Introduce a new kind of dissipation operators. Kreiss-Oliger type dissipation

operator suitably modified near the boundary. Since the dissipation operator
in the interior uses a stencil that is one point wider than the derivative
operator, an additional check on the number of ghostzones in multi processor
runs have been added. Only implemented for the 8-4 and optimized 6-5
operators.


git-svn-id: https://svn.cct.lsu.edu/repos/numrel/LSUThorns/SummationByParts/trunk@53 f69c4107-0314-4c4f-9ad4-17e986b73f4a

6 files changed, 1319 insertions, 4 deletions

diff --git a/param.ccl b/param.ccl
index 4e3fda5..ff72a06 100644
--- a/param.ccl
+++ b/param.ccl
@@ -27,6 +27,12 @@ BOOLEAN scale_with_h "Should we scale the dissipation with the grid spacing h"
 {
 } "no"
 
+KEYWORD dissipation_type "Type of dissipation operator" STEERABLE=always
+{
+  "Mattson-Svard-Nordstrom" :: "Mattson, Svaerd and Nordstroem type"
+  "Kreiss-Oliger" :: "Kreiss-Oliger modified near the boundaries"
+} "Mattson-Svard-Nordstrom"
+
 REAL epsdis "Dissipation strength" STEERABLE=always
 {
   *:* :: "Values typical between 0 and 1"
diff --git a/src/CheckGridSizes.F90 b/src/CheckGridSizes.F90
index 3240f6a..b6af08e 100644
--- a/src/CheckGridSizes.F90
+++ b/src/CheckGridSizes.F90
@@ -25,6 +25,16 @@ subroutine SBP_CheckGridSizes(CCTK_ARGUMENTS)
   bc(2) = cctk_bbox(3)+cctk_bbox(4)+1    ! 1 processor boundary -> bc = 2
   bc(3) = cctk_bbox(5)+cctk_bbox(6)+1    ! 2 processor boundaries -> bc = 1
 
+  if ( ( use_dissipation > 0 ) .and. &
+       ( CCTK_EQUALS(dissipation_type,"Kreiss-Oliger" ) ) .and. &
+       ( any (cctk_nghostzones < order / 2 + 1) ) .and. &
+       ( CCTK_nProcs(cctkGH) > 1 ) ) then
+    write(info_message,'(a22,i1,a13,i2,a32)') 'You need ghostsize >= ', &
+                                    order/2+1, ' to run with ', order+2, &
+                                    ' order Kreiss-Oliger dissipation'
+    call CCTK_WARN(0,info_message) 
+  end if
+
   if ( any (cctk_nghostzones < order / 2) .and. CCTK_nProcs(cctkGH) > 1 )  then
     write(info_message,'(a22,i1,a13,i1,a25)') 'You need ghostsize >= ', &
                                     order/2, ' to run with ', order, &
diff --git a/src/Dissipation_6_5_min_err_coeff_alt.F90 b/src/Dissipation_6_5_min_err_coeff_alt.F90
new file mode 100644
index 0000000..102ac5d
--- /dev/null
+++ b/src/Dissipation_6_5_min_err_coeff_alt.F90
@@ -0,0 +1,753 @@
+! $Header$
+
+#include "cctk.h"
+#include "cctk_Parameters.h"
+#include "cctk_Functions.h"
+
+
+subroutine dissipation_6_5_alt (var, lsh, gsh, lbnd, bb, gsize, &
+                                               delta, epsdisl, dfl, rhs)
+
+  implicit none
+
+  DECLARE_CCTK_PARAMETERS
+  DECLARE_CCTK_FUNCTIONS
+
+  CCTK_INT, dimension(3), intent(in) ::  lsh, gsh, lbnd
+  CCTK_INT :: ni, nj, nk
+  CCTK_REAL, dimension(lsh(1),lsh(2),lsh(3)), intent(in) :: var
+  CCTK_REAL, dimension(lsh(1),lsh(2),lsh(3)), intent(inout) :: rhs
+  CCTK_INT, dimension(6), intent(in) :: bb
+  CCTK_INT, dimension(3), intent(in) :: gsize
+  CCTK_REAL, dimension(3), intent(in) :: delta
+  CCTK_REAL, intent(in) :: epsdisl, dfl
+
+  CCTK_REAL :: zero = 0.0
+  integer, parameter :: wp = kind(zero)
+  integer :: i, j, k, center
+  CCTK_REAL, dimension(:,:), allocatable :: a, d, b, h, tmp
+  CCTK_REAL :: idel
+
+  CCTK_INT :: il, ir, jl, jr, kl, kr
+
+  ni = lsh(1); nj = lsh(2); nk = lsh(3)
+
+  allocate ( a(ni,ni), d(ni,ni), b(ni,ni), h(ni,ni), tmp(ni,ni) )
+  a = zero; d = zero; b = zero; h = zero; tmp = zero
+
+  call set_bmatrix ( b, bb(1:2), lsh(1), gsh(1), lbnd(1), delta(1), dfl )
+
+  call set_hmatrix ( h, bb(1:2) )
+
+  call set_dmatrix ( d, bb(1:2) )
+
+  a = -transpose ( matmul ( h, matmul ( transpose(d), matmul ( b, d ) ) ) )
+
+  idel = epsdisl /  ( 256.0_wp * delta(1) )
+
+  if ( bb(1) == 0 ) then
+
+    il = 1 + gsize(1)
+
+  else
+
+    rhs(1,:,:) = rhs(1,:,:) + &
+                 ( a(1,1) * var(1,:,:) + a(2,1) * var(2,:,:) + &
+                   a(3,1) * var(3,:,:) + a(4,1) * var(4,:,:) + &
+                   a(5,1) * var(5,:,:) ) * idel
+    rhs(2,:,:) = rhs(2,:,:) + &
+                 ( a(1,2) * var(1,:,:) + a(2,2) * var(2,:,:) + &
+                   a(3,2) * var(3,:,:) + a(4,2) * var(4,:,:) + &
+                   a(5,2) * var(5,:,:) + a(6,2) * var(6,:,:) + &
+                   a(7,2) * var(7,:,:) + a(8,2) * var(8,:,:) + &
+                   a(9,2) * var(9,:,:) + a(10,2) * var(10,:,:) + &
+                   a(11,2) * var(11,:,:) ) * idel
+    rhs(3,:,:) = rhs(3,:,:) + &
+                 ( a(1,3) * var(1,:,:) + a(2,3) * var(2,:,:) + &
+                   a(3,3) * var(3,:,:) + a(4,3) * var(4,:,:) + &
+                   a(5,3) * var(5,:,:) + a(6,3) * var(6,:,:) + &
+                   a(7,3) * var(7,:,:) + a(8,3) * var(8,:,:) + &
+                   a(9,3) * var(9,:,:) + a(10,3) * var(10,:,:) + &
+                   a(11,3) * var(11,:,:) ) * idel
+    rhs(4,:,:) = rhs(4,:,:) + &
+                 ( a(1,4) * var(1,:,:) + a(2,4) * var(2,:,:) + &
+                   a(3,4) * var(3,:,:) + a(4,4) * var(4,:,:) + &
+                   a(5,4) * var(5,:,:) + a(6,4) * var(6,:,:) + &
+                   a(7,4) * var(7,:,:) + a(8,4) * var(8,:,:) + &
+                   a(9,4) * var(9,:,:) + a(10,4) * var(10,:,:) + &
+                   a(11,4) * var(11,:,:) ) * idel
+    rhs(5,:,:) = rhs(5,:,:) + &
+                 ( a(1,5) * var(1,:,:) + a(2,5) * var(2,:,:) + &
+                   a(3,5) * var(3,:,:) + a(4,5) * var(4,:,:) + &
+                   a(5,5) * var(5,:,:) + a(6,5) * var(6,:,:) + &
+                   a(7,5) * var(7,:,:) + a(8,5) * var(8,:,:) + &
+                   a(9,5) * var(9,:,:) + a(10,5) * var(10,:,:) + &
+                   a(11,5) * var(11,:,:) ) * idel
+    rhs(6,:,:) = rhs(6,:,:) + &
+                 ( a(1,6) * var(1,:,:) + a(2,6) * var(2,:,:) + &
+                   a(3,6) * var(3,:,:) + a(4,6) * var(4,:,:) + &
+                   a(5,6) * var(5,:,:) + a(6,6) * var(6,:,:) + &
+                   a(7,6) * var(7,:,:) + a(8,6) * var(8,:,:) + &
+                   a(9,6) * var(9,:,:) + a(10,6) * var(10,:,:) + &
+                   a(11,6) * var(11,:,:) ) * idel
+    rhs(7,:,:) = rhs(7,:,:) + &
+                 ( a(1,7) * var(1,:,:) + a(2,7) * var(2,:,:) + &
+                   a(3,7) * var(3,:,:) + a(4,7) * var(4,:,:) + &
+                   a(5,7) * var(5,:,:) + a(6,7) * var(6,:,:) + &
+                   a(7,7) * var(7,:,:) + a(8,7) * var(8,:,:) + &
+                   a(9,7) * var(9,:,:) + a(10,7) * var(10,:,:) + &
+                   a(11,7) * var(11,:,:) ) * idel
+
+    il = 8
+
+  end if
+
+  if ( bb(2) == 0 ) then
+
+    ir = ni - gsize(1)
+
+  else
+
+    rhs(ni-6,:,:) = rhs(ni-6,:,:) + &
+                    ( a(ni-10,ni-6) * var(ni-10,:,:) + &
+                      a(ni-9,ni-6) * var(ni-9,:,:) + &
+                      a(ni-8,ni-6) * var(ni-8,:,:) + &
+                      a(ni-7,ni-6) * var(ni-7,:,:) + &
+                      a(ni-6,ni-6) * var(ni-6,:,:) + &
+                      a(ni-5,ni-6) * var(ni-5,:,:) + &
+                      a(ni-4,ni-6) * var(ni-4,:,:) + &
+                      a(ni-3,ni-6) * var(ni-3,:,:) + &
+                      a(ni-2,ni-6) * var(ni-2,:,:) + &
+                      a(ni-1,ni-6) * var(ni-1,:,:) + &
+                      a(ni,ni-6) * var(ni,:,:) ) * idel
+    rhs(ni-5,:,:) = rhs(ni-5,:,:) + &
+                    ( a(ni-10,ni-5) * var(ni-10,:,:) + &
+                      a(ni-9,ni-5) * var(ni-9,:,:) + &
+                      a(ni-8,ni-5) * var(ni-8,:,:) + &
+                      a(ni-7,ni-5) * var(ni-7,:,:) + &
+                      a(ni-6,ni-5) * var(ni-6,:,:) + &
+                      a(ni-5,ni-5) * var(ni-5,:,:) + &
+                      a(ni-4,ni-5) * var(ni-4,:,:) + &
+                      a(ni-3,ni-5) * var(ni-3,:,:) + &
+                      a(ni-2,ni-5) * var(ni-2,:,:) + &
+                      a(ni-1,ni-5) * var(ni-1,:,:) + &
+                      a(ni,ni-5) * var(ni,:,:) ) * idel
+    rhs(ni-4,:,:) = rhs(ni-4,:,:) + &
+                    ( a(ni-10,ni-4) * var(ni-10,:,:) + &
+                      a(ni-9,ni-4) * var(ni-9,:,:) + &
+                      a(ni-8,ni-4) * var(ni-8,:,:) + &
+                      a(ni-7,ni-4) * var(ni-7,:,:) + &
+                      a(ni-6,ni-4) * var(ni-6,:,:) + &
+                      a(ni-5,ni-4) * var(ni-5,:,:) + &
+                      a(ni-4,ni-4) * var(ni-4,:,:) + &
+                      a(ni-3,ni-4) * var(ni-3,:,:) + &
+                      a(ni-2,ni-4) * var(ni-2,:,:) + &
+                      a(ni-1,ni-4) * var(ni-1,:,:) + &
+                      a(ni,ni-4) * var(ni,:,:) ) * idel
+    rhs(ni-3,:,:) = rhs(ni-3,:,:) + &
+                    ( a(ni-10,ni-3) * var(ni-10,:,:) + &
+                      a(ni-9,ni-3) * var(ni-9,:,:) + &
+                      a(ni-8,ni-3) * var(ni-8,:,:) + &
+                      a(ni-7,ni-3) * var(ni-7,:,:) + &
+                      a(ni-6,ni-3) * var(ni-6,:,:) + &
+                      a(ni-5,ni-3) * var(ni-5,:,:) + &
+                      a(ni-4,ni-3) * var(ni-4,:,:) + &
+                      a(ni-3,ni-3) * var(ni-3,:,:) + &
+                      a(ni-2,ni-3) * var(ni-2,:,:) + &
+                      a(ni-1,ni-3) * var(ni-1,:,:) + &
+                      a(ni,ni-3) * var(ni,:,:) ) * idel
+    rhs(ni-2,:,:) = rhs(ni-2,:,:) + &
+                    ( a(ni-10,ni-2) * var(ni-10,:,:) + &
+                      a(ni-9,ni-2) * var(ni-9,:,:) + &
+                      a(ni-8,ni-2) * var(ni-8,:,:) + &
+                      a(ni-7,ni-2) * var(ni-7,:,:) + &
+                      a(ni-6,ni-2) * var(ni-6,:,:) + &
+                      a(ni-5,ni-2) * var(ni-5,:,:) + &
+                      a(ni-4,ni-2) * var(ni-4,:,:) + &
+                      a(ni-3,ni-2) * var(ni-3,:,:) + &
+                      a(ni-2,ni-2) * var(ni-2,:,:) + &
+                      a(ni-1,ni-2) * var(ni-1,:,:) + &
+                      a(ni,ni-2) * var(ni,:,:) ) * idel
+    rhs(ni-1,:,:) = rhs(ni-1,:,:) + &
+                    ( a(ni-10,ni-1) * var(ni-10,:,:) + &
+                      a(ni-9,ni-1) * var(ni-9,:,:) + &
+                      a(ni-8,ni-1) * var(ni-8,:,:) + &
+                      a(ni-7,ni-1) * var(ni-7,:,:) + &
+                      a(ni-6,ni-1) * var(ni-6,:,:) + &
+                      a(ni-5,ni-1) * var(ni-5,:,:) + &
+                      a(ni-4,ni-1) * var(ni-4,:,:) + &
+                      a(ni-3,ni-1) * var(ni-3,:,:) + &
+                      a(ni-2,ni-1) * var(ni-2,:,:) + &
+                      a(ni-1,ni-1) * var(ni-1,:,:) + &
+                      a(ni,ni-1) * var(ni,:,:) ) * idel
+    rhs(ni,:,:)   = rhs(ni,:,:) + &
+                    ( a(ni-4,ni) * var(ni-4,:,:) + &
+                      a(ni-3,ni) * var(ni-3,:,:) + &
+                      a(ni-2,ni) * var(ni-2,:,:) + &
+                      a(ni-1,ni) * var(ni-1,:,:) + &
+                      a(ni,ni) * var(ni,:,:) ) * idel
+
+    ir = ni - 7
+
+  end if
+
+  do i = il, ir
+
+    rhs(i,:,:) = rhs(i,:,:) + &
+                   ( a(i-4,i) * var(i-4,:,:) + &
+                     a(i-3,i) * var(i-3,:,:) + &
+                     a(i-2,i) * var(i-2,:,:) + &
+                     a(i-1,i) * var(i-1,:,:) + &
+                     a(i,i) * var(i,:,:) + &
+                     a(i+1,i) * var(i+1,:,:) + &
+                     a(i+2,i) * var(i+2,:,:) + &
+                     a(i+3,i) * var(i+3,:,:) + &
+                     a(i+4,i) * var(i+4,:,:) ) * idel
+
+  end do
+
+  deallocate ( a, d, b, h, tmp )
+
+  allocate ( a(nj,nj), d(nj,nj), b(nj,nj), h(nj,nj), tmp(nj,nj) )
+  a = zero; d = zero; b = zero; h = zero;
+
+  call set_bmatrix ( b, bb(3:4), lsh(2), gsh(2), lbnd(2), delta(2), dfl )
+  
+  call set_hmatrix ( h, bb(3:4) )
+
+  call set_dmatrix ( d, bb(3:4) )
+
+  a = -transpose ( matmul ( h, matmul ( transpose(d), matmul ( b, d ) ) ) )
+
+  idel = epsdisl /  ( 256.0_wp * delta(2) )
+ 
+   if ( bb(3) == 0 ) then
+
+     jl = 1 + gsize(2)
+
+   else
+
+    rhs(:,1,:) = rhs(:,1,:) + &
+                 ( a(1,1) * var(:,1,:) + a(2,1) * var(:,2,:) + &
+                   a(3,1) * var(:,3,:) + a(4,1) * var(:,4,:) + &
+                   a(5,1) * var(:,5,:) ) * idel
+    rhs(:,2,:) = rhs(:,2,:) + &
+                 ( a(1,2) * var(:,1,:) + a(2,2) * var(:,2,:) + &
+                   a(3,2) * var(:,3,:) + a(4,2) * var(:,4,:) + &
+                   a(5,2) * var(:,5,:) + a(6,2) * var(:,6,:) + &
+                   a(7,2) * var(:,7,:) + a(8,2) * var(:,8,:) + &
+                   a(9,2) * var(:,9,:) + a(10,2) * var(:,10,:) + &
+                   a(11,2) * var(:,11,:) ) * idel
+    rhs(:,3,:) = rhs(:,3,:) + &
+                 ( a(1,3) * var(:,1,:) + a(2,3) * var(:,2,:) + &
+                   a(3,3) * var(:,3,:) + a(4,3) * var(:,4,:) + &
+                   a(5,3) * var(:,5,:) + a(6,3) * var(:,6,:) + &
+                   a(7,3) * var(:,7,:) + a(8,3) * var(:,8,:) + &
+                   a(9,3) * var(:,9,:) + a(10,3) * var(:,10,:) + &
+                   a(11,3) * var(:,11,:) ) * idel
+    rhs(:,4,:) = rhs(:,4,:) + &
+                 ( a(1,4) * var(:,1,:) + a(2,4) * var(:,2,:) + &
+                   a(3,4) * var(:,3,:) + a(4,4) * var(:,4,:) + &
+                   a(5,4) * var(:,5,:) + a(6,4) * var(:,6,:) + &
+                   a(7,4) * var(:,7,:) + a(8,4) * var(:,8,:) + &
+                   a(9,4) * var(:,9,:) + a(10,4) * var(:,10,:) + &
+                   a(11,4) * var(:,11,:) ) * idel
+    rhs(:,5,:) = rhs(:,5,:) + &
+                 ( a(1,5) * var(:,1,:) + a(2,5) * var(:,2,:) + &
+                   a(3,5) * var(:,3,:) + a(4,5) * var(:,4,:) + &
+                   a(5,5) * var(:,5,:) + a(6,5) * var(:,6,:) + &
+                   a(7,5) * var(:,7,:) + a(8,5) * var(:,8,:) + &
+                   a(9,5) * var(:,9,:) + a(10,5) * var(:,10,:) + &
+                   a(11,5) * var(:,11,:) ) * idel
+    rhs(:,6,:) = rhs(:,6,:) + &
+                 ( a(1,6) * var(:,1,:) + a(2,6) * var(:,2,:) + &
+                   a(3,6) * var(:,3,:) + a(4,6) * var(:,4,:) + &
+                   a(5,6) * var(:,5,:) + a(6,6) * var(:,6,:) + &
+                   a(7,6) * var(:,7,:) + a(8,6) * var(:,8,:) + &
+                   a(9,6) * var(:,9,:) + a(10,6) * var(:,10,:) + &
+                   a(11,6) * var(:,11,:) ) * idel
+    rhs(:,7,:) = rhs(:,7,:) + &
+                 ( a(1,7) * var(:,1,:) + a(2,7) * var(:,2,:) + &
+                   a(3,7) * var(:,3,:) + a(4,7) * var(:,4,:) + &
+                   a(5,7) * var(:,5,:) + a(6,7) * var(:,6,:) + &
+                   a(7,7) * var(:,7,:) + a(8,7) * var(:,8,:) + &
+                   a(9,7) * var(:,9,:) + a(10,7) * var(:,10,:) + &
+                   a(11,7) * var(:,11,:) ) * idel
+
+    jl = 8
+
+  end if
+
+  if ( bb(4) == 0 ) then
+
+    jr = nj - gsize(2)
+
+  else
+
+    rhs(:,nj-6,:) = rhs(:,nj-6,:) + &
+                    ( a(nj-10,nj-6) * var(:,nj-10,:) + &
+                      a(nj-9,nj-6) * var(:,nj-9,:) + &
+                      a(nj-8,nj-6) * var(:,nj-8,:) + &
+                      a(nj-7,nj-6) * var(:,nj-7,:) + &
+                      a(nj-6,nj-6) * var(:,nj-6,:) + &
+                      a(nj-5,nj-6) * var(:,nj-5,:) + &
+                      a(nj-4,nj-6) * var(:,nj-4,:) + &
+                      a(nj-3,nj-6) * var(:,nj-3,:) + &
+                      a(nj-2,nj-6) * var(:,nj-2,:) + &
+                      a(nj-1,nj-6) * var(:,nj-1,:) + &
+                      a(nj,nj-6) * var(:,nj,:) ) * idel
+    rhs(:,nj-5,:) = rhs(:,nj-5,:) + &
+                    ( a(nj-10,nj-5) * var(:,nj-10,:) + &
+                      a(nj-9,nj-5) * var(:,nj-9,:) + &
+                      a(nj-8,nj-5) * var(:,nj-8,:) + &
+                      a(nj-7,nj-5) * var(:,nj-7,:) + &
+                      a(nj-6,nj-5) * var(:,nj-6,:) + &
+                      a(nj-5,nj-5) * var(:,nj-5,:) + &
+                      a(nj-4,nj-5) * var(:,nj-4,:) + &
+                      a(nj-3,nj-5) * var(:,nj-3,:) + &
+                      a(nj-2,nj-5) * var(:,nj-2,:) + &
+                      a(nj-1,nj-5) * var(:,nj-1,:) + &
+                      a(nj,nj-5) * var(:,nj,:) ) * idel
+    rhs(:,nj-4,:) = rhs(:,nj-4,:) + &
+                    ( a(nj-10,nj-4) * var(:,nj-10,:) + &
+                      a(nj-9,nj-4) * var(:,nj-9,:) + &
+                      a(nj-8,nj-4) * var(:,nj-8,:) + &
+                      a(nj-7,nj-4) * var(:,nj-7,:) + &
+                      a(nj-6,nj-4) * var(:,nj-6,:) + &
+                      a(nj-5,nj-4) * var(:,nj-5,:) + &
+                      a(nj-4,nj-4) * var(:,nj-4,:) + &
+                      a(nj-3,nj-4) * var(:,nj-3,:) + &
+                      a(nj-2,nj-4) * var(:,nj-2,:) + &
+                      a(nj-1,nj-4) * var(:,nj-1,:) + &
+                      a(nj,nj-4) * var(:,nj,:) ) * idel
+    rhs(:,nj-3,:) = rhs(:,nj-3,:) + &
+                    ( a(nj-10,nj-3) * var(:,nj-10,:) + &
+                      a(nj-9,nj-3) * var(:,nj-9,:) + &
+                      a(nj-8,nj-3) * var(:,nj-8,:) + &
+                      a(nj-7,nj-3) * var(:,nj-7,:) + &
+                      a(nj-6,nj-3) * var(:,nj-6,:) + &
+                      a(nj-5,nj-3) * var(:,nj-5,:) + &
+                      a(nj-4,nj-3) * var(:,nj-4,:) + &
+                      a(nj-3,nj-3) * var(:,nj-3,:) + &
+                      a(nj-2,nj-3) * var(:,nj-2,:) + &
+                      a(nj-1,nj-3) * var(:,nj-1,:) + &
+                      a(nj,nj-3) * var(:,nj,:) ) * idel
+    rhs(:,nj-2,:) = rhs(:,nj-2,:) + &
+                    ( a(nj-10,nj-2) * var(:,nj-10,:) + &
+                      a(nj-9,nj-2) * var(:,nj-9,:) + &
+                      a(nj-8,nj-2) * var(:,nj-8,:) + &
+                      a(nj-7,nj-2) * var(:,nj-7,:) + &
+                      a(nj-6,nj-2) * var(:,nj-6,:) + &
+                      a(nj-5,nj-2) * var(:,nj-5,:) + &
+                      a(nj-4,nj-2) * var(:,nj-4,:) + &
+                      a(nj-3,nj-2) * var(:,nj-3,:) + &
+                      a(nj-2,nj-2) * var(:,nj-2,:) + &
+                      a(nj-1,nj-2) * var(:,nj-1,:) + &
+                      a(nj,nj-2) * var(:,nj,:) ) * idel
+    rhs(:,nj-1,:) = rhs(:,nj-1,:) + &
+                    ( a(nj-10,nj-1) * var(:,nj-10,:) + &
+                      a(nj-9,nj-1) * var(:,nj-9,:) + &
+                      a(nj-8,nj-1) * var(:,nj-8,:) + &
+                      a(nj-7,nj-1) * var(:,nj-7,:) + &
+                      a(nj-6,nj-1) * var(:,nj-6,:) + &
+                      a(nj-5,nj-1) * var(:,nj-5,:) + &
+                      a(nj-4,nj-1) * var(:,nj-4,:) + &
+                      a(nj-3,nj-1) * var(:,nj-3,:) + &
+                      a(nj-2,nj-1) * var(:,nj-2,:) + &
+                      a(nj-1,nj-1) * var(:,nj-1,:) + &
+                      a(nj,nj-1) * var(:,nj,:) ) * idel
+    rhs(:,nj,:)   = rhs(:,nj,:) + &
+                    ( a(nj-4,nj) * var(:,nj-4,:) + &
+                      a(nj-3,nj) * var(:,nj-3,:) + &
+                      a(nj-2,nj) * var(:,nj-2,:) + &
+                      a(nj-1,nj) * var(:,nj-1,:) + &
+                      a(nj,nj) * var(:,nj,:) ) * idel
+
+    jr = nj - 7
+
+  end if
+
+  do j = jl, jr
+
+    rhs(:,j,:) = rhs(:,j,:) + &
+                   ( a(j-4,j) * var(:,j-4,:) + &
+                     a(j-3,j) * var(:,j-3,:) + &
+                     a(j-2,j) * var(:,j-2,:) + &
+                     a(j-1,j) * var(:,j-1,:) + &
+                     a(j,j) * var(:,j,:) + &
+                     a(j+1,j) * var(:,j+1,:) + &
+                     a(j+2,j) * var(:,j+2,:) + &
+                     a(j+3,j) * var(:,j+3,:) + &
+                     a(j+4,j) * var(:,j+4,:) ) * idel
+
+  end do
+
+  deallocate ( a, d, b, h, tmp )
+
+  allocate ( a(nk,nk), d(nk,nk), b(nk,nk), h(nk,nk), tmp(nk,nk) )
+  a = zero; d = zero; b = zero; h = zero; tmp = zero
+
+  call set_bmatrix ( b, bb(5:6), lsh(3), gsh(3), lbnd(3), delta(3), dfl )
+
+  call set_hmatrix ( h, bb(5:6) )
+
+  call set_dmatrix ( d, bb(5:6) )
+
+  a = -transpose ( matmul ( h, matmul ( transpose(d), matmul ( b, d ) ) ) )
+
+  idel = epsdisl /  ( 256.0_wp * delta(3) )
+
+  if ( bb(5) == 0 ) then
+
+    kl = 1 + gsize(3)
+
+  else
+
+    rhs(:,:,1) = rhs(:,:,1) + &
+                 ( a(1,1) * var(:,:,1) + a(2,1) * var(:,:,2) + &
+                   a(3,1) * var(:,:,3) + a(4,1) * var(:,:,4) + &
+                   a(5,1) * var(:,:,5) ) * idel
+    rhs(:,:,2) = rhs(:,:,2) + &
+                 ( a(1,2) * var(:,:,1) + a(2,2) * var(:,:,2) + &
+                   a(3,2) * var(:,:,3) + a(4,2) * var(:,:,4) + &
+                   a(5,2) * var(:,:,5) + a(6,2) * var(:,:,6) + &
+                   a(7,2) * var(:,:,7) + a(8,2) * var(:,:,8) + &
+                   a(9,2) * var(:,:,9) + a(10,2) * var(:,:,10) + &
+                   a(11,2) * var(:,:,11) ) * idel
+    rhs(:,:,3) = rhs(:,:,3) + &
+                 ( a(1,3) * var(:,:,1) + a(2,3) * var(:,:,2) + &
+                   a(3,3) * var(:,:,3) + a(4,3) * var(:,:,4) + &
+                   a(5,3) * var(:,:,5) + a(6,3) * var(:,:,6) + &
+                   a(7,3) * var(:,:,7) + a(8,3) * var(:,:,8) + &
+                   a(9,3) * var(:,:,9) + a(10,3) * var(:,:,10) + &
+                   a(11,3) * var(:,:,11) ) * idel
+    rhs(:,:,4) = rhs(:,:,4) + &
+                 ( a(1,4) * var(:,:,1) + a(2,4) * var(:,:,2) + &
+                   a(3,4) * var(:,:,3) + a(4,4) * var(:,:,4) + &
+                   a(5,4) * var(:,:,5) + a(6,4) * var(:,:,6) + &
+                   a(7,4) * var(:,:,7) + a(8,4) * var(:,:,8) + &
+                   a(9,4) * var(:,:,9) + a(10,4) * var(:,:,10) + &
+                   a(11,4) * var(:,:,11) ) * idel
+    rhs(:,:,5) = rhs(:,:,5) + &
+                 ( a(1,5) * var(:,:,1) + a(2,5) * var(:,:,2) + &
+                   a(3,5) * var(:,:,3) + a(4,5) * var(:,:,4) + &
+                   a(5,5) * var(:,:,5) + a(6,5) * var(:,:,6) + &
+                   a(7,5) * var(:,:,7) + a(8,5) * var(:,:,8) + &
+                   a(9,5) * var(:,:,9) + a(10,5) * var(:,:,10) + &
+                   a(11,5) * var(:,:,11) ) * idel
+    rhs(:,:,6) = rhs(:,:,6) + &
+                 ( a(1,6) * var(:,:,1) + a(2,6) * var(:,:,2) + &
+                   a(3,6) * var(:,:,3) + a(4,6) * var(:,:,4) + &
+                   a(5,6) * var(:,:,5) + a(6,6) * var(:,:,6) + &
+                   a(7,6) * var(:,:,7) + a(8,6) * var(:,:,8) + &
+                   a(9,6) * var(:,:,9) + a(10,6) * var(:,:,10) + &
+                   a(11,6) * var(:,:,11) ) * idel
+    rhs(:,:,7) = rhs(:,:,7) + &
+                 ( a(1,7) * var(:,:,1) + a(2,7) * var(:,:,2) + &
+                   a(3,7) * var(:,:,3) + a(4,7) * var(:,:,4) + &
+                   a(5,7) * var(:,:,5) + a(6,7) * var(:,:,6) + &
+                   a(7,7) * var(:,:,7) + a(8,7) * var(:,:,8) + &
+                   a(9,7) * var(:,:,9) + a(10,7) * var(:,:,10) + &
+                   a(11,7) * var(:,:,11) ) * idel
+
+    kl = 8
+
+  end if
+
+  if ( bb(6) == 0 ) then
+
+    kr = nk - gsize(3)
+
+  else
+
+    rhs(:,:,nk-6) = rhs(:,:,nk-6) + &
+                    ( a(nk-10,nk-6) * var(:,:,nk-10) + &
+                      a(nk-9,nk-6) * var(:,:,nk-9) + &
+                      a(nk-8,nk-6) * var(:,:,nk-8) + &
+                      a(nk-7,nk-6) * var(:,:,nk-7) + &
+                      a(nk-6,nk-6) * var(:,:,nk-6) + &
+                      a(nk-5,nk-6) * var(:,:,nk-5) + &
+                      a(nk-4,nk-6) * var(:,:,nk-4) + &
+                      a(nk-3,nk-6) * var(:,:,nk-3) + &
+                      a(nk-2,nk-6) * var(:,:,nk-2) + &
+                      a(nk-1,nk-6) * var(:,:,nk-1) + &
+                      a(nk,nk-6) * var(:,:,nk) ) * idel
+    rhs(:,:,nk-5) = rhs(:,:,nk-5) + &
+                    ( a(nk-10,nk-5) * var(:,:,nk-10) + &
+                      a(nk-9,nk-5) * var(:,:,nk-9) + &
+                      a(nk-8,nk-5) * var(:,:,nk-8) + &
+                      a(nk-7,nk-5) * var(:,:,nk-7) + &
+                      a(nk-6,nk-5) * var(:,:,nk-6) + &
+                      a(nk-5,nk-5) * var(:,:,nk-5) + &
+                      a(nk-4,nk-5) * var(:,:,nk-4) + &
+                      a(nk-3,nk-5) * var(:,:,nk-3) + &
+                      a(nk-2,nk-5) * var(:,:,nk-2) + &
+                      a(nk-1,nk-5) * var(:,:,nk-1) + &
+                      a(nk,nk-5) * var(:,:,nk) ) * idel
+    rhs(:,:,nk-4) = rhs(:,:,nk-4) + &
+                    ( a(nk-10,nk-4) * var(:,:,nk-10) + &
+                      a(nk-9,nk-4) * var(:,:,nk-9) + &
+                      a(nk-8,nk-4) * var(:,:,nk-8) + &
+                      a(nk-7,nk-4) * var(:,:,nk-7) + &
+                      a(nk-6,nk-4) * var(:,:,nk-6) + &
+                      a(nk-5,nk-4) * var(:,:,nk-5) + &
+                      a(nk-4,nk-4) * var(:,:,nk-4) + &
+                      a(nk-3,nk-4) * var(:,:,nk-3) + &
+                      a(nk-2,nk-4) * var(:,:,nk-2) + &
+                      a(nk-1,nk-4) * var(:,:,nk-1) + &
+                      a(nk,nk-4) * var(:,:,nk) ) * idel
+    rhs(:,:,nk-3) = rhs(:,:,nk-3) + &
+                    ( a(nk-10,nk-3) * var(:,:,nk-10) + &
+                      a(nk-9,nk-3) * var(:,:,nk-9) + &
+                      a(nk-8,nk-3) * var(:,:,nk-8) + &
+                      a(nk-7,nk-3) * var(:,:,nk-7) + &
+                      a(nk-6,nk-3) * var(:,:,nk-6) + &
+                      a(nk-5,nk-3) * var(:,:,nk-5) + &
+                      a(nk-4,nk-3) * var(:,:,nk-4) + &
+                      a(nk-3,nk-3) * var(:,:,nk-3) + &
+                      a(nk-2,nk-3) * var(:,:,nk-2) + &
+                      a(nk-1,nk-3) * var(:,:,nk-1) + &
+                      a(nk,nk-3) * var(:,:,nk) ) * idel
+    rhs(:,:,nk-2) = rhs(:,:,nk-2) + &
+                    ( a(nk-10,nk-2) * var(:,:,nk-10) + &
+                      a(nk-9,nk-2) * var(:,:,nk-9) + &
+                      a(nk-8,nk-2) * var(:,:,nk-8) + &
+                      a(nk-7,nk-2) * var(:,:,nk-7) + &
+                      a(nk-6,nk-2) * var(:,:,nk-6) + &
+                      a(nk-5,nk-2) * var(:,:,nk-5) + &
+                      a(nk-4,nk-2) * var(:,:,nk-4) + &
+                      a(nk-3,nk-2) * var(:,:,nk-3) + &
+                      a(nk-2,nk-2) * var(:,:,nk-2) + &
+                      a(nk-1,nk-2) * var(:,:,nk-1) + &
+                      a(nk,nk-2) * var(:,:,nk) ) * idel
+    rhs(:,:,nk-1) = rhs(:,:,nk-1) + &
+                    ( a(nk-10,nk-1) * var(:,:,nk-10) + &
+                      a(nk-9,nk-1) * var(:,:,nk-9) + &
+                      a(nk-8,nk-1) * var(:,:,nk-8) + &
+                      a(nk-7,nk-1) * var(:,:,nk-7) + &
+                      a(nk-6,nk-1) * var(:,:,nk-6) + &
+                      a(nk-5,nk-1) * var(:,:,nk-5) + &
+                      a(nk-4,nk-1) * var(:,:,nk-4) + &
+                      a(nk-3,nk-1) * var(:,:,nk-3) + &
+                      a(nk-2,nk-1) * var(:,:,nk-2) + &
+                      a(nk-1,nk-1) * var(:,:,nk-1) + &
+                      a(nk,nk-1) * var(:,:,nk) ) * idel
+    rhs(:,:,nk)   = rhs(:,:,nk) + &
+                    ( a(nk-4,nk) * var(:,:,nk-4) + &
+                      a(nk-3,nk) * var(:,:,nk-3) + &
+                      a(nk-2,nk) * var(:,:,nk-2) + &
+                      a(nk-1,nk) * var(:,:,nk-1) + &
+                      a(nk,nk) * var(:,:,nk) ) * idel
+
+    kr = nk - 7
+
+  end if
+
+  do k = kl, kr
+
+    rhs(:,:,k) = rhs(:,:,k) + &
+                   ( a(k-4,k) * var(:,:,k-4) + &
+                     a(k-3,k) * var(:,:,k-3) + &
+                     a(k-2,k) * var(:,:,k-2) + &
+                     a(k-1,k) * var(:,:,k-1) + &
+                     a(k,k) * var(:,:,k) + &
+                     a(k+1,k) * var(:,:,k+1) + &
+                     a(k+2,k) * var(:,:,k+2) + &
+                     a(k+3,k) * var(:,:,k+3) + &
+                     a(k+4,k) * var(:,:,k+4) ) * idel
+
+  end do
+
+  deallocate ( a, d, b, h, tmp )
+
+contains
+
+  subroutine set_dmatrix ( d, bb )
+
+    implicit none
+
+    CCTK_REAL, dimension(:,:), intent(out) :: d
+    CCTK_INT, dimension(2), intent(in) :: bb
+    CCTK_INT :: n
+    CCTK_REAL, dimension(5), save :: ac = (/ 1.0_wp, -4.0_wp, 6.0_wp, &
+                                                     -4.0_wp, 1.0_wp /)
+    CCTK_INT :: i
+
+    d = zero
+
+    n = size(d,1)
+
+    if ( bb(1) == 0 ) then
+      d(1,1:3) = ac(3:5)
+      d(2,1:4) = ac(2:5)
+    else
+      d(1,1:5) = ac
+      d(2,1:5) = ac
+    end if
+    if ( bb(2) == 0 ) then
+      d(n-1,n-3:n) = ac(1:4)
+      d(n,n-2:n) = ac(1:3)
+    else
+      d(n-1,n-4:n) = ac
+      d(n,n-4:n) = ac
+    end if
+    do i = 3, n-2
+      d(i,i-2:i+2) = ac
+    end do
+  end subroutine set_dmatrix
+
+
+  subroutine set_bmatrix ( b, bb, lsh, gsh, lbnd, h, dfl )
+
+    implicit none
+
+    CCTK_REAL, dimension(:,:), intent(out) :: b
+    CCTK_INT, dimension(2), intent(in) :: bb
+    CCTK_INT, intent(in) :: lsh, gsh, lbnd
+    CCTK_REAL, intent(in) :: h, dfl
+    CCTK_INT :: n, nwt
+    CCTK_INT :: i
+    CCTK_REAL :: xp, xmax
+
+    CCTK_REAL :: zero = 0.0
+    integer, parameter :: wp = kind(zero)
+
+    n = size(b,1)
+    xp = ( gsh - 1 ) * dfl - 1
+
+    do i = 1, n
+      b(i,i) = bf ( real(i+lbnd-1,wp), xp, real(gsh-1,wp), h )
+    end do
+
+  end subroutine set_bmatrix
+    
+
+  subroutine set_hmatrix ( h, bb )
+
+    implicit none
+
+    CCTK_REAL, dimension(:,:), intent(out) :: h
+    CCTK_INT, dimension(2), intent(in) :: bb
+    CCTK_INT :: n, i
+
+    CCTK_REAL :: zero = 0.0
+    integer, parameter :: wp = kind(zero)
+
+    n = size(h,1)
+
+    h = zero
+
+    do i = 1, n
+      h(i,i) = 1.0_wp
+    end do
+
+    if ( bb(1) /= 0 ) then
+      h(1:7,1:7) = sigma ( )
+    end if
+
+    if ( bb(2) /= 0 ) then
+      h(n:n-6:-1,n:n-6:-1) = sigma ( )
+    end if
+
+  end subroutine set_hmatrix
+    
+
+  function bf ( x, xp, xmax, h )
+
+    implicit none
+
+    CCTK_REAL :: bf
+    CCTK_REAL, intent(in) :: x, xp, xmax, h
+    CCTK_REAL :: h2, h21, xp2, xp3
+
+    CCTK_REAL :: zero = 0.0
+    integer, parameter :: wp = kind(zero)
+
+    if ( x < xp ) then
+
+      h2 = h**2
+      h21 = 1.0_wp - h2
+      xp2 = 1.0_wp / xp**2
+      xp3 = xp2 / xp
+      bf = ( -2.0_wp * h21 * xp3 * x + 3.0_wp * h21 * xp2 ) * x**2 + h2
+
+    else if ( x > xmax - xp ) then
+
+      h2 = h**2
+      h21 = 1.0_wp - h2
+      xp2 = 1.0_wp / xp**2
+      xp3 = xp2 / xp
+      bf = ( 2.0_wp * h21 * xp3 * ( x - xmax ) + &
+             3.0_wp * h21 * xp2 ) * ( x - xmax )**2 + h2
+
+    else
+
+      bf = 1.0_wp
+
+    end if
+
+  end function bf
+
+
+  function sigma ( )
+
+    implicit none
+
+    CCTK_REAL, dimension(7,7) :: sigma
+
+    CCTK_REAL :: zero = 0.0
+    integer, parameter :: wp = kind(zero)
+
+    sigma(1,1) = 4.930709842221048047321555312222552006914_wp
+    sigma(2,1) = 0_wp
+    sigma(3,1) = 0_wp
+    sigma(4,1) = 0_wp
+    sigma(5,1) = 0_wp
+    sigma(6,1) = 0_wp
+    sigma(7,1) = 0_wp
+    sigma(1,2) = 0_wp
+    sigma(2,2) = 1.499128158967098993672808967791430710830_wp
+    sigma(3,2) = 0.8363320637711490458766332755492551638364_wp
+    sigma(4,2) = -0.2634194189384563273844251938374368097488_wp
+    sigma(5,2) = -0.1281142262970477369698649073120970227895_wp
+    sigma(6,2) = -0.1830121923043950334684235233648902467425_wp
+    sigma(7,2) = 0.01275879120879511857581469566228951245742_wp
+    sigma(1,3) = 0_wp
+    sigma(2,3) = 0.8363320637711490458766332755492551638364_wp
+    sigma(3,3) = 0.8785380112113613457715293301885586949116_wp
+    sigma(4,3) = 0.1454039706555408804118493444561963110723_wp
+    sigma(5,3) = -0.03346859376328961536059718572568704595897_wp
+    sigma(6,3) = -0.1759548942026651677201193466207997400242_wp
+    sigma(7,3) = 0.02020404709761823823384626194775259449799_wp
+    sigma(1,4) = 0_wp
+    sigma(2,4) = -0.2634194189384563273844251938374368097488_wp
+    sigma(3,4) = 0.1454039706555408804118493444561963110723_wp
+    sigma(4,4) = 0.5690707861055695191099807759535994201984_wp
+    sigma(5,4) = 0.3374169937858825026860519890688362591356_wp
+    sigma(6,4) = -0.03076801586199402080957339555604653302670_wp
+    sigma(7,4) = 0.004077760901760668929595481886645691229036_wp
+    sigma(1,5) = 0_wp
+    sigma(2,5) = -0.1281142262970477369698649073120970227895_wp
+    sigma(3,5) = -0.03346859376328961536059718572568704595897_wp
+    sigma(4,5) = 0.3374169937858825026860519890688362591356_wp
+    sigma(5,5) = 0.5001980842834785426891480539161939116986_wp
+    sigma(6,5) = 0.2904403943485980286998891564955850119600_wp
+    sigma(7,5) = -0.05655813410599246578174268632557910837116_wp
+    sigma(1,6) = 0_wp
+    sigma(2,6) = -0.1830121923043950334684235233648902467425_wp
+    sigma(3,6) = -0.1759548942026651677201193466207997400242_wp
+    sigma(4,6) = -0.03076801586199402080957339555604653302670_wp
+    sigma(5,6) = 0.2904403943485980286998891564955850119600_wp
+    sigma(6,6) = 0.8640467497799918355533313312208192675134_wp
+    sigma(7,6) = 0.03704582714017916999084939064121697271831_wp
+    sigma(1,7) = 0_wp
+    sigma(2,7) = 0.01275879120879511857581469566228951245742_wp
+    sigma(3,7) = 0.02020404709761823823384626194775259449799_wp
+    sigma(4,7) = 0.004077760901760668929595481886645691229036_wp
+    sigma(5,7) = -0.05655813410599246578174268632557910837116_wp
+    sigma(6,7) = 0.03704582714017916999084939064121697271831_wp
+    sigma(7,7) = 0.9909401061257062767072573096147576992963_wp
+
+  end function sigma
+
+end subroutine dissipation_6_5_alt
diff --git a/src/Dissipation_8_4_alt.F90 b/src/Dissipation_8_4_alt.F90
new file mode 100644
index 0000000..594b531
--- /dev/null
+++ b/src/Dissipation_8_4_alt.F90
@@ -0,0 +1,513 @@
+! $Header$
+
+#include "cctk.h"
+#include "cctk_Parameters.h"
+
+subroutine dissipation_8_4_alt (var, ni, nj, nk, bb, gsize, delta, epsilon, rhs)
+
+  implicit none
+
+  DECLARE_CCTK_PARAMETERS
+
+  integer ::  ni, nj, nk
+  CCTK_REAL, dimension(ni,nj,nk), intent(in) :: var
+  CCTK_REAL, dimension(ni,nj,nk), intent(inout) :: rhs
+  CCTK_INT, dimension(6), intent(in) :: bb
+  CCTK_INT, dimension(3), intent(in) :: gsize
+  CCTK_REAL, dimension(3), intent(in) :: delta
+  CCTK_REAL, intent(in) :: epsilon 
+
+  CCTK_REAL :: zero = 0.0
+  integer, parameter :: wp = kind(zero)
+  CCTK_REAL, dimension(13,8) :: a
+  CCTK_REAL :: idel
+
+  CCTK_INT :: il, ir, jl, jr, kl, kr
+
+  call set_coeff ( a )
+
+  idel = epsilon / ( 1024 * delta(1) )
+
+  if ( bb(1) == 0 ) then
+    il = 1 + gsize(1)
+  else
+    rhs(1,:,:) = rhs(1,:,:) + &
+                 ( a(1,1) * var(1,:,:) + a(2,1) * var(2,:,:) + &
+                   a(3,1) * var(3,:,:) + a(4,1) * var(4,:,:) + &
+                   a(5,1) * var(5,:,:) + a(6,1) * var(6,:,:) ) * idel
+    rhs(2,:,:) = rhs(2,:,:) + &
+                 ( a(1,2) * var(1,:,:) + a(2,2) * var(2,:,:) + &
+                   a(3,2) * var(3,:,:) + a(4,2) * var(4,:,:) + &
+                   a(5,2) * var(5,:,:) + a(6,2) * var(6,:,:) + &
+                   a(7,2) * var(7,:,:) ) * idel
+    rhs(3,:,:) = rhs(3,:,:) + &
+                 ( a(1,3) * var(1,:,:) + a(2,3) * var(2,:,:) + &
+                   a(3,3) * var(3,:,:) + a(4,3) * var(4,:,:) + &
+                   a(5,3) * var(5,:,:) + a(6,3) * var(6,:,:) + &
+                   a(7,3) * var(7,:,:) + a(8,3) * var(8,:,:) ) * idel
+    rhs(4,:,:) = rhs(4,:,:) + &
+                 ( a(1,4) * var(1,:,:) + a(2,4) * var(2,:,:) + &
+                   a(3,4) * var(3,:,:) + a(4,4) * var(4,:,:) + &
+                   a(5,4) * var(5,:,:) + a(6,4) * var(6,:,:) + &
+                   a(7,4) * var(7,:,:) + a(8,4) * var(8,:,:) + &
+                   a(9,4) * var(9,:,:) ) * idel
+    rhs(5,:,:) = rhs(5,:,:) + &
+                 ( a(1,5) * var(1,:,:) + a(2,5) * var(2,:,:) + &
+                   a(3,5) * var(3,:,:) + a(4,5) * var(4,:,:) + &
+                   a(5,5) * var(5,:,:) + a(6,5) * var(6,:,:) + &
+                   a(7,5) * var(7,:,:) + a(8,5) * var(8,:,:) + &
+                   a(9,5) * var(9,:,:) + a(10,5) * var(10,:,:) ) * idel
+    rhs(6,:,:) = rhs(6,:,:) + &
+                 ( a(1,6) * var(1,:,:) + a(2,6) * var(2,:,:) + &
+                   a(3,6) * var(3,:,:) + a(4,6) * var(4,:,:) + &
+                   a(5,6) * var(5,:,:) + a(6,6) * var(6,:,:) + &
+                   a(7,6) * var(7,:,:) + a(8,6) * var(8,:,:) + &
+                   a(9,6) * var(9,:,:) + a(10,6) * var(10,:,:) + &
+                   a(11,6) * var(11,:,:) ) * idel
+    rhs(7,:,:) = rhs(7,:,:) + &
+                 ( a(2,7) * var(2,:,:) + a(3,7) * var(3,:,:) + &
+                   a(4,7) * var(4,:,:) + a(5,7) * var(5,:,:) + &
+                   a(6,7) * var(6,:,:) + a(7,7) * var(7,:,:) + &
+                   a(8,7) * var(8,:,:) + a(9,7) * var(9,:,:) + &
+                   a(10,7) * var(10,:,:) + a(11,7) * var(11,:,:) + &
+                   a(12,7) * var(12,:,:) ) * idel
+    rhs(8,:,:) = rhs(8,:,:) + &
+                 ( a(3,8) * var(3,:,:) + a(4,8) * var(4,:,:) + &
+                   a(5,8) * var(5,:,:) + a(6,8) * var(6,:,:) + &
+                   a(7,8) * var(7,:,:) + a(8,8) * var(8,:,:) + &
+                   a(9,8) * var(9,:,:) + a(10,8) * var(10,:,:) + &
+                   a(11,8) * var(11,:,:) + a(12,8) * var(12,:,:) + &
+                   a(13,8) * var(13,:,:) ) * idel
+
+    il = 9
+  end if
+  if ( bb(2) == 0 ) then
+    ir = ni - gsize(1)
+  else
+    rhs(ni-7,:,:) = rhs(ni-7,:,:) + &
+                 ( a(3,8) * var(ni-2,:,:) + a(4,8) * var(ni-3,:,:) + &
+                   a(5,8) * var(ni-4,:,:) + a(6,8) * var(ni-5,:,:) + &
+                   a(7,8) * var(ni-6,:,:) + a(8,8) * var(ni-7,:,:) + &
+                   a(9,8) * var(ni-8,:,:) + a(10,8) * var(ni-9,:,:) + &
+                   a(11,8) * var(ni-10,:,:) + a(12,8) * var(ni-11,:,:) + &
+                   a(13,8) * var(ni-12,:,:) ) * idel
+    rhs(ni-6,:,:) = rhs(ni-6,:,:) + &
+                 ( a(2,7) * var(ni-1,:,:) + a(3,7) * var(ni-2,:,:) + &
+                   a(4,7) * var(ni-3,:,:) + a(5,7) * var(ni-4,:,:) + &
+                   a(6,7) * var(ni-5,:,:) + a(7,7) * var(ni-6,:,:) + &
+                   a(8,7) * var(ni-7,:,:) + a(9,7) * var(ni-8,:,:) + &
+                   a(10,7) * var(ni-9,:,:) + a(11,7) * var(ni-10,:,:) + &
+                   a(12,7) * var(ni-11,:,:) ) * idel
+    rhs(ni-5,:,:) = rhs(ni-5,:,:) + &
+                 ( a(1,6) * var(ni,:,:) + a(2,6) * var(ni-1,:,:) + &
+                   a(3,6) * var(ni-2,:,:) + a(4,6) * var(ni-3,:,:) + &
+                   a(5,6) * var(ni-4,:,:) + a(6,6) * var(ni-5,:,:) + &
+                   a(7,6) * var(ni-6,:,:) + a(8,6) * var(ni-7,:,:) + &
+                   a(9,6) * var(ni-8,:,:) + a(10,6) * var(ni-9,:,:) + &
+                   a(11,6) * var(ni-10,:,:) ) * idel
+    rhs(ni-4,:,:) = rhs(ni-4,:,:) + &
+                 ( a(1,5) * var(ni,:,:) + a(2,5) * var(ni-1,:,:) + &
+                   a(3,5) * var(ni-2,:,:) + a(4,5) * var(ni-3,:,:) + &
+                   a(5,5) * var(ni-4,:,:) + a(6,5) * var(ni-5,:,:) + &
+                   a(7,5) * var(ni-6,:,:) + a(8,5) * var(ni-7,:,:) + &
+                   a(9,5) * var(ni-8,:,:) + a(10,5) * var(ni-9,:,:) ) * idel
+    rhs(ni-3,:,:) = rhs(ni-3,:,:) + &
+                 ( a(1,4) * var(ni,:,:) + a(2,4) * var(ni-1,:,:) + &
+                   a(3,4) * var(ni-2,:,:) + a(4,4) * var(ni-3,:,:) + &
+                   a(5,4) * var(ni-4,:,:) + a(6,4) * var(ni-5,:,:) + &
+                   a(7,4) * var(ni-6,:,:) + a(8,4) * var(ni-7,:,:) + &
+                   a(9,4) * var(ni-8,:,:) ) * idel
+    rhs(ni-2,:,:) = rhs(ni-2,:,:) + &
+                 ( a(1,3) * var(ni,:,:) + a(2,3) * var(ni-1,:,:) + &
+                   a(3,3) * var(ni-2,:,:) + a(4,3) * var(ni-3,:,:) + &
+                   a(5,3) * var(ni-4,:,:) + a(6,3) * var(ni-5,:,:) + &
+                   a(7,3) * var(ni-6,:,:) + a(8,3) * var(ni-7,:,:) ) * idel
+    rhs(ni-1,:,:) = rhs(ni-1,:,:) + &
+                 ( a(1,2) * var(ni,:,:) + a(2,2) * var(ni-1,:,:) + &
+                   a(3,2) * var(ni-2,:,:) + a(4,2) * var(ni-3,:,:) + &
+                   a(5,2) * var(ni-4,:,:) + a(6,2) * var(ni-5,:,:) + &
+                   a(7,2) * var(ni-6,:,:) ) * idel
+    rhs(ni,:,:)   = rhs(ni,:,:) + &
+                 ( a(1,1) * var(ni,:,:) + a(2,1) * var(ni-1,:,:) + &
+                   a(3,1) * var(ni-2,:,:) + a(4,1) * var(ni-3,:,:) + &
+                   a(5,1) * var(ni-4,:,:) + a(6,1) * var(ni-5,:,:) ) * idel
+
+    ir = ni - 8
+  end if
+  rhs(il:ir,:,:) = rhs(il:ir,:,:) + &
+                   ( -252.0_wp * var(il:ir,:,:) + &
+                      210.0_wp * ( var(il-1:ir-1,:,:) + &
+                                   var(il+1:ir+1,:,:) ) - &
+                      120.0_wp * ( var(il-2:ir-2,:,:) + &
+                                   var(il+2:ir+2,:,:) ) + &
+                       45.0_wp * ( var(il-3:ir-3,:,:) + &
+                                   var(il+3:ir+3,:,:) ) - &
+                       10.0_wp * ( var(il-4:ir-4,:,:) + &
+                                   var(il+4:ir+4,:,:) ) + &
+                                 ( var(il-5:ir-5,:,:) + &
+                                   var(il+5:ir+5,:,:) ) ) * idel
+
+  call set_coeff ( a )
+
+  idel = epsilon / ( 1024 * delta(2) )
+
+  if ( bb(3) == 0 ) then
+    jl = 1 + gsize(2)
+  else
+    rhs(:,1,:) = rhs(:,1,:) + &
+                 ( a(1,1) * var(:,1,:) + a(2,1) * var(:,2,:) + &
+                   a(3,1) * var(:,3,:) + a(4,1) * var(:,4,:) + &
+                   a(5,1) * var(:,5,:) + a(6,1) * var(:,6,:) ) * idel
+    rhs(:,2,:) = rhs(:,2,:) + &
+                 ( a(1,2) * var(:,1,:) + a(2,2) * var(:,2,:) + &
+                   a(3,2) * var(:,3,:) + a(4,2) * var(:,4,:) + &
+                   a(5,2) * var(:,5,:) + a(6,2) * var(:,6,:) + &
+                   a(7,2) * var(:,7,:) ) * idel
+    rhs(:,3,:) = rhs(:,3,:) + &
+                 ( a(1,3) * var(:,1,:) + a(2,3) * var(:,2,:) + &
+                   a(3,3) * var(:,3,:) + a(4,3) * var(:,4,:) + &
+                   a(5,3) * var(:,5,:) + a(6,3) * var(:,6,:) + &
+                   a(7,3) * var(:,7,:) + a(8,3) * var(:,8,:) ) * idel
+    rhs(:,4,:) = rhs(:,4,:) + &
+                 ( a(1,4) * var(:,1,:) + a(2,4) * var(:,2,:) + &
+                   a(3,4) * var(:,3,:) + a(4,4) * var(:,4,:) + &
+                   a(5,4) * var(:,5,:) + a(6,4) * var(:,6,:) + &
+                   a(7,4) * var(:,7,:) + a(8,4) * var(:,8,:) + &
+                   a(9,4) * var(:,9,:) ) * idel
+    rhs(:,5,:) = rhs(:,5,:) + &
+                 ( a(1,5) * var(:,1,:) + a(2,5) * var(:,2,:) + &
+                   a(3,5) * var(:,3,:) + a(4,5) * var(:,4,:) + &
+                   a(5,5) * var(:,5,:) + a(6,5) * var(:,6,:) + &
+                   a(7,5) * var(:,7,:) + a(8,5) * var(:,8,:) + &
+                   a(9,5) * var(:,9,:) + a(10,5) * var(:,10,:) ) * idel
+    rhs(:,6,:) = rhs(:,6,:) + &
+                 ( a(1,6) * var(:,1,:) + a(2,6) * var(:,2,:) + &
+                   a(3,6) * var(:,3,:) + a(4,6) * var(:,4,:) + &
+                   a(5,6) * var(:,5,:) + a(6,6) * var(:,6,:) + &
+                   a(7,6) * var(:,7,:) + a(8,6) * var(:,8,:) + &
+                   a(9,6) * var(:,9,:) + a(10,6) * var(:,10,:) + &
+                   a(11,6) * var(:,11,:) ) * idel
+    rhs(:,7,:) = rhs(:,7,:) + &
+                 ( a(2,7) * var(:,2,:) + a(3,7) * var(:,3,:) + &
+                   a(4,7) * var(:,4,:) + a(5,7) * var(:,5,:) + &
+                   a(6,7) * var(:,6,:) + a(7,7) * var(:,7,:) + &
+                   a(8,7) * var(:,8,:) + a(9,7) * var(:,9,:) + &
+                   a(10,7) * var(:,10,:) + a(11,7) * var(:,11,:) + &
+                   a(12,7) * var(:,12,:) ) * idel
+    rhs(:,8,:) = rhs(:,8,:) + &
+                 ( a(3,8) * var(:,3,:) + a(4,8) * var(:,4,:) + &
+                   a(5,8) * var(:,5,:) + a(6,8) * var(:,6,:) + &
+                   a(7,8) * var(:,7,:) + a(8,8) * var(:,8,:) + &
+                   a(9,8) * var(:,9,:) + a(10,8) * var(:,10,:) + &
+                   a(11,8) * var(:,11,:) + a(12,8) * var(:,12,:) + &
+                   a(13,8) * var(:,13,:) ) * idel
+
+    jl = 9
+  end if
+  if ( bb(4) == 0 ) then
+    jr = nj - gsize(2)
+  else
+    rhs(:,nj-7,:) = rhs(:,nj-7,:) + &
+                 ( a(3,8) * var(:,nj-2,:) + a(4,8) * var(:,nj-3,:) + &
+                   a(5,8) * var(:,nj-4,:) + a(6,8) * var(:,nj-5,:) + &
+                   a(7,8) * var(:,nj-6,:) + a(8,8) * var(:,nj-7,:) + &
+                   a(9,8) * var(:,nj-8,:) + a(10,8) * var(:,nj-9,:) + &
+                   a(11,8) * var(:,nj-10,:) + a(12,8) * var(:,nj-11,:) + &
+                   a(13,8) * var(:,nj-12,:) ) * idel
+    rhs(:,nj-6,:) = rhs(:,nj-6,:) + &
+                 ( a(2,7) * var(:,nj-1,:) + a(3,7) * var(:,nj-2,:) + &
+                   a(4,7) * var(:,nj-3,:) + a(5,7) * var(:,nj-4,:) + &
+                   a(6,7) * var(:,nj-5,:) + a(7,7) * var(:,nj-6,:) + &
+                   a(8,7) * var(:,nj-7,:) + a(9,7) * var(:,nj-8,:) + &
+                   a(10,7) * var(:,nj-9,:) + a(11,7) * var(:,nj-10,:) + &
+                   a(12,7) * var(:,nj-11,:) ) * idel
+    rhs(:,nj-5,:) = rhs(:,nj-5,:) + &
+                 ( a(1,6) * var(:,nj,:) + a(2,6) * var(:,nj-1,:) + &
+                   a(3,6) * var(:,nj-2,:) + a(4,6) * var(:,nj-3,:) + &
+                   a(5,6) * var(:,nj-4,:) + a(6,6) * var(:,nj-5,:) + &
+                   a(7,6) * var(:,nj-6,:) + a(8,6) * var(:,nj-7,:) + &
+                   a(9,6) * var(:,nj-8,:) + a(10,6) * var(:,nj-9,:) + &
+                   a(11,6) * var(:,nj-10,:) ) * idel
+    rhs(:,nj-4,:) = rhs(:,nj-4,:) + &
+                 ( a(1,5) * var(:,nj,:) + a(2,5) * var(:,nj-1,:) + &
+                   a(3,5) * var(:,nj-2,:) + a(4,5) * var(:,nj-3,:) + &
+                   a(5,5) * var(:,nj-4,:) + a(6,5) * var(:,nj-5,:) + &
+                   a(7,5) * var(:,nj-6,:) + a(8,5) * var(:,nj-7,:) + &
+                   a(9,5) * var(:,nj-8,:) + a(10,5) * var(:,nj-9,:) ) * idel
+    rhs(:,nj-3,:) = rhs(:,nj-3,:) + &
+                 ( a(1,4) * var(:,nj,:) + a(2,4) * var(:,nj-1,:) + &
+                   a(3,4) * var(:,nj-2,:) + a(4,4) * var(:,nj-3,:) + &
+                   a(5,4) * var(:,nj-4,:) + a(6,4) * var(:,nj-5,:) + &
+                   a(7,4) * var(:,nj-6,:) + a(8,4) * var(:,nj-7,:) + &
+                   a(9,4) * var(:,nj-8,:) ) * idel
+    rhs(:,nj-2,:) = rhs(:,nj-2,:) + &
+                 ( a(1,3) * var(:,nj,:) + a(2,3) * var(:,nj-1,:) + &
+                   a(3,3) * var(:,nj-2,:) + a(4,3) * var(:,nj-3,:) + &
+                   a(5,3) * var(:,nj-4,:) + a(6,3) * var(:,nj-5,:) + &
+                   a(7,3) * var(:,nj-6,:) + a(8,3) * var(:,nj-7,:) ) * idel
+    rhs(:,nj-1,:) = rhs(:,nj-1,:) + &
+                 ( a(1,2) * var(:,nj,:) + a(2,2) * var(:,nj-1,:) + &
+                   a(3,2) * var(:,nj-2,:) + a(4,2) * var(:,nj-3,:) + &
+                   a(5,2) * var(:,nj-4,:) + a(6,2) * var(:,nj-5,:) + &
+                   a(7,2) * var(:,nj-6,:) ) * idel
+    rhs(:,nj,:)   = rhs(:,nj,:) + &
+                 ( a(1,1) * var(:,nj,:) + a(2,1) * var(:,nj-1,:) + &
+                   a(3,1) * var(:,nj-2,:) + a(4,1) * var(:,nj-3,:) + &
+                   a(5,1) * var(:,nj-4,:) + a(6,1) * var(:,nj-5,:) ) * idel
+
+    jr = nj - 8
+  end if
+  rhs(:,jl:jr,:) = rhs(:,jl:jr,:) + &
+                   ( -252.0_wp * var(:,jl:jr,:) + &
+                      210.0_wp * ( var(:,jl-1:jr-1,:) + &
+                                   var(:,jl+1:jr+1,:) ) - &
+                      120.0_wp * ( var(:,jl-2:jr-2,:) + &
+                                   var(:,jl+2:jr+2,:) ) + &
+                       45.0_wp * ( var(:,jl-3:jr-3,:) + &
+                                   var(:,jl+3:jr+3,:) ) - &
+                       10.0_wp * ( var(:,jl-4:jr-4,:) + &
+                                   var(:,jl+4:jr+4,:) ) + &
+                                 ( var(:,jl-5:jr-5,:) + &
+                                   var(:,jl+5:jr+5,:) ) ) * idel
+
+  call set_coeff ( a )
+
+  idel = epsilon / ( 1024 * delta(3) )
+
+  if ( bb(5) == 0 ) then
+    kl = 1 + gsize(3)
+  else
+    rhs(:,:,1) = rhs(:,:,1) + &
+                 ( a(1,1) * var(:,:,1) + a(2,1) * var(:,:,2) + &
+                   a(3,1) * var(:,:,3) + a(4,1) * var(:,:,4) + &
+                   a(5,1) * var(:,:,5) + a(6,1) * var(:,:,6) ) * idel
+    rhs(:,:,2) = rhs(:,:,2) + &
+                 ( a(1,2) * var(:,:,1) + a(2,2) * var(:,:,2) + &
+                   a(3,2) * var(:,:,3) + a(4,2) * var(:,:,4) + &
+                   a(5,2) * var(:,:,5) + a(6,2) * var(:,:,6) + &
+                   a(7,2) * var(:,:,7) ) * idel
+    rhs(:,:,3) = rhs(:,:,3) + &
+                 ( a(1,3) * var(:,:,1) + a(2,3) * var(:,:,2) + &
+                   a(3,3) * var(:,:,3) + a(4,3) * var(:,:,4) + &
+                   a(5,3) * var(:,:,5) + a(6,3) * var(:,:,6) + &
+                   a(7,3) * var(:,:,7) + a(8,3) * var(:,:,8) ) * idel
+    rhs(:,:,4) = rhs(:,:,4) + &
+                 ( a(1,4) * var(:,:,1) + a(2,4) * var(:,:,2) + &
+                   a(3,4) * var(:,:,3) + a(4,4) * var(:,:,4) + &
+                   a(5,4) * var(:,:,5) + a(6,4) * var(:,:,6) + &
+                   a(7,4) * var(:,:,7) + a(8,4) * var(:,:,8) + &
+                   a(9,4) * var(:,:,9) ) * idel
+    rhs(:,:,5) = rhs(:,:,5) + &
+                 ( a(1,5) * var(:,:,1) + a(2,5) * var(:,:,2) + &
+                   a(3,5) * var(:,:,3) + a(4,5) * var(:,:,4) + &
+                   a(5,5) * var(:,:,5) + a(6,5) * var(:,:,6) + &
+                   a(7,5) * var(:,:,7) + a(8,5) * var(:,:,8) + &
+                   a(9,5) * var(:,:,9) + a(10,5) * var(:,:,10) ) * idel
+    rhs(:,:,6) = rhs(:,:,6) + &
+                 ( a(1,6) * var(:,:,1) + a(2,6) * var(:,:,2) + &
+                   a(3,6) * var(:,:,3) + a(4,6) * var(:,:,4) + &
+                   a(5,6) * var(:,:,5) + a(6,6) * var(:,:,6) + &
+                   a(7,6) * var(:,:,7) + a(8,6) * var(:,:,8) + &
+                   a(9,6) * var(:,:,9) + a(10,6) * var(:,:,10) + &
+                   a(11,6) * var(:,:,11) ) * idel
+    rhs(:,:,7) = rhs(:,:,7) + &
+                 ( a(2,7) * var(:,:,2) + a(3,7) * var(:,:,3) + &
+                   a(4,7) * var(:,:,4) + a(5,7) * var(:,:,5) + &
+                   a(6,7) * var(:,:,6) + a(7,7) * var(:,:,7) + &
+                   a(8,7) * var(:,:,8) + a(9,7) * var(:,:,9) + &
+                   a(10,7) * var(:,:,10) + a(11,7) * var(:,:,11) + &
+                   a(12,7) * var(:,:,12) ) * idel
+    rhs(:,:,8) = rhs(:,:,8) + &
+                 ( a(3,8) * var(:,:,3) + a(4,8) * var(:,:,4) + &
+                   a(5,8) * var(:,:,5) + a(6,8) * var(:,:,6) + &
+                   a(7,8) * var(:,:,7) + a(8,8) * var(:,:,8) + &
+                   a(9,8) * var(:,:,9) + a(10,8) * var(:,:,10) + &
+                   a(11,8) * var(:,:,11) + a(12,8) * var(:,:,12) + &
+                   a(13,8) * var(:,:,13) ) * idel
+
+    kl = 9
+  end if
+  if ( bb(6) == 0 ) then
+    kr = nk - gsize(3)
+  else
+    rhs(:,:,nk-7) = rhs(:,:,nk-7) + &
+                 ( a(3,8) * var(:,:,nk-2) + a(4,8) * var(:,:,nk-3) + &
+                   a(5,8) * var(:,:,nk-4) + a(6,8) * var(:,:,nk-5) + &
+                   a(7,8) * var(:,:,nk-6) + a(8,8) * var(:,:,nk-7) + &
+                   a(9,8) * var(:,:,nk-8) + a(10,8) * var(:,:,nk-9) + &
+                   a(11,8) * var(:,:,nk-10) + a(12,8) * var(:,:,nk-11) + &
+                   a(13,8) * var(:,:,nk-12) ) * idel
+    rhs(:,:,nk-6) = rhs(:,:,nk-6) + &
+                 ( a(2,7) * var(:,:,nk-1) + a(3,7) * var(:,:,nk-2) + &
+                   a(4,7) * var(:,:,nk-3) + a(5,7) * var(:,:,nk-4) + &
+                   a(6,7) * var(:,:,nk-5) + a(7,7) * var(:,:,nk-6) + &
+                   a(8,7) * var(:,:,nk-7) + a(9,7) * var(:,:,nk-8) + &
+                   a(10,7) * var(:,:,nk-9) + a(11,7) * var(:,:,nk-10) + &
+                   a(12,7) * var(:,:,nk-11) ) * idel
+    rhs(:,:,nk-5) = rhs(:,:,nk-5) + &
+                 ( a(1,6) * var(:,:,nk) + a(2,6) * var(:,:,nk-1) + &
+                   a(3,6) * var(:,:,nk-2) + a(4,6) * var(:,:,nk-3) + &
+                   a(5,6) * var(:,:,nk-4) + a(6,6) * var(:,:,nk-5) + &
+                   a(7,6) * var(:,:,nk-6) + a(8,6) * var(:,:,nk-7) + &
+                   a(9,6) * var(:,:,nk-8) + a(10,6) * var(:,:,nk-9) + &
+                   a(11,6) * var(:,:,nk-10) ) * idel
+    rhs(:,:,nk-4) = rhs(:,:,nk-4) + &
+                 ( a(1,5) * var(:,:,nk) + a(2,5) * var(:,:,nk-1) + &
+                   a(3,5) * var(:,:,nk-2) + a(4,5) * var(:,:,nk-3) + &
+                   a(5,5) * var(:,:,nk-4) + a(6,5) * var(:,:,nk-5) + &
+                   a(7,5) * var(:,:,nk-6) + a(8,5) * var(:,:,nk-7) + &
+                   a(9,5) * var(:,:,nk-8) + a(10,5) * var(:,:,nk-9) ) * idel
+    rhs(:,:,nk-3) = rhs(:,:,nk-3) + &
+                 ( a(1,4) * var(:,:,nk) + a(2,4) * var(:,:,nk-1) + &
+                   a(3,4) * var(:,:,nk-2) + a(4,4) * var(:,:,nk-3) + &
+                   a(5,4) * var(:,:,nk-4) + a(6,4) * var(:,:,nk-5) + &
+                   a(7,4) * var(:,:,nk-6) + a(8,4) * var(:,:,nk-7) + &
+                   a(9,4) * var(:,:,nk-8) ) * idel
+    rhs(:,:,nk-2) = rhs(:,:,nk-2) + &
+                 ( a(1,3) * var(:,:,nk) + a(2,3) * var(:,:,nk-1) + &
+                   a(3,3) * var(:,:,nk-2) + a(4,3) * var(:,:,nk-3) + &
+                   a(5,3) * var(:,:,nk-4) + a(6,3) * var(:,:,nk-5) + &
+                   a(7,3) * var(:,:,nk-6) + a(8,3) * var(:,:,nk-7) ) * idel
+    rhs(:,:,nk-1) = rhs(:,:,nk-1) + &
+                 ( a(1,2) * var(:,:,nk) + a(2,2) * var(:,:,nk-1) + &
+                   a(3,2) * var(:,:,nk-2) + a(4,2) * var(:,:,nk-3) + &
+                   a(5,2) * var(:,:,nk-4) + a(6,2) * var(:,:,nk-5) + &
+                   a(7,2) * var(:,:,nk-6) ) * idel
+    rhs(:,:,nk)   = rhs(:,:,nk) + &
+                 ( a(1,1) * var(:,:,nk) + a(2,1) * var(:,:,nk-1) + &
+                   a(3,1) * var(:,:,nk-2) + a(4,1) * var(:,:,nk-3) + &
+                   a(5,1) * var(:,:,nk-4) + a(6,1) * var(:,:,nk-5) ) * idel
+
+    kr = nk - 8
+  end if
+  rhs(:,:,kl:kr) = rhs(:,:,kl:kr) + &
+                   ( -252.0_wp * var(:,:,kl:kr) + &
+                      210.0_wp * ( var(:,:,kl-1:kr-1) + &
+                                   var(:,:,kl+1:kr+1) ) - &
+                      120.0_wp * ( var(:,:,kl-2:kr-2) + &
+                                   var(:,:,kl+2:kr+2) ) + &
+                       45.0_wp * ( var(:,:,kl-3:kr-3) + &
+                                   var(:,:,kl+3:kr+3) ) - &
+                       10.0_wp * ( var(:,:,kl-4:kr-4) + &
+                                   var(:,:,kl+4:kr+4) ) + &
+                                 ( var(:,:,kl-5:kr-5) + &
+                                   var(:,:,kl+5:kr+5) ) ) * idel
+
+contains
+
+  subroutine set_coeff ( a )
+
+    implicit none
+
+    CCTK_REAL, dimension(13,8), intent(OUT) :: a
+    CCTK_REAL :: zero = 0.0
+    integer, parameter :: wp = kind(zero)
+
+    a(1,1) = -3.3910872088637970174997113084967416241083103770745_wp
+    a(2,1) = 16.955436044318985087498556542483708120541551885372_wp
+    a(3,1) = -33.910872088637970174997113084967416241083103770745_wp
+    a(4,1) = 33.910872088637970174997113084967416241083103770745_wp
+    a(5,1) = -16.955436044318985087498556542483708120541551885372_wp
+    a(6,1) = 3.3910872088637970174997113084967416241083103770745_wp
+    a(7,1) = 0.0_wp
+    a(8,1) = 0.0_wp
+    a(9,1) = 0.0_wp
+    a(10,1) = 0.0_wp
+    a(11,1) = 0.0_wp
+    a(12,1) = 0.0_wp
+    a(13,1) = 0.0_wp
+    a(1,2) = 3.2771399440263630592058029074141137010783820566473_wp
+    a(2,2) = -17.041127708937087907870175118553391245607586694566_wp
+    a(3,2) = 36.048539384289993651263831981555250711862202623121_wp
+    a(4,2) = -39.325679328316356710469634888969364412940584679768_wp
+    a(5,2) = 22.939979608184541414440620351898795907548674396531_wp
+    a(6,2) = -6.5542798880527261184116058148282274021567641132947_wp
+    a(7,2) = 0.65542798880527261184116058148282274021567641132947_wp
+    a(8,2) = 0.0_wp
+    a(9,2) = 0.0_wp
+    a(10,2) = 0.0_wp
+    a(11,2) = 0.0_wp
+    a(12,2) = 0.0_wp
+    a(13,2) = 0.0_wp
+    a(1,3) = -38.842059631038967294446317614758441308222147295410_wp
+    a(2,3) = 213.63132797071432011945474688117142719522181012475_wp
+    a(3,3) = -489.40995135109098791002360194595636048359905592216_wp
+    a(4,3) = 602.05192428110399306391792302875584027744328307885_wp
+    a(5,3) = -427.26265594142864023890949376234285439044362024951_wp
+    a(6,3) = 174.78926833967535282500842926641298588699966282934_wp
+    a(7,3) = -38.842059631038967294446317614758441308222147295410_wp
+    a(8,3) = 3.8842059631038967294446317614758441308222147295410_wp
+    a(9,3) = 0.0_wp
+    a(10,3) = 0.0_wp
+    a(11,3) = 0.0_wp
+    a(12,3) = 0.0_wp
+    a(13,3) = 0.0_wp
+    a(1,4) = 5.5613835719414344378807953109542612676331552744485_wp
+    a(2,4) = -33.368301431648606627284771865725567605798931646691_wp
+    a(3,4) = 86.201445365092233787152327319791049648313906753952_wp
+    a(4,4) = -125.68726872587641829610597402756630464850930920254_wp
+    a(5,4) = 114.00836322479940597655630387456235598647968312619_wp
+    a(6,4) = -66.736602863297213254569543731451135211597863293382_wp
+    a(7,4) = 25.026226073736454970463578899294175704349198735018_wp
+    a(8,4) = -5.5613835719414344378807953109542612676331552744485_wp
+    a(9,4) = 0.55613835719414344378807953109542612676331552744485_wp
+    a(10,4) = 0.0_wp
+    a(11,4) = 0.0_wp
+    a(12,4) = 0.0_wp
+    a(13,4) = 0.0_wp
+    a(1,5) = -12.115101476661536355654081268132755978592914829047_wp
+    a(2,5) = 84.805710336630754489578568876929291850150403803330_wp
+    a(3,5) = -266.53223248655379982438978789892063152904412623904_wp
+    a(4,5) = 496.71916054312299058181733199344299512230950799093_wp
+    a(5,5) = -608.17809412840912505383487966026435012536432441817_wp
+    a(6,5) = 508.83426201978452693747141326157575110090242281998_wp
+    a(7,5) = -290.76243543987687253569795043518614348622995589713_wp
+    a(8,5) = 109.03591328995382720088673141319480380733623346142_wp
+    a(9,5) = -24.230202953323072711308162536265511957185829658094_wp
+    a(10,5) = 2.4230202953323072711308162536265511957185829658094_wp
+    a(11,5) = 0.0_wp
+    a(12,5) = 0.0_wp
+    a(13,5) = 0.0_wp
+    a(1,6) = 0.78217600900123184961735065035840034142603567514089_wp
+    a(2,6) = -7.8217600900123184961735065035840034142603567514089_wp
+    a(3,6) = 35.197920405055433232780779266128015364171605381340_wp
+    a(4,6) = -93.861121080147821954082078043008040971124281016906_wp
+    a(5,6) = 164.25696189025868841964363657526407169946749177959_wp
+    a(6,6) = -197.10835426831042610357236389031688603936099013550_wp
+    a(7,6) = 164.25696189025868841964363657526407169946749177959_wp
+    a(8,6) = -93.861121080147821954082078043008040971124281016906_wp
+    a(9,6) = 35.197920405055433232780779266128015364171605381340_wp
+    a(10,6) = -7.8217600900123184961735065035840034142603567514089_wp
+    a(11,6) = 0.78217600900123184961735065035840034142603567514089_wp
+    a(12,6) = 0.0_wp
+    a(13,6) = 0.0_wp
+    a(1,7) = 0.0_wp
+    a(2,7) = 1.0830767761393601764536458481012280421614377748694_wp
+    a(3,7) = -10.830767761393601764536458481012280421614377748694_wp
+    a(4,7) = 48.738454926271207940414063164555261897264699869122_wp
+    a(5,7) = -129.96921313672322117443750177214736505937253298433_wp
+    a(6,7) = 227.44612298926563705526562810125788885390193272257_wp
+    a(7,7) = -272.93534758711876446631875372150946662468231926708_wp
+    a(8,7) = 227.44612298926563705526562810125788885390193272257_wp
+    a(9,7) = -129.96921313672322117443750177214736505937253298433_wp
+    a(10,7) = 48.738454926271207940414063164555261897264699869122_wp
+    a(11,7) = -10.830767761393601764536458481012280421614377748694_wp
+    a(12,7) = 1.0830767761393601764536458481012280421614377748694_wp
+    a(13,7) = 0.0_wp
+    a(1,8) = 0.0_wp
+    a(2,8) = 0.0_wp
+    a(3,8) = 0.99075245444434671889501396229410272246695863420506_wp
+    a(4,8) = -9.9075245444434671889501396229410272246695863420506_wp
+    a(5,8) = 44.583860449995602350275628303234622511013138539228_wp
+    a(6,8) = -118.89029453332160626740167547529232669603503610461_wp
+    a(7,8) = 208.05801543331281096795293208176157171806131318306_wp
+    a(8,8) = -249.66961851997537316154351849811388606167357581967_wp
+    a(9,8) = 208.05801543331281096795293208176157171806131318306_wp
+    a(10,8) = -118.89029453332160626740167547529232669603503610461_wp
+    a(11,8) = 44.583860449995602350275628303234622511013138539228_wp
+    a(12,8) = -9.9075245444434671889501396229410272246695863420506_wp
+    a(13,8) = 0.99075245444434671889501396229410272246695863420506_wp
+
+  end subroutine set_coeff
+
+end subroutine dissipation_8_4_alt
diff --git a/src/dissipation.c b/src/dissipation.c
index 6426431..a1557cc 100644
--- a/src/dissipation.c
+++ b/src/dissipation.c
@@ -27,6 +27,16 @@ void CCTK_FCALL CCTK_FNAME(dissipation_6_5_opt) (const CCTK_REAL *var,
                                              const CCTK_REAL *epsdis,
                                              const CCTK_REAL *diss_fraction,
                                              CCTK_REAL *rhs);
+void CCTK_FCALL CCTK_FNAME(dissipation_6_5_alt) (const CCTK_REAL *var,
+                                             const CCTK_INT *ni,
+                                             const CCTK_INT *nj,
+                                             const CCTK_INT *nk,
+                                             const CCTK_INT *bbox,
+                                             const CCTK_INT *gsize,
+                                             const CCTK_REAL *dx,
+                                             const CCTK_REAL *epsdis,
+                                             const CCTK_REAL *diss_fraction,
+                                             CCTK_REAL *rhs);
 void CCTK_FCALL CCTK_FNAME(dissipation_2_1) (const CCTK_REAL *var,
                                              const CCTK_INT *ni,
                                              const CCTK_INT *nj,
@@ -63,6 +73,15 @@ void CCTK_FCALL CCTK_FNAME(dissipation_8_4) (const CCTK_REAL *var,
                                              const CCTK_REAL *dx,
                                              const CCTK_REAL *epsdis,
                                              CCTK_REAL *rhs);
+void CCTK_FCALL CCTK_FNAME(dissipation_8_4_alt) (const CCTK_REAL *var,
+                                             const CCTK_INT *ni,
+                                             const CCTK_INT *nj,
+                                             const CCTK_INT *nk,
+                                             const CCTK_INT *bbox,
+                                             const CCTK_INT *gsize,
+                                             const CCTK_REAL *dx,
+                                             const CCTK_REAL *epsdis,
+                                             CCTK_REAL *rhs);
 
 static void
 apply (int const varindex, char const * const optstring, void * const arg);
@@ -170,9 +189,15 @@ apply (int const varindex, char const * const optstring, void * const arg)
       break;
     }
     case 8: {
-      CCTK_FNAME(dissipation_8_4)
-        (varptr, &cctk_lsh[0], &cctk_lsh[1], &cctk_lsh[2],
+      if ( CCTK_Equals(dissipation_type,"Mattson-Svard-Nordstrom") ) {
+        CCTK_FNAME(dissipation_8_4)
+          (varptr, &cctk_lsh[0], &cctk_lsh[1], &cctk_lsh[2],
+                            bbox, gsize, dx, &epsdis, rhsptr);
+      } else {
+        CCTK_FNAME(dissipation_8_4_alt)
+          (varptr, &cctk_lsh[0], &cctk_lsh[1], &cctk_lsh[2],
                             bbox, gsize, dx, &epsdis, rhsptr);
+      }
       break;
     }
     default:
@@ -187,9 +212,15 @@ apply (int const varindex, char const * const optstring, void * const arg)
       break;
     }
     case 6: {
-      CCTK_FNAME(dissipation_6_5_opt)
-        (varptr, cctk_lsh, cctk_gsh, cctk_lbnd,
+      if ( CCTK_Equals(dissipation_type,"Mattson-Svard-Nordstrom") ) {
+        CCTK_FNAME(dissipation_6_5_opt)
+          (varptr, cctk_lsh, cctk_gsh, cctk_lbnd,
+                            bbox, gsize, dx, &epsdis, &diss_fraction, rhsptr);
+      } else {
+        CCTK_FNAME(dissipation_6_5_alt)
+          (varptr, cctk_lsh, cctk_gsh, cctk_lbnd,
                             bbox, gsize, dx, &epsdis, &diss_fraction, rhsptr);
+      }
       break;
     }
     default:
diff --git a/src/make.code.defn b/src/make.code.defn
index 8767095..6ff753b 100644
--- a/src/make.code.defn
+++ b/src/make.code.defn
@@ -22,8 +22,10 @@ SRCS =  call_derivs.c \
         Dissipation_4_2.F90 \
         Dissipation_6_3.F90 \
         Dissipation_8_4.F90 \
+        Dissipation_8_4_alt.F90 \
         Dissipation_4_3_min_err_coeff.F90 \
         Dissipation_6_5_min_err_coeff.F90 \
+        Dissipation_6_5_min_err_coeff_alt.F90 \
         get_coeffs.c \
         Coefficients_2_1.F90 \
         Coefficients_4_2.F90 \