9 12 16 0.792696388078995
+2 0 0 0 0 9 12 17 0.475488947236456
+2 0 0 0 0 9 12 18 0.0760651477352584
+2 0 0 0 0 9 12 19 -0.336511006839538
+2 0 0 0 0 9 12 20 -0.690901351225255
+2 0 0 0 0 9 12 21 -0.925828575342396
+2 0 0 0 0 9 12 22 -1.00067162789428
+2 0 0 0 0 9 12 23 -0.902489465166894
+2 0 0 0 0 9 12 24 -0.648258675052755
+2 0 0 0 0 9 12 25 -0.281938070776816
+2 0 0 0 0 9 12 26 0.133132187263398
+2 0 0 0 0 9 12 27 0.525182680657818
+2 0 0 0 0 9 12 28 0.826424317431632
+2 0 0 0 0 9 12 29 0.98476968189229
+2 0 0 0 0 9 12 30 0.97283942200207
+2 0 0 0 0 9 12 31 0.792696388078995
+2 0 0 0 0 9 12 32 0.47548894723645
+2 0 0 0 0 9 12 33 0.0760651477352512
+
+
+# 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 0.845517218278481
+3 0 0 0 0 9 12 1 0.553938303270452
+3 0 0 0 0 9 12 2 0.166578423255461
+3 0 0 0 0 9 12 3 -0.249584379457865
+3 0 0 0 0 9 12 4 -0.622591775560019
+3 0 0 0 0 9 12 5 -0.88794739759913
+3 0 0 0 0 9 12 6 -0.999768847844488
+3 0 0 0 0 9 12 7 -0.938721181682688
+3 0 0 0 0 9 12 8 -0.715360095193741
+3 0 0 0 0 9 12 9 -0.368306749403353
+3 0 0 0 0 9 12 10 0.0424301793206506
+3 0 0 0 0 9 12 11 0.445830544574036
+3 0 0 0 0 9 12 12 0.772142758427225
+3 0 0 0 0 9 12 13 0.964944474651603
+3 0 0 0 0 9 12 14 0.990898524963371
+3 0 0 0 0 9 12 15 0.845517218278479
+3 0 0 0 0 9 12 16 0.553938303270454
+3 0 0 0 0 9 12 17 0.166578423255466
+3 0 0 0 0 9 12 18 -0.249584379457859
+3 0 0 0 0 9 12 19 -0.622591775560014
+3 0 0 0 0 9 12 20 -0.887947397599127
+3 0 0 0 0 9 12 21 -0.999768847844487
+3 0 0 0 0 9 12 22 -0.93872118168269
+3 0 0 0 0 9 12 23 -0.715360095193745
+3 0 0 0 0 9 12 24 -0.36830674940336
+3 0 0 0 0 9 12 25 0.0424301793206439
+3 0 0 0 0 9 12 26 0.44583054457403
+3 0 0 0 0 9 12 27 0.77214275842722
+3 0 0 0 0 9 12 28 0.964944474651601
+3 0 0 0 0 9 12 29 0.990898524963371
+3 0 0 0 0 9 12 30 0.845517218278481
+3 0 0 0 0 9 12 31 0.553938303270452
+3 0 0 0 0 9 12 32 0.166578423255461
+3 0 0 0 0 9 12 33 -0.249584379457865
+
+
+# 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 0.627971516258223
+4 0 0 0 0 9 12 1 0.25607053922517
+4 0 0 0 0 9 12 2 -0.160107360367728
+4 0 0 0 0 9 12 3 -0.548601242823342
+4 0 0 0 0 9 12 4 -0.842236986508969
+4 0 0 0 0 9 12 5 -0.99024230374438
+4 0 0 0 0 9 12 6 -0.967025730593478
+4 0 0 0 0 9 12 7 -0.776601623469998
+4 0 0 0 0 9 12 8 -0.451896040444295
+4 0 0 0 0 9 12 9 -0.0490535266791284
+4 0 0 0 0 9 12 10 0.36227078748616
+4 0 0 0 0 9 12 11 0.710955191368307
+4 0 0 0 0 9 12 12 0.936708983837727
+4 0 0 0 0 9 12 13 1.00049728326764
+4 0 0 0 0 9 12 14 0.891290513188097
+4 0 0 0 0 9 12 15 0.627971516258222
+4 0 0 0 0 9 12 16 0.256070539225173
+4 0 0 0 0 9 12 17 -0.160107360367724
+4 0 0 0 0 9 12 18 -0.548601242823337
+4 0 0 0 0 9 12 19 -0.842236986508965
+4 0 0 0 0 9 12 20 -0.990242303744379
+4 0 0 0 0 9 12 21 -0.967025730593479
+4 0 0 0 0 9 12 22 -0.776601623470003
+4 0 0 0 0 9 12 23 -0.451896040444302
+4 0 0 0 0 9 12 24 -0.0490535266791351
+4 0 0 0 0 9 12 25 0.362270787486154
+4 0 0 0 0 9 12 26 0.710955191368302
+4 0 0 0 0 9 12 27 0.936708983837724
+4 0 0 0 0 9 12 28 1.00049728326764
+4 0 0 0 0 9 12 29 0.891290513188099
+4 0 0 0 0 9 12 30 0.627971516258223
+4 0 0 0 0 9 12 31 0.25607053922517
+4 0 0 0 0 9 12 32 -0.160107360367728
+4 0 0 0 0 9 12 33 -0.548601242823342
+
+
+# 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 0.343416194797169
+5 0 0 0 0 9 12 1 -0.0691220141445078
+5 0 0 0 0 9 12 2 -0.469708398886811
+5 0 0 0 0 9 12 3 -0.789077934294743
+5 0 0 0 0 9 12 4 -0.972008726315128
+5 0 0 0 0 9 12 5 -0.986870379133566
+5 0 0 0 0 9 12 6 -0.831093177963874
+5 0 0 0 0 9 12 7 -0.531612416079736
+5 0 0 0 0 9 12 8 -0.140211037908228
+5 0 0 0 0 9 12 9 0.275434102494904
+5 0 0 0 0 9 12 10 0.643454184336399
+5 0 0 0 0 9 12 11 0.900215192108381
+5 0 0 0 0 9 12 12 1.00132081496655
+5 0 0 0 0 9 12 13 0.929288972202972
+5 0 0 0 0 9 12 14 0.696574623820226
+5 0 0 0 0 9 12 15 0.34341619479717
+5 0 0 0 0 9 12 16 -0.0691220141445039
+5 0 0 0 0 9 12 17 -0.469708398886808
+5 0 0 0 0 9 12 18 -0.789077934294741
+5 0 0 0 0 9 12 19 -0.972008726315126
+5 0 0 0 0 9 12 20 -0.986870379133567
+5 0 0 0 0 9 12 21 -0.831093177963878
+5 0 0 0 0 9 12 22 -0.531612416079741
+5 0 0 0 0 9 12 23 -0.140211037908235
+5 0 0 0 0 9 12 24 0.275434102494897
+5 0 0 0 0 9 12 25 0.643454184336394
+5 0 0 0 0 9 12 26 0.900215192108378
+5 0 0 0 0 9 12 27 1.00132081496655
+5 0 0 0 0 9 12 28 0.929288972202974
+5 0 0 0 0 9 12 29 0.696574623820229
+5 0 0 0 0 9 12 30 0.343416194797169
+5 0 0 0 0 9 12 31 -0.0691220141445078
+5 0 0 0 0 9 12 32 -0.469708398886811
+5 0 0 0 0 9 12 33 -0.789077934294743
+
+
+# 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 0.0222155989448779
+6 0 0 0 0 9 12 1 -0.386938691789114
+6 0 0 0 0 9 12 2 -0.729187767485107
+6 0 0 0 0 9 12 3 -0.945353653720023
+6 0 0 0 0 9 12 4 -0.998059304958421
+6 0 0 0 0 9 12 5 -0.87819143528537
+6 0 0 0 0 9 12 6 -0.606476288332749
+6 0 0 0 0 9 12 7 -0.229895881463287
+6 0 0 0 0 9 12 8 0.186435611849696
+6 0 0 0 0 9 12 9 0.570530694159504
+6 0 0 0 0 9 12 10 0.855975836340493
+6 0 0 0 0 9 12 11 0.993414980121865
+6 0 0 0 0 9 12 12 0.959083648948396
+6 0 0 0 0 9 12 13 0.758918041870331
+6 0 0 0 0 9 12 14 0.42752861079892
+6 0 0 0 0 9 12 15 0.0222155989448799
+6 0 0 0 0 9 12 16 -0.386938691789111
+6 0 0 0 0 9 12 17 -0.729187767485105
+6 0 0 0 0 9 12 18 -0.945353653720023
+6 0 0 0 0 9 12 19 -0.998059304958422
+6 0 0 0 0 9 12 20 -0.878191435285373
+6 0 0 0 0 9 12 21 -0.606476288332755
+6 0 0 0 0 9 12 22 -0.229895881463293
+6 0 0 0 0 9 12 23 0.186435611849689
+6 0 0 0 0 9 12 24 0.570530694159498
+6 0 0 0 0 9 12 25 0.855975836340489
+6 0 0 0 0 9 12 26 0.993414980121864
+6 0 0 0 0 9 12 27 0.959083648948397
+6 0 0 0 0 9 12 28 0.758918041870335
+6 0 0 0 0 9 12 29 0.427528610798923
+6 0 0 0 0 9 12 30 0.0222155989448779
+6 0 0 0 0 9 12 31 -0.386938691789114
+6 0 0 0 0 9 12 32 -0.729187767485107
+6 0 0 0 0 9 12 33 -0.945353653720023
+
+