new SBP coefficients of Diener, Dorband, Schnetter, Tiglio (2007) (#129)

* WIP: new SBP coefficients of Diener, Dorband, Schnetter, Tiglio (2007)

* SBP first-derivative operators of DienerDorbandSchnetterTiglio2007

* set version to v0.5.14

Project.toml

@@ -1,7 +1,7 @@
 name = "SummationByPartsOperators"
 uuid = "9f78cca6-572e-554e-b819-917d2f1cf240"
 author = ["Hendrik Ranocha"]
-version = "0.5.14-pre"
+version = "0.5.14"
 
 [deps]
 ArgCheck = "dce04be8-c92d-5529-be00-80e4d2c0e197"

dev/DienerDorbandSchnetterTiglio2007/Derivatives_2_1

@@ -0,0 +1,12 @@
+  a(1) = 1.0/2.0
+
+  q(1,1) = -1.0
+  q(2,1) = 1.0
+  q(3,1) = 0
+
+  q(1,2) = -1.0/2.0
+  q(2,2) = 0
+  q(3,2) = 1.0/2.0
+
+# from https://bitbucket.org/cactuscode/cactusnumerical/src/master/SummationByParts/src/GetScalProdDiag.F90
+  CCTK_REAL, dimension(2), parameter :: bmask_2 = (/ 0.5_wp, 1.0_wp /)

dev/DienerDorbandSchnetterTiglio2007/Derivatives_4_2

@@ -0,0 +1,36 @@
+  a(1) = 2.0/3.0
+  a(2) = -1.0/12.0
+
+  q(1,1) = -24.0/17.0
+  q(2,1) = 59.0/34.0
+  q(3,1) = -4.0/17.0
+  q(4,1) = -3.0/34.0
+  q(5,1) = 0
+  q(6,1) = 0
+
+  q(1,2) = -1.0/2.0
+  q(2,2) = 0
+  q(3,2) = 1.0/2.0
+  q(4,2) = 0
+  q(5,2) = 0
+  q(6,2) = 0
+
+  q(1,3) = 4.0/43.0
+  q(2,3) = -59.0/86.0
+  q(3,3) = 0
+  q(4,3) = 59.0/86.0
+  q(5,3) = -4.0/43.0
+  q(6,3) = 0
+
+  q(1,4) = 3.0/98.0
+  q(2,4) = 0
+  q(3,4) = -59.0/98.0
+  q(4,4) = 0
+  q(5,4) = 32.0/49.0
+  q(6,4) = -4.0/49.0
+
+  # from https://bitbucket.org/cactuscode/cactusnumerical/src/master/SummationByParts/src/GetScalProdDiag.F90
+  CCTK_REAL, dimension(4), parameter :: bmask_4 = (/ 17.0_wp/48.0_wp, &
+                                                     59.0_wp/48.0_wp, &
+                                                     43.0_wp/48.0_wp, &
+                                                     49.0_wp/48.0_wp /)

dev/DienerDorbandSchnetterTiglio2007/Derivatives_4_3_min_err_coeff

@@ -0,0 +1,42 @@
+  a(1) = 2.0/3.0
+  a(2) = -1.0/12.0
+
+  q(1,1) = -2.09329763466349871588733
+  q(2,1) = 4.0398572053206615302160
+  q(3,1) = -3.0597858079809922953240
+  q(4,1) = 1.37319053865399486354933
+  q(5,1) = -0.25996430133016538255400
+  q(6,1) = 0
+  q(7,1) = 0
+
+  q(1,2) = -0.31641585285940445272297
+  q(2,2) = -0.53930788973980422327388
+  q(3,2) = 0.98517732028644343383297
+  q(4,2) = -0.05264665989297578146709
+  q(5,2) = -0.113807251750624235013258
+  q(6,2) = 0.039879767889849911803103
+  q(7,2) = -0.0028794339334846531588787
+
+  q(1,3) = 0.13026916185021164524452
+  q(2,3) = -0.87966858995059249256890
+  q(3,3) = 0.38609640961100070000134
+  q(4,3) = 0.31358369072435588745988
+  q(5,3) = 0.085318941913678384633511
+  q(6,3) = -0.039046615792734640274641
+  q(7,3) = 0.0034470016440805155042908
+
+  q(1,4) = -0.01724512193824647912172
+  q(2,4) = 0.16272288227127504381134
+  q(3,4) = -0.81349810248648813029217
+  q(4,4) = 0.13833269266479833215645
+  q(5,4) = 0.59743854328548053399616
+  q(6,4) = -0.066026434346299887619324
+  q(7,4) = -0.0017244594505194129307249
+
+  q(1,5) = -0.00883569468552192965061
+  q(2,5) = 0.03056074759203203857284
+  q(3,5) = 0.05021168274530854232278
+  q(4,5) = -0.66307364652444929534068
+  q(5,5) = 0.014878787464005191116088
+  q(6,5) = 0.65882706381707471953820
+  q(7,5) = -0.082568940408449266558615

dev/DienerDorbandSchnetterTiglio2007/Derivatives_6_3

@@ -0,0 +1,71 @@
+  a(1) = 3.0/4.0
+  a(2) = -3.0/20.0
+  a(3) = 1.0/60.0
+
+  q(1,1) = -21600.0/13649.0
+  q(2,1) = 81763.0/40947.0
+  q(3,1) = 131.0/27298.0
+  q(4,1) = -9143.0/13649.0
+  q(5,1) = 20539.0/81894.0
+  q(6,1) = 0
+  q(7,1) = 0
+  q(8,1) = 0
+  q(9,1) = 0
+
+  q(1,2) = -81763.0/180195.0
+  q(2,2) = 0
+  q(3,2) = 7357.0/36039.0
+  q(4,2) = 30637.0/72078.0
+  q(5,2) = -2328.0/12013.0
+  q(6,2) = 6611.0/360390.0
+  q(7,2) = 0
+  q(8,2) = 0
+  q(9,2) = 0
+
+  q(1,3) = -131.0/54220.0
+  q(2,3) = -7357.0/16266.0
+  q(3,3) = 0
+  q(4,3) = 645.0/2711.0
+  q(5,3) = 11237.0/32532.0
+  q(6,3) = -3487.0/27110.0
+  q(7,3) = 0
+  q(8,3) = 0
+  q(9,3) = 0
+
+  q(1,4) = 9143.0/53590.0
+  q(2,4) = -30637.0/64308.0
+  q(3,4) =  -645.0/5359.0
+  q(4,4) = 0
+  q(5,4) = 13733.0/32154.0
+  q(6,4) = -67.0/4660.0
+  q(7,4) = 72.0/5359.0
+  q(8,4) = 0
+  q(9,4) = 0
+
+  q(1,5) = -20539.0/236310.0
+  q(2,5) = 2328.0/7877.0
+  q(3,5) = -11237.0/47262.0
+  q(4,5) = -13733.0/23631.0
+  q(5,5) = 0
+  q(6,5) = 89387.0/118155.0
+  q(7,5) = -1296.0/7877.0
+  q(8,5) = 144.0/7877.0
+  q(9,5) = 0
+
+  q(1,6) = 0
+  q(2,6) = -6611.0/262806.0
+  q(3,6) = 3487.0/43801.0
+  q(4,6) = 1541.0/87602.0
+  q(5,6) = -89387.0/131403.0
+  q(6,6) = 0
+  q(7,6) = 32400.0/43801.0
+  q(8,6) = -6480.0/43801.0
+  q(9,6) = 720.0/43801.0
+
+  # from https://bitbucket.org/cactuscode/cactusnumerical/src/master/SummationByParts/src/GetScalProdDiag.F90
+  CCTK_REAL, dimension(6), parameter :: bmask_6 = (/ 13649.0_wp/43200._wp, &
+                                                     12013.0_wp/8640._wp, &
+                                                     2711.0_wp/4320.0_wp, &
+                                                     5359.0_wp/4320.0_wp, &
+                                                     7877.0_wp/8640.0_wp, &
+                                                     43801.0_wp/43200.0_wp /)

dev/DienerDorbandSchnetterTiglio2007/Derivatives_6_3_min_err_coeff

@@ -0,0 +1,71 @@
+  a(1) = 3.0/4.0
+  a(2) = -3.0/20.0
+  a(3) = 1.0/60.0
+
+  q(1,1) = -1.582533518939116418785258993332844897062
+  q(2,1) = 2.033426786468126253898161347360808173712
+  q(3,1) = -0.1417052898146741610733887894481170575600
+  q(4,1) = -0.4501096599735708523162117824920488989702
+  q(5,1) = 0.1042956382142412661862395105494407610836
+  q(6,1) = 0.03662604404499391209045870736276191879693
+  q(7,1) = 0
+  q(8,1) = 0
+  q(9,1) = 0
+
+  q(1,2) = -0.4620701275035953590186631853846278325646
+  q(2,2) = 0
+  q(3,2) = 0.2873679417026202568532985205129449923126
+  q(4,2) = 0.2585974499280928196267362923074433487080
+  q(5,2) = -0.06894808744606961472005221923058251153103
+  q(6,2) = -0.01494717668104810274131940820517799692506
+  q(7,2) = 0
+  q(8,2) = 0
+  q(9,2) = 0
+
+  q(1,3) = 0.07134398748360337973038301686379010397038
+  q(2,3) = -0.6366933020423417826592908754928085932593
+  q(3,3) = 0
+  q(4,3) = 0.6067199374180168986519150843189505198519
+  q(5,3) = -0.02338660408468356531858175098561718651857
+  q(6,3) = -0.01798401877459493040442547470431484404443
+  q(7,3) = 0
+  q(8,3) = 0
+  q(9,3) = 0
+
+  q(1,4) = 0.1146397975178068401430112823144985150596
+  q(2,4) = -0.2898424301162697370942324201800071793273
+  q(3,4) = -0.3069262456316931913128086944558079603132
+  q(4,4) = 0
+  q(5,4) = 0.5203848121857539166740071338174418292578
+  q(6,4) = -0.05169127637022742348368508279860701098408
+  q(7,4) = 0.01343534241462959507370778130248180630715
+  q(8,4) = 0
+  q(9,4) = 0
+
+  q(1,5) = -0.03614399304268576976452921364705641609825
+  q(2,5) = 0.1051508663818248421520867474440761344449
+  q(3,5) = 0.01609777419666805778308369351834662756172
+  q(4,5) = -0.7080721616106272031118456849378369336023
+  q(5,5) = 0
+  q(6,5) = 0.7692160858661111736140494493705980473867
+  q(7,5) = -0.1645296432652024882569506157166433921544
+  q(8,5) = 0.01828107147391138758410562396851593246160
+  q(9,5) = 0
+
+  q(1,6) = -0.01141318406360863692889821914555232596651
+  q(2,6) = 0.02049729840293952857599941220163960606616
+  q(3,6) = 0.01113095018331244864875173213474522093204
+  q(4,6) = 0.06324365883611076515355091406993789453750
+  q(5,6) = -0.6916640154753724474963890679085181638850
+  q(6,6) = 0
+  q(7,6) = 0.7397091390607520376247117645715851236273
+  q(8,6) = -0.1479418278121504075249423529143170247255
+  q(9,6) = 0.01643798086801671194721581699047966941394
+
+  # from https://bitbucket.org/cactuscode/cactusnumerical/src/master/SummationByParts/src/GetScalProdDiag.F90
+  CCTK_REAL, dimension(6), parameter :: bmask_6 = (/ 13649.0_wp/43200._wp, &
+                                                     12013.0_wp/8640._wp, &
+                                                     2711.0_wp/4320.0_wp, &
+                                                     5359.0_wp/4320.0_wp, &
+                                                     7877.0_wp/8640.0_wp, &
+                                                     43801.0_wp/43200.0_wp /)

dev/DienerDorbandSchnetterTiglio2007/Derivatives_6_5_min_err_coeff

@@ -0,0 +1,80 @@
+  a(1) = 3.0/4.0
+  a(2) = -3.0/20.0
+  a(3) = 1.0/60.0
+
+  q(1,1) = -2.465354921110524023660777656111276003457
+  q(2,1) = 6.092129526663144141964665936667656020742
+  q(3,1) = -7.730323816657860354911664841669140051855
+  q(4,1) = 6.973765088877147139882219788892186735807
+  q(5,1) = -3.980323816657860354911664841669140051855
+  q(6,1) = 1.292129526663144141964665936667656020742
+  q(7,1) = -0.1820215877771906903274443227779426701237
+  q(8,1) = 0
+  q(9,1) = 0
+  q(10,1) = 0
+
+  q(1,2) = -0.2234725650784319828746535134412736890421
+  q(2,2) = -0.9329308121107134563129925525068570679651
+  q(3,2) = 1.586820596545839371759081303802027231274
+  q(4,2) = -0.3647002340377160216914505558624668821400
+  q(5,2) = -0.2666957784872806143914117440166232718819
+  q(6,2) = 0.3112949048634705032101261273629794071371
+  q(7,2) = -0.1404504214762266650000768489896480092493
+  q(8,2) = 0.03488568514730479833596013512958238764128
+  q(9,2) = -0.004964021886392518344179263072091597647654
+  q(10,2) = 0.0002126465201465853095969115943714918742904
+
+  q(1,3) = 0.1582216737061633151406179477554921935333
+  q(2,3) = -1.137049298003377811733609086574457439398
+  q(3,3) = 1.212364522932578587741649981040340946798
+  q(4,3) = -0.9562288729513894906148167047868730813830
+  q(5,3) = 1.066548057336766350478498057851678826640
+  q(6,3) = -0.3478788551267041838265477441805600110467
+  q(7,3) = -0.03133923293520187620333693909408071632123
+  q(8,3) = 0.04098845955755862691072597869183962277781
+  q(9,3) = -0.005963188634687155197078928402509551508436
+  q(10,3) = 0.0003367341182936373038974376991292099082999
+
+  q(1,4) = 0.02915734641890708196910927068736798144670
+  q(2,4) = -0.1169665089768926152768236581512624861308
+  q(3,4) = -0.1112219092451476301503253995474190870412
+  q(4,4) = -0.7924486261248032107393766820001361351677
+  q(5,4) = 1.266650704820613624987450232358951199911
+  q(6,4) = -0.2899273290506621673153239836530375587273
+  q(7,4) = 0.002515684257201926199329020583484434062150
+  q(8,4) = 0.01329713961871764653006682056620518602804
+  q(9,4) = -0.001124464399630667352932212208930962568134
+  q(10,4) = 0.00006796268169601114882659136477742818715059
+
+  q(1,5) = -0.04582150000326981674750984653096293434777
+  q(2,5) = 0.2240986548857151482718685516611524323427
+  q(3,5) = -0.3246718493011818141660859125588209338018
+  q(4,5) = -0.3929792921782506986152017485694441380503
+  q(5,5) = 0.1166355818729375628072830916953646214341
+  q(6,5) = 0.3449626905957060254933930895775644438105
+  q(7,5) = 0.1430419813354607083034935179267283951745
+  q(8,5) = -0.07764802499372607792980458731991885121073
+  q(9,5) = 0.01332439335504217034559288889042994978834
+  q(10,5) = -0.0009426355684332077630290447720929851395193
+
+  q(1,6) = 0.003172814452954821196677290327889903944225
+  q(2,6) = 0.00001061446045061551877105554145609103530766
+  q(3,6) = -0.08747763580209736614983637747947172321794
+  q(4,6) = 0.3975827322299876034907453299884380895682
+  q(5,6) = -1.148835072393422871630425744497391344782
+  q(6,6) = 0.3583006649535242306065761818925080902380
+  q(7,6) = 0.5647665154270147564019144982190032455071
+  q(8,6) = -0.09698196887272109736153117076061707705561
+  q(9,6) = 0.008843905091972988427261446924164441884143
+  q(10,6) = 0.0006174304523363194998474898440202828786385
+
+  q(1,7) = -0.008639107540858839028043929986084287776394
+  q(2,7) = 0.04722773954485212324714352753530343274219
+  q(3,7) = -0.1008747537650261142294540111407681552350
+  q(4,7) = 0.08043834953845218736895768965086958762389
+  q(5,7) = 0.1295138674713300902982857323205417604553
+  q(6,7) = -0.7909424166489541737614153656634872155367
+  q(7,7) = 0.03807866847647628589685997987877954466259
+  q(8,7) = 0.7367055699548196242687865288427927434250
+  q(9,7) = -0.1480235854665196220062411065981933720158
+  q(10,7) = 0.01651566843542843794512095516024596165494