Routines for getting the coefficients for the various derivatives. By request from Bela.

git-svn-id: https://svn.cct.lsu.edu/repos/numrel/LSUThorns/SummationByParts/trunk@23 f69c4107-0314-4c4f-9ad4-17e986b73f4a

1 files changed, 231 insertions, 0 deletions

diff --git a/src/Coefficients_8_4.F90 b/src/Coefficients_8_4.F90
new file mode 100644
index 0000000..eb029ba
--- /dev/null
+++ b/src/Coefficients_8_4.F90
@@ -0,0 +1,231 @@
+#include "cctk.h"
+#include "cctk_Functions.h"
+#include "cctk_Parameters.h"
+
+subroutine set_coeff_8_4 ( nsize, loc_order, bb, gsize, imin, imax, dd )
+
+  implicit none
+
+  DECLARE_CCTK_FUNCTIONS
+  DECLARE_CCTK_PARAMETERS
+
+  CCTK_REAL, parameter :: zero = 0.0
+  integer, parameter :: wp = kind(zero)
+  CCTK_INT, intent(IN) :: nsize, loc_order
+  CCTK_INT, dimension(2), intent(IN) :: bb
+  CCTK_INT, intent(IN) :: gsize
+  CCTK_INT, dimension(nsize), intent(OUT) :: imin, imax
+  CCTK_REAL, dimension(nsize,nsize), intent(OUT) :: dd
+
+  CCTK_REAL, dimension(4), save :: a
+  CCTK_REAL, dimension(12,8), save :: q 
+  CCTK_REAL, parameter :: x1 = 0.541_wp, x2 = -0.0675_wp, x3 = 0.748_wp
+
+  CCTK_INT :: i, il, ir
+
+  logical, save :: first = .true.
+
+  if ( first ) then
+    a(1) = 4.0_wp/5.0_wp; a(2) = -1.0_wp/5.0_wp
+    a(3) = 4.0_wp/105.0_wp; a(4) = -1.0_wp/280.0_wp
+
+    q(1,1) = -2540160.0_wp/1498139.0_wp
+    q(2,1) = 9.0_wp * ( 2257920.0_wp*x1 + 11289600.0_wp*x2 + &
+                        22579200.0_wp*x3 - 15849163.0_wp ) / 5992556.0_wp
+    q(3,1) = 3.0_wp * ( -33868800.0_wp*x1 - 162570240.0_wp*x2 - &
+                         304819200.0_wp*x3 + 235236677.0_wp ) / 5992556.0_wp
+    q(4,1) = ( 609638400.0_wp*x1 + 2743372800.0_wp*x2 + &
+               4572288000.0_wp * x3 - 3577778591.0_wp ) / 17977668.0_wp
+    q(5,1) = 3.0_wp * ( -16934400*x1 - 67737600.0_wp*x2 - &
+                         84672000.0_wp*x3 + 67906303.0_wp ) / 1498139.0_wp
+    q(6,1) = 105.0_wp * ( 967680.0_wp*x1 + 2903040.0_wp*x2 - &
+                          305821.0_wp ) / 5992556.0_wp
+    q(7,1) = 49.0_wp * ( -1244160.0_wp*x1 + 18662400.0_wp * x3 - &
+                          13322233.0_wp ) / 17977668.0_wp
+    q(8,1) = 3.0_wp * ( -6773760.0_wp*x2 - 33868800.0_wp*x3 + &
+                         24839327.0_wp ) / 5992556.0_wp
+    q(9,1) = zero; q(10,1) = zero; q(11,1) = zero; q(12,1) = zero
+
+    q(1,2) = 9.0_wp * ( -2257920.0_wp*x1 - 11289600.0_wp*x2 - &
+                         22579200.0_wp*x3 + 15849163.0_wp ) / 31004596.0_wp
+    q(2,2) = zero
+    q(3,2) = 3.0_wp * ( 7257600.0_wp*x1 + 33868800.0_wp*x2 + &
+                        60963840.0_wp*x3 - 47167457.0_wp ) / 2214614.0_wp
+    q(4,2) = 3.0_wp * ( -9676800.0_wp*x1 - 42336000.0_wp*x2 - &
+                         67737600.0_wp*x3 + 53224573.0_wp ) / 1107307.0_wp
+    q(5,2) = 7.0_wp * ( 55987200.0_wp*x1 + 217728000.0_wp*x2 + &
+                        261273600.0_wp*x3 - 211102099.0_wp ) / 13287684.0_wp
+    q(6,2) = 3.0_wp * ( -11612160.0_wp*x1 - 33868800.0_wp*x2 + &
+                         3884117.0_wp ) / 2214614.0_wp
+    q(7,2) = 150.0_wp * ( 24192.0_wp*x1 - 338688.0_wp*x3 + &
+                          240463.0_wp ) / 1107307.0_wp
+    q(8,2) = ( 152409600.0_wp*x2 + 731566080.0_wp*x3 - &
+               536324953.0_wp ) / 46506894.0_wp
+    q(9,2) = zero; q(10,2) = zero; q(11,2) = zero; q(12,2) = zero
+
+    q(1,3) = ( 33868800.0_wp*x1 + 162570240.0_wp*x2 + &
+               304819200.0_wp*x3 - 235236677.0_wp ) / 1743924.0_wp
+    q(2,3) = ( -7257600.0_wp*x1 - 33868800.0_wp*x2 - &
+                60963840.0_wp*x3 + 47167457.0_wp ) / 124566.0_wp
+    q(3,3) = zero
+    q(4,3) = ( 24192000.0_wp*x1 + 101606400.0_wp*x2 + &
+               152409600.0_wp*x3 - 120219461.0_wp ) / 124566.0_wp
+    q(5,3) = ( -72576000.0_wp*x1 - 270950400.0_wp*x2 - &
+                304819200.0_wp*x3 + 249289259.0_wp ) / 249132.0_wp
+    q(6,3) = 9.0_wp * ( 806400.0_wp*x1 + 2257920.0_wp*x2 - &
+                        290167.0_wp ) / 41522.0_wp
+    q(7,3) = 6.0_wp * ( -134400.0_wp*x1 + 1693440.0_wp*x3 - &
+                         1191611.0_wp ) / 20761.0_wp
+    q(8,3) = 5.0_wp * ( -2257920.0_wp*x2 - 10160640.0_wp*x3 + &
+                         7439833.0_wp ) / 290654.0_wp
+    q(9,3) = zero; q(10,3) = zero; q(11,3) = zero; q(12,3) = zero
+
+    q(1,4) = ( -609638400.0_wp*x1 - 2743372800.0_wp*x2 - &
+               4572288000.0_wp*x3 + 3577778591.0_wp ) / 109619916.0_wp
+    q(2,4) = 3.0_wp * ( 9676800.0_wp*x1 + 42336000.0_wp*x2 + &
+                        67737600.0_wp*x3 - 53224573.0_wp ) / 1304999.0_wp
+    q(3,4) = 3.0_wp * ( -24192000.0_wp*x1 - 101606400.0_wp*x2 - &
+                         152409600.0_wp*x3 + 120219461.0_wp ) / 2609998.0_wp
+    q(4,4) = zero
+    q(5,4) = 9.0_wp * ( 16128000.0_wp*x1 + 56448000.0_wp*x2 + &
+                        56448000.0_wp*x3 - 47206049.0_wp ) / 5219996.0_wp
+    q(6,4) = 3.0_wp * ( -19353600.0_wp*x1 - 50803200.0_wp*x2 + &
+                         7628371.0_wp ) / 2609998.0_wp
+    q(7,4) = 2.0_wp * ( 10886400.0_wp*x1 - 114307200.0_wp*x3 + &
+                        79048289.0_wp ) / 3914997.0_wp
+    q(8,4) = 75.0_wp * ( 1354752.0_wp*x2 + 5419008.0_wp*x3 - &
+                         3952831.0_wp ) / 18269986.0_wp
+    q(9,4) = zero; q(10,4) = zero; q(11,4) = zero; q(12,4) = zero
+
+    q(1,5) = 3.0_wp * ( 16934400.0_wp*x1 + 67737600.0_wp*x2 + &
+                        84672000.0_wp*x3 - 67906303.0_wp ) / 2096689.0_wp
+    q(2,5) = 7.0_wp * ( -55987200.0_wp*x1 - 217728000.0_wp*x2 - &
+                         261273600.0_wp*x3 + 211102099.0_wp ) / 3594324.0_wp
+    q(3,5) = 3.0_wp * ( 72576000.0_wp*x1 + 270950400.0_wp*x2 + &
+                        304819200.0_wp*x3 - 249289259.0_wp ) / 1198108.0_wp
+    q(4,5) = 9.0_wp * ( -16128000.0_wp*x1 - 56448000.0_wp*x2 - &
+                         56448000.0_wp*x3 + 47206049.0_wp ) / 1198108.0_wp
+    q(5,5) = zero
+    q(6,5) = 105.0_wp * ( 414720.0_wp*x1 + 967680.0_wp*x2 - &
+                          165527.0_wp ) / 1198108.0_wp
+    q(7,5) = 15.0_wp * ( -967680.0_wp*x1 + 6773760.0_wp*x3 - &
+                          4472029.0_wp ) / 1198108.0_wp
+    q(8,5) = ( -304819200.0_wp*x2 - 914457600.0_wp*x3 + &
+               657798011.0_wp ) / 25160268.0_wp
+    q(9,5) = -2592.0_wp/299527.0_wp; 
+    q(10,5) = zero; q(11,5) = zero; q(12,5) = zero
+
+    q(1,6) = 5.0_wp * ( -967680.0_wp*x1 - 2903040.0_wp*x2 + &
+                         305821.0_wp ) / 1237164.0_wp
+    q(2,6) = ( 11612160.0_wp*x1 + 33868800.0_wp*x2 - &
+               3884117.0_wp ) / 618582.0_wp
+    q(3,6) = 9.0_wp * ( -806400.0_wp*x1 - 2257920.0_wp*x2 + &
+                         290167.0_wp ) / 206194.0_wp
+    q(4,6) = ( 19353600.0_wp*x1 + 50803200.0_wp*x2 - &
+               7628371.0_wp ) / 618582.0_wp
+    q(5,6) = 35.0_wp * ( -414720.0_wp*x1 - 967680.0_wp*x2 + &
+                          165527.0_wp ) / 1237164.0_wp
+    q(6,6) = zero; q(7,6) = 80640.0_wp*x1 / 103097.0_wp
+    q(8,6) = 80640.0_wp*x2 / 103097.0_wp; q(9,6) = 3072.0_wp / 103097.0_wp
+    q(10,6) = -288.0_wp/103097.0_wp; q(11,6) = zero; q(12,6) = zero
+
+    q(1,7) = 7.0_wp * ( 1244160.0_wp*x1 - 18662400.0_wp*x3 + &
+                        13322233.0_wp ) / 8041092.0_wp
+    q(2,7) = 150.0_wp * ( -24192.0_wp*x1 + 338688.0_wp*x3 - &
+                           240463.0_wp ) / 670091.0_wp
+    q(3,7) = 54.0_wp * ( 134400.0_wp*x1 - 1693440.0_wp*x3 + &
+                         1191611.0_wp ) / 670091.0_wp
+    q(4,7) = 2.0_wp * ( -10886400.0_wp*x1 + 114307200.0_wp*x3 - &
+                         79048289.0_wp ) / 2010273.0_wp
+    q(5,7) = 15.0_wp * ( 967680.0_wp*x1 - 6773760.0_wp*x3 + &
+                         4472029.0_wp ) / 2680364.0_wp
+    q(6,7) = -725760.0_wp*x1 / 670091.0_wp; q(7,7) = zero
+    q(8,7) = 725760.0_wp*x3 / 670091.0_wp; q(9,7) = -145152.0_wp/670091.0_wp
+    q(10,7) = 27648.0_wp/670091.0_wp; q(11,7) = -2592.0_wp/670091.0_wp
+    q(12,7) = zero
+
+    q(1,8) = 3.0_wp * ( 6773760.0_wp*x2 + 33868800.0_wp*x3 - &
+                        24839327.0_wp ) / 20510956.0_wp
+    q(2,8) = ( -152409600.0_wp*x2 - 731566080.0_wp*x3 + &
+                536324953.0_wp ) / 30766434.0_wp
+    q(3,8) = 45.0_wp * ( 2257920.0_wp*x2 + 10160640.0_wp*x3 - &
+                         7439833.0_wp ) / 10255478.0_wp
+    q(4,8) = 75.0_wp * ( -1354752.0_wp*x2 - 5419008.0_wp*x3 + &
+                          3952831.0_wp ) / 10255478.0_wp
+    q(5,8) = ( 304819200.0_wp*x2 + 914457600.0_wp*x3 - &
+               657798011.0_wp ) / 61532868.0_wp
+    q(6,8) = -5080320.0_wp*x2 / 5127739.0_wp
+    q(7,8) = -5080320.0_wp*x3 / 5127739.0_wp; q(8,8) = zero
+    q(9,8) = 4064256.0_wp/5127739.0_wp; q(10,8) = -1016064.0_wp/5127739.0_wp
+    q(11,8) = 193536.0_wp/5127739.0_wp; q(12,8) = -18144.0_wp/5127739.0_wp
+
+    first = .false. 
+  end if
+
+  dd = zero
+  imin = 0
+  imax = -1
+
+  if ( bb(1) == 0 ) then
+    il = 1 + gsize
+  else
+    dd(1:8,1) = q(1:8,1)
+    imin(1) = 1; imax(1) = 8
+
+    dd(1:8,2) = q(1:8,2)
+    imin(2) = 1; imax(2) = 8
+
+    dd(1:8,3) = q(1:8,3)
+    imin(3) = 1; imax(3) = 8
+
+    dd(1:8,4) = q(1:8,4)
+    imin(4) = 1; imax(4) = 8
+
+    dd(1:9,5) = q(1:9,5)
+    imin(5) = 1; imax(5) = 9
+
+    dd(1:10,6) = q(1:10,6)
+    imin(6) = 1; imax(6) = 10
+
+    dd(1:11,7) = q(1:11,7)
+    imin(7) = 1; imax(7) = 11
+
+    dd(1:12,8) = q(1:12,8)
+    imin(8) = 1; imax(8) = 12
+
+    il = 9
+  end if
+  if ( bb(2) == 0 ) then
+    ir = nsize - gsize
+  else
+    dd(nsize-11:nsize,nsize-7) = -q(12:1:-1,8)
+    imin(nsize-7) = nsize-11; imax(nsize-7) = nsize
+
+    dd(nsize-10:nsize,nsize-6) = -q(11:1:-1,7)
+    imin(nsize-6) = nsize-10; imax(nsize-6) = nsize
+
+    dd(nsize-9:nsize,nsize-5) = -q(10:1:-1,6)
+    imin(nsize-5) = nsize-9; imax(nsize-5) = nsize
+
+    dd(nsize-8:nsize,nsize-4) = -q(9:1:-1,5)
+    imin(nsize-4) = nsize-8; imax(nsize-4) = nsize
+
+    dd(nsize-7:nsize,nsize-3) = -q(8:1:-1,4)
+    imin(nsize-3) = nsize-7; imax(nsize-3) = nsize
+
+    dd(nsize-7:nsize,nsize-2) = -q(8:1:-1,3)
+    imin(nsize-2) = nsize-7; imax(nsize-2) = nsize
+
+    dd(nsize-7:nsize,nsize-1) = -q(8:1:-1,2)
+    imin(nsize-1) = nsize-7; imax(nsize-1) = nsize
+
+    dd(nsize-7:nsize,nsize) = -q(8:1:-1,1)
+    imin(nsize) = nsize-7; imax(nsize) = nsize
+
+    ir = nsize - 8
+  end if
+  do i = il, ir
+    dd(i-4:i-1,i) = -a(4:1:-1); dd(i+1:i+4,i) = a(1:4)
+    imin(i) = i-4; imax(i) = i+4
+  end do 
+end subroutine set_coeff_8_4