Added 4-3 Full restricted norm operators. Added parameter to choose the type

of differences (diagonal, full restricted). Added routine to return the
coefficient of the norm at the boundary. Added routine to return the
mask for the norm calculation.


git-svn-id: https://svn.cct.lsu.edu/repos/numrel/LSUThorns/SummationByParts/trunk@10 f69c4107-0314-4c4f-9ad4-17e986b73f4a

1 files changed, 242 insertions, 0 deletions

diff --git a/src/Derivatives_4_3.F90 b/src/Derivatives_4_3.F90
new file mode 100644
index 0000000..011a074
--- /dev/null
+++ b/src/Derivatives_4_3.F90
@@ -0,0 +1,242 @@
+#include "cctk.h"
+#include "cctk_Functions.h"
+#include "cctk_Parameters.h"
+
+subroutine deriv_gf_4_3 ( var, ni, nj, nk, dir, bb, gsize, delta, dvar )
+
+  implicit none
+
+  DECLARE_CCTK_FUNCTIONS
+  DECLARE_CCTK_PARAMETERS
+
+  CCTK_REAL, parameter :: zero = 0.0
+  integer, parameter :: wp = kind(zero)
+  CCTK_INT, intent(IN) :: ni, nj, nk
+  CCTK_REAL, dimension(ni,nj,nk), intent(IN) :: var
+  CCTK_INT, intent(IN) :: dir
+  CCTK_INT, intent(IN) :: bb(2)
+  CCTK_INT, intent(IN) :: gsize
+  CCTK_REAL, intent(IN) :: delta
+  CCTK_REAL, dimension(ni,nj,nk), intent(OUT) :: dvar
+
+  CCTK_REAL, dimension(2), save :: a
+  CCTK_REAL, dimension(7,5), save :: q 
+  CCTK_REAL :: idel
+  CCTK_REAL :: f0, f1, f2, f3
+
+  CCTK_INT :: il, ir, jl, jr, kl, kr
+
+  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
+
+  idel = 1.0_wp / delta
+
+  direction: select case (dir)
+  case (0) direction
+    if ( bb(1) == 0 ) then
+      il = 1 + gsize
+    else
+      dvar(1,:,:) = ( q(1,1) * var(1,:,:) + q(2,1) * var(2,:,:) + &
+                      q(3,1) * var(3,:,:) + q(4,1) * var(4,:,:) ) * idel
+      dvar(2,:,:) = ( q(1,2) * var(1,:,:) + q(2,2) * var(2,:,:) + &
+                      q(3,2) * var(3,:,:) + q(4,2) * var(4,:,:) + &
+                      q(5,2) * var(5,:,:) + q(6,2) * var(6,:,:) ) * idel
+      dvar(3,:,:) = ( q(1,3) * var(1,:,:) + q(2,3) * var(2,:,:) + &
+                      q(3,3) * var(3,:,:) + q(4,3) * var(4,:,:) + &
+                      q(5,3) * var(5,:,:) + q(6,3) * var(6,:,:) ) * idel
+      dvar(4,:,:) = ( q(1,4) * var(1,:,:) + q(2,4) * var(2,:,:) + &
+                      q(3,4) * var(3,:,:) + q(4,4) * var(4,:,:) + &
+                      q(5,4) * var(5,:,:) + q(6,4) * var(6,:,:) + &
+                      q(7,4) * var(7,:,:) ) * idel
+      dvar(5,:,:) = ( q(1,5) * var(1,:,:) + q(2,5) * var(2,:,:) + &
+                      q(3,5) * var(3,:,:) + q(4,5) * var(4,:,:) + &
+                      q(5,5) * var(5,:,:) + q(6,5) * var(6,:,:) + &
+                      q(7,5) * var(7,:,:) ) * idel
+      il = 6
+    end if
+    if ( bb(2) == 0 ) then
+      ir = ni - gsize
+    else
+      dvar(ni-4,:,:) = - ( q(1,5) * var(ni,:,:) + q(2,5) * var(ni-1,:,:) + &
+                           q(3,5) * var(ni-2,:,:) + q(4,5) * var(ni-3,:,:) + &
+                           q(5,5) * var(ni-4,:,:) + q(6,5) * var(ni-5,:,:) + &
+                           q(7,5) * var(ni-6,:,:) ) * idel
+      dvar(ni-3,:,:) = - ( q(1,4) * var(ni,:,:) + q(2,4) * var(ni-1,:,:) + &
+                           q(3,4) * var(ni-2,:,:) + q(4,4) * var(ni-3,:,:) + &
+                           q(5,4) * var(ni-4,:,:) + q(6,4) * var(ni-5,:,:) + &
+                           q(7,4) * var(ni-6,:,:) ) * idel
+      dvar(ni-2,:,:) = - ( q(1,3) * var(ni,:,:) + q(2,3) * var(ni-1,:,:) + &
+                           q(3,3) * var(ni-2,:,:) + q(4,3) * var(ni-3,:,:) + &
+                           q(5,3) * var(ni-4,:,:) + &
+                           q(6,3) * var(ni-5,:,:) ) * idel
+      dvar(ni-1,:,:) = - ( q(1,2) * var(ni,:,:) + q(2,2) * var(ni-1,:,:) + &
+                           q(3,2) * var(ni-2,:,:) + q(4,2) * var(ni-3,:,:) + &
+                           q(5,2) * var(ni-4,:,:) + &
+                           q(6,2) * var(ni-5,:,:) ) * idel
+      dvar(ni,:,:)   = - ( q(1,1) * var(ni,:,:) + q(2,1) * var(ni-1,:,:) + &
+                           q(3,1) * var(ni-2,:,:) + &
+                           q(4,1) * var(ni-3,:,:) ) * idel
+      ir = ni - 5
+    end if
+    dvar(il:ir,:,:) = ( a(1) * ( var(il+1:ir+1,:,:) - &
+                                 var(il-1:ir-1,:,:) ) + &
+                        a(2) * ( var(il+2:ir+2,:,:) - &
+                                 var(il-2:ir-2,:,:) ) ) * idel
+  case (1) direction
+    if ( bb(1) == 0 ) then
+      jl = 1 + gsize
+    else
+      dvar(:,1,:) = ( q(1,1) * var(:,1,:) + q(2,1) * var(:,2,:) + &
+                      q(3,1) * var(:,3,:) + q(4,1) * var(:,4,:) ) * idel
+      dvar(:,2,:) = ( q(1,2) * var(:,1,:) + q(2,2) * var(:,2,:) + &
+                      q(3,2) * var(:,3,:) + q(4,2) * var(:,4,:) + &
+                      q(5,2) * var(:,5,:) + q(6,2) * var(:,6,:) ) * idel
+      dvar(:,3,:) = ( q(1,3) * var(:,1,:) + q(2,3) * var(:,2,:) + &
+                      q(3,3) * var(:,3,:) + q(4,3) * var(:,4,:) + &
+                      q(5,3) * var(:,5,:) + q(6,3) * var(:,6,:) ) * idel
+      dvar(:,4,:) = ( q(1,4) * var(:,1,:) + q(2,4) * var(:,2,:) + &
+                      q(3,4) * var(:,3,:) + q(4,4) * var(:,4,:) + &
+                      q(5,4) * var(:,5,:) + q(6,4) * var(:,6,:) + &
+                      q(7,4) * var(:,7,:) ) * idel
+      dvar(:,5,:) = ( q(1,5) * var(:,1,:) + q(2,5) * var(:,2,:) + &
+                      q(3,5) * var(:,3,:) + q(4,5) * var(:,4,:) + &
+                      q(5,5) * var(:,5,:) + q(6,5) * var(:,6,:) + &
+                      q(7,5) * var(:,7,:) ) * idel
+      jl = 6
+    end if
+    if ( bb(2) == 0 ) then
+      jr = nj - gsize
+    else
+      dvar(:,nj-4,:) = - ( q(1,5) * var(:,nj,:) + q(2,5) * var(:,nj-1,:) + &
+                           q(3,5) * var(:,nj-2,:) + q(4,5) * var(:,nj-3,:) + &
+                           q(5,5) * var(:,nj-4,:) + q(6,5) * var(:,nj-5,:) + &
+                           q(7,5) * var(:,nj-6,:) ) * idel
+      dvar(:,nj-3,:) = - ( q(1,4) * var(:,nj,:) + q(2,4) * var(:,nj-1,:) + &
+                           q(3,4) * var(:,nj-2,:) + q(4,4) * var(:,nj-3,:) + &
+                           q(5,4) * var(:,nj-4,:) + q(6,4) * var(:,nj-5,:) + &
+                           q(7,4) * var(:,nj-6,:) ) * idel
+      dvar(:,nj-2,:) = - ( q(1,3) * var(:,nj,:) + q(2,3) * var(:,nj-1,:) + &
+                           q(3,3) * var(:,nj-2,:) + q(4,3) * var(:,nj-3,:) + &
+                           q(5,3) * var(:,nj-4,:) + &
+                           q(6,3) * var(:,nj-5,:) ) * idel
+      dvar(:,nj-1,:) = - ( q(1,2) * var(:,nj,:) + q(2,2) * var(:,nj-1,:) + &
+                           q(3,2) * var(:,nj-2,:) + q(4,2) * var(:,nj-3,:) + &
+                           q(5,2) * var(:,nj-4,:) + &
+                           q(6,2) * var(:,nj-5,:) ) * idel
+      dvar(:,nj,:)   = - ( q(1,1) * var(:,nj,:) + q(2,1) * var(:,nj-1,:) + &
+                           q(3,1) * var(:,nj-2,:) + &
+                           q(4,1) * var(:,nj-3,:) ) * idel
+      jr = nj - 5
+    end if
+    dvar(:,jl:jr,:) = ( a(1) * ( var(:,jl+1:jr+1,:) - &
+                                 var(:,jl-1:jr-1,:) ) + &
+                        a(2) * ( var(:,jl+2:jr+2,:) - &
+                                 var(:,jl-2:jr-2,:) ) ) * idel
+  case (2) direction
+    if ( bb(1) == 0 ) then
+      kl = 1 + gsize
+    else
+      dvar(:,:,1) = ( q(1,1) * var(:,:,1) + q(2,1) * var(:,:,2) + &
+                      q(3,1) * var(:,:,3) + q(4,1) * var(:,:,4) ) * idel
+      dvar(:,:,2) = ( q(1,2) * var(:,:,1) + q(2,2) * var(:,:,2) + &
+                      q(3,2) * var(:,:,3) + q(4,2) * var(:,:,4) + &
+                      q(5,2) * var(:,:,5) + q(6,2) * var(:,:,6) ) * idel
+      dvar(:,:,3) = ( q(1,3) * var(:,:,1) + q(2,3) * var(:,:,2) + &
+                      q(3,3) * var(:,:,3) + q(4,3) * var(:,:,4) + &
+                      q(5,3) * var(:,:,5) + q(6,3) * var(:,:,6) ) * idel
+      dvar(:,:,4) = ( q(1,4) * var(:,:,1) + q(2,4) * var(:,:,2) + &
+                      q(3,4) * var(:,:,3) + q(4,4) * var(:,:,4) + &
+                      q(5,4) * var(:,:,5) + q(6,4) * var(:,:,6) + &
+                      q(7,4) * var(:,:,7) ) * idel
+      dvar(:,:,5) = ( q(1,5) * var(:,:,1) + q(2,5) * var(:,:,2) + &
+                      q(3,5) * var(:,:,3) + q(4,5) * var(:,:,4) + &
+                      q(5,5) * var(:,:,5) + q(6,5) * var(:,:,6) + &
+                      q(7,5) * var(:,:,7) ) * idel
+      kl = 6
+    end if
+    if ( bb(2) == 0 ) then
+      kr = nk - gsize
+    else 
+      dvar(:,:,nk-4) = - ( q(1,5) * var(:,:,nk) + q(2,5) * var(:,:,nk-1) + &
+                           q(3,5) * var(:,:,nk-2) + q(4,5) * var(:,:,nk-3) + &
+                           q(5,5) * var(:,:,nk-4) + q(6,5) * var(:,:,nk-5) + &
+                           q(7,5) * var(:,:,nk-6) ) * idel
+      dvar(:,:,nk-3) = - ( q(1,4) * var(:,:,nk) + q(2,4) * var(:,:,nk-1) + &
+                           q(3,4) * var(:,:,nk-2) + q(4,4) * var(:,:,nk-3) + &
+                           q(5,4) * var(:,:,nk-4) + q(6,4) * var(:,:,nk-5) + &
+                           q(7,4) * var(:,:,nk-6) ) * idel
+      dvar(:,:,nk-2) = - ( q(1,3) * var(:,:,nk) + q(2,3) * var(:,:,nk-1) + &
+                           q(3,3) * var(:,:,nk-2) + q(4,3) * var(:,:,nk-3) + &
+                           q(5,3) * var(:,:,nk-4) + &
+                           q(6,3) * var(:,:,nk-5) ) * idel
+      dvar(:,:,nk-1) = - ( q(1,2) * var(:,:,nk) + q(2,2) * var(:,:,nk-1) + &
+                           q(3,2) * var(:,:,nk-2) + q(4,2) * var(:,:,nk-3) + &
+                           q(5,2) * var(:,:,nk-4) + &
+                           q(6,2) * var(:,:,nk-5) ) * idel
+      dvar(:,:,nk)   = - ( q(1,1) * var(:,:,nk) + q(2,1) * var(:,:,nk-1) + &
+                           q(3,1) * var(:,:,nk-2) + &
+                           q(4,1) * var(:,:,nk-3) ) * idel
+      kr = nk - 5
+    end if
+    dvar(:,:,kl:kr) = ( a(1) * ( var(:,:,kl+1:kr+1) - &
+                                 var(:,:,kl-1:kr-1) ) + &
+                        a(2) * ( var(:,:,kl+2:kr+2) - &
+                                 var(:,:,kl-2:kr-2) ) ) * idel
+  end select direction
+end subroutine deriv_gf_4_3