SBP first-derivative operators of DienerDorbandSchnetterTiglio2007

ranocha · Mar 4, 2022 · c98508e · c98508e
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diff --git a/dev/DienerDorbandSchnetterTiglio2007/Derivatives_2_1 b/dev/DienerDorbandSchnetterTiglio2007/Derivatives_2_1
@@ -1,9 +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 /)
diff --git a/dev/DienerDorbandSchnetterTiglio2007/Derivatives_4_2 b/dev/DienerDorbandSchnetterTiglio2007/Derivatives_4_2
@@ -1,30 +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 /)
diff --git a/dev/DienerDorbandSchnetterTiglio2007/Derivatives_6_3 b/dev/DienerDorbandSchnetterTiglio2007/Derivatives_6_3
@@ -1,7 +1,7 @@
   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
@@ -11,7 +11,7 @@
   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
@@ -21,7 +21,7 @@
   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
@@ -31,7 +31,7 @@
   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
@@ -41,7 +41,7 @@
   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
@@ -51,7 +51,7 @@
   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
@@ -62,3 +62,10 @@
   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 /)
diff --git a/dev/DienerDorbandSchnetterTiglio2007/Derivatives_6_3_min_err_coeff b/dev/DienerDorbandSchnetterTiglio2007/Derivatives_6_3_min_err_coeff
@@ -62,3 +62,10 @@
   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 /)
diff --git a/dev/DienerDorbandSchnetterTiglio2007/Derivatives_8_4 b/dev/DienerDorbandSchnetterTiglio2007/Derivatives_8_4
@@ -1,12 +1,12 @@
   x1 = 0.541
   x2 = -0.0675
   x3 = 0.748
-  
+
   a(1) = 4.0/5.0
   a(2) = -1.0/5.0
   a(3) = 4.0/105.0
   a(4) = -1.0/280.0
-  
+
   q(1,1) = -2540160.0/1498139.0
   q(2,1) = 9.0 * ( 2257920.0*x1 + 11289600.0*x2 + 22579200.0*x3 - 15849163.0 ) / 5992556.0
   q(3,1) = 3.0 * ( -33868800.0*x1 - 162570240.0*x2 - 304819200.0*x3 + 235236677.0 ) / 5992556.0
@@ -19,7 +19,7 @@
   q(10,1) = 0
   q(11,1) = 0
   q(12,1) = 0
-  
+
   q(1,2) = 9.0 * ( -2257920.0*x1 - 11289600.0*x2 - 22579200.0*x3 + 15849163.0 ) / 31004596.0
   q(2,2) = 0
   q(3,2) = 3.0 * ( 7257600.0*x1 + 33868800.0*x2 + 60963840.0*x3 - 47167457.0 ) / 2214614.0
@@ -32,7 +32,7 @@
   q(10,2) = 0
   q(11,2) = 0
   q(12,2) = 0
-  
+
   q(1,3) = ( 33868800.0*x1 + 162570240.0*x2 + 304819200.0*x3 - 235236677.0 ) / 1743924.0
   q(2,3) = ( -7257600.0*x1 - 33868800.0*x2 - 60963840.0*x3 + 47167457.0 ) / 124566.0
   q(3,3) = 0
@@ -45,7 +45,7 @@
   q(10,3) = 0
   q(11,3) = 0
   q(12,3) = 0
-  
+
   q(1,4) = ( -609638400.0*x1 - 2743372800.0*x2 - 4572288000.0*x3 + 3577778591.0 ) / 109619916.0
   q(2,4) = 3.0 * ( 9676800.0*x1 + 42336000.0*x2 + 67737600.0*x3 - 53224573.0 ) / 1304999.0
   q(3,4) = 3.0 * ( -24192000.0*x1 - 101606400.0*x2 - 152409600.0*x3 + 120219461.0 ) / 2609998.0
@@ -58,7 +58,7 @@
   q(10,4) = 0
   q(11,4) = 0
   q(12,4) = 0
-  
+
   q(1,5) = 3.0 * ( 16934400.0*x1 + 67737600.0*x2 + 84672000.0*x3 - 67906303.0 ) / 2096689.0
   q(2,5) = 7.0 * ( -55987200.0*x1 - 217728000.0*x2 - 261273600.0*x3 + 211102099.0 ) / 3594324.0
   q(3,5) = 3.0 * ( 72576000.0*x1 + 270950400.0*x2 + 304819200.0*x3 - 249289259.0 ) / 1198108.0
@@ -68,11 +68,11 @@
   q(7,5) = 15.0 * ( -967680.0*x1 + 6773760.0*x3 - 4472029.0 ) / 1198108.0
   q(8,5) = ( -304819200.0*x2 - 914457600.0*x3 + 657798011.0 ) / 25160268.0
   q(9,5) = -2592.0/299527.0
-  
+
   q(10,5) = 0
   q(11,5) = 0
   q(12,5) = 0
-  
+
   q(1,6) = 5.0 * ( -967680.0*x1 - 2903040.0*x2 + 305821.0 ) / 1237164.0
   q(2,6) = ( 11612160.0*x1 + 33868800.0*x2 - 3884117.0 ) / 618582.0
   q(3,6) = 9.0 * ( -806400.0*x1 - 2257920.0*x2 + 290167.0 ) / 206194.0
@@ -85,7 +85,7 @@
   q(10,6) = -288.0/103097.0
   q(11,6) = 0
   q(12,6) = 0
-  
+
   q(1,7) = 7.0 * ( 1244160.0*x1 - 18662400.0*x3 + 13322233.0 ) / 8041092.0
   q(2,7) = 150.0 * ( -24192.0*x1 + 338688.0*x3 - 240463.0 ) / 670091.0
   q(3,7) = 54.0 * ( 134400.0*x1 - 1693440.0*x3 + 1191611.0 ) / 670091.0
@@ -98,7 +98,7 @@
   q(10,7) = 27648.0/670091.0
   q(11,7) = -2592.0/670091.0
   q(12,7) = 0
-  
+
   q(1,8) = 3.0 * ( 6773760.0*x2 + 33868800.0*x3 - 24839327.0 ) / 20510956.0
   q(2,8) = ( -152409600.0*x2 - 731566080.0*x3 + 536324953.0 ) / 30766434.0
   q(3,8) = 45.0 * ( 2257920.0*x2 + 10160640.0*x3 - 7439833.0 ) / 10255478.0
@@ -111,3 +111,13 @@
   q(10,8) = -1016064.0/5127739.0
   q(11,8) = 193536.0/5127739.0
   q(12,8) = -18144.0/5127739.0
+
+  # from https://bitbucket.org/cactuscode/cactusnumerical/src/master/SummationByParts/src/GetScalProdDiag.F90
+  CCTK_REAL, dimension(8), parameter :: bmask_8 = (/ 1498139.0_wp/5080320.0_wp,&
+                                                     1107307.0_wp/725760.0_wp, &
+                                                     20761.0_wp/80640.0_wp, &
+                                                     1304999.0_wp/725760.0_wp, &
+                                                     299527.0_wp/725760.0_wp, &
+                                                     103097.0_wp/80640.0_wp, &
+                                                     670091.0_wp/725760.0_wp, &
+                                                     5127739.0_wp/5080320.0_wp/)
diff --git a/dev/DienerDorbandSchnetterTiglio2007/Derivatives_8_4_min_err_coeff b/dev/DienerDorbandSchnetterTiglio2007/Derivatives_8_4_min_err_coeff
@@ -107,3 +107,12 @@
   q(11,8) = 0.03774295064549892262457196046834677037969
   q(12,8) = -0.003538401623015523996053621293907509723096
 
+  # from https://bitbucket.org/cactuscode/cactusnumerical/src/master/SummationByParts/src/GetScalProdDiag.F90
+  CCTK_REAL, dimension(8), parameter :: bmask_8 = (/ 1498139.0_wp/5080320.0_wp,&
+                                                     1107307.0_wp/725760.0_wp, &
+                                                     20761.0_wp/80640.0_wp, &
+                                                     1304999.0_wp/725760.0_wp, &
+                                                     299527.0_wp/725760.0_wp, &
+                                                     103097.0_wp/80640.0_wp, &
+                                                     670091.0_wp/725760.0_wp, &
+                                                     5127739.0_wp/5080320.0_wp/)