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, 133 insertions, 0 deletions

diff --git a/src/Coefficients_4_3.F90 b/src/Coefficients_4_3.F90
new file mode 100644
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+++ b/src/Coefficients_4_3.F90
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+#include "cctk.h"
+#include "cctk_Functions.h"
+#include "cctk_Parameters.h"
+
+subroutine set_coeff_4_3 ( 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(2), save :: a
+  CCTK_REAL, dimension(7,5), save :: q 
+  CCTK_REAL :: f0, f1, f2, f3
+
+  CCTK_INT :: i, il, ir
+
+  logical, save :: first = .true.
+
+  if ( first ) then
+    a(1) = 2.0_wp/3.0_wp; a(2) = -1.0_wp/12.0_wp
+
+    f0 = sqrt(26116897.0_wp)
+    f1 = -56764003702447356523.0_wp + 8154993476273221.0_wp * f0
+    f2 = -55804550303.0_wp + 9650225.0_wp * f0
+    f3 = 3262210757.0_wp + 271861.0_wp * f0
+
+    q(1,1) = -11._wp/6.0_wp; q(2,1) = 3.0_wp
+    q(3,1) = -3.0_wp/2.0_wp; q(4,1) = 1.0_wp/3.0_wp
+    q(5,1) = zero; q(6,1) = zero; q(7,1) = zero
+
+    q(1,2) =  -24.0_wp * ( -779042810827742869.0_wp + &
+                            104535124033147.0_wp * f0 ) / f1
+    q(2,2) = -( -176530817412806109689.0_wp + &
+                 29768274816875927.0_wp * f0 ) / ( 6.0_wp * f1 )
+    q(3,2) = 343.0_wp * ( -171079116122226871.0_wp + &
+                           27975630462649.0_wp * f0 ) / f1
+    q(4,2) = -3.0_wp * ( -7475554291248533227.0_wp + &
+                          1648464218793925.0_wp * f0 ) / ( 2.0_wp * f1 )
+    q(5,2) = ( -2383792768180030915.0_wp + &
+                1179620587812973.0_wp * f0 ) / ( 3.0_wp * f1 )
+    q(6,2) = -1232.0_wp * ( -115724529581315.0_wp + 37280576429.0_wp * f0 ) / f1
+    q(7,2) = zero
+
+    q(1,3) = -12.0_wp * ( -380966843.0_wp + 86315.0_wp * f0 ) / f2
+    q(2,3) = ( 5024933015.0_wp + 2010631.0_wp * f0 ) / ( 3.0_wp * f2 )
+    q(3,3) = -231.0_wp * ( -431968921.0_wp + 86711.0_wp * f0 ) / ( 2.0_wp * f2 )
+    q(4,3) = ( -65931742559.0_wp + 12256337.0_wp * f0 ) / f2
+    q(5,3) = -( -50597298167.0_wp + 9716873.0_wp * f0 ) / ( 6.0_wp * f2 )
+    q(6,3) = -88.0_wp * ( -15453061.0_wp + 2911.0_wp * f0 ) / f2
+    q(7,3) = zero
+
+    q(1,4) = 48.0_wp * ( -56020909845192541.0_wp + &
+                          9790180507043.0_wp * f0 ) / f1
+    q(2,4) = ( -9918249049237586011.0_wp + &
+                1463702013196501.0_wp * f0 ) / ( 6.0_wp * f1)
+    q(3,4) = -13.0_wp * ( -4130451756851441723.0_wp + &
+                           664278707201077.0_wp * f0 ) / f1
+    q(4,4) = 3.0_wp * ( -26937108467782666617.0_wp + &
+                         5169063172799767.0_wp * f0 ) / ( 2.0_wp * f1 )
+    q(5,4) = -( 6548308508012371315.0_wp + &
+                3968886380989379.0_wp * f0 ) / ( 3.0_wp * f1 )
+    q(6,4) = 88.0_wp * ( -91337851897923397.0_wp + &
+                          19696768305507.0_wp * f0 ) / f1
+    q(7,4) = 242.0_wp * ( -120683.0_wp + 15.0_wp * f0 ) / f3
+
+    q(1,5) = 264.0_wp * ( -120683.0_wp + 15.0_wp * f0 ) / f3
+    q(2,5) = ( -43118111.0_wp + 23357.0_wp * f0 ) / ( 3.0_wp * f3 )
+    q(3,5) = -47.0_wp * ( -28770085.0_wp + 2259.0_wp * f0 ) / ( 2.0_wp * f3 ) 
+    q(4,5) = -3.0_wp * ( 1003619433.0_wp + 11777.0_wp * f0 ) / f3
+    q(5,5) = -11.0_wp * ( -384168269.0_wp + 65747.0_wp * f0 ) / ( 6.0_wp * f3 )
+    q(6,5) = 22.0_wp * ( 87290207.0_wp + 10221.0_wp * f0 ) / f3
+    q(7,5) = -66.0_wp * ( 3692405.0_wp + 419.0_wp * f0 ) / f3
+    first = .false.
+  end if
+
+  dd = zero
+  imin = 0
+  imax = -1
+
+  if ( bb(1) == 0 ) then
+    il = 1 + gsize
+  else
+    dd(1:4,1) = q(1:4,1)
+    imin(1) = 1; imax(1) = 4
+
+    dd(1:6,2) = q(1:6,2)
+    imin(2) = 1; imax(2) = 6
+
+    dd(1:6,3) = q(1:6,3)
+    imin(3) = 1; imax(3) = 6
+
+    dd(1:7,4) = q(1:7,4)
+    imin(4) = 1; imax(4) = 7
+
+    dd(1:7,5) = q(1:7,5)
+    imin(5) = 1; imax(5) = 7
+
+    il = 6
+  end if
+  if ( bb(2) == 0 ) then
+    ir = nsize - gsize
+  else
+    dd(nsize-6:nsize,nsize-4) = -q(7:1:-1,5)
+    imin(nsize-4) = nsize-6; imax(nsize-4) = nsize
+
+    dd(nsize-6:nsize,nsize-3) = -q(7:1:-1,4)
+    imin(nsize-3) = nsize-6; imax(nsize-3) = nsize
+   
+    dd(nsize-5:nsize,nsize-2) = -q(6:1:-1,3)
+    imin(nsize-2) = nsize-5; imax(nsize-2) = nsize
+
+    dd(nsize-5:nsize,nsize-1) = -q(6:1:-1,2)
+    imin(nsize-1) = nsize-5; imax(nsize-1) = nsize
+
+    dd(nsize-3:nsize,nsize) = -q(4:1:-1,1)
+    imin(nsize) = nsize-3; imax(nsize) = nsize
+
+    ir = nsize - 5
+  end if
+  do i = il, ir
+    dd(i-2:i-1,i) = -a(2:1:-1); dd(i+1:i+2,i) = a(1:2)
+    imin(i) = i-2; imax(i) = i+2
+  end do
+end subroutine set_coeff_4_3