Added an optimized 6-3 operator and dissipation operators for the remaining

diagonal norm operators.


git-svn-id: https://svn.cct.lsu.edu/repos/numrel/LSUThorns/SummationByParts/trunk@38 f69c4107-0314-4c4f-9ad4-17e986b73f4a

7 files changed, 1019 insertions, 1 deletions

diff --git a/src/Derivatives_6_3_min_err_coeff.F90 b/src/Derivatives_6_3_min_err_coeff.F90
new file mode 100644
index 0000000..603c66c
--- /dev/null
+++ b/src/Derivatives_6_3_min_err_coeff.F90
@@ -0,0 +1,281 @@
+#include "cctk.h"
+#include "cctk_Functions.h"
+#include "cctk_Parameters.h"
+
+subroutine deriv_gf_6_3_opt ( 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(3), save :: a
+  CCTK_REAL, dimension(9,6), save :: q 
+  CCTK_REAL :: idel
+
+  CCTK_INT :: il, ir, jl, jr, kl, kr
+
+  logical, save :: first = .true.
+
+  if ( first ) then
+    a(1) = 3.0_wp/4.0_wp; a(2) = -3.0_wp/20.0_wp; a(3) = 1.0_wp/60.0_wp
+
+    q(1,1) = -1.582533518939116418785258993332844897062_wp
+    q(2,1) = 2.033426786468126253898161347360808173712_wp
+    q(3,1) = -0.1417052898146741610733887894481170575600_wp
+    q(4,1) = -0.4501096599735708523162117824920488989702_wp
+    q(5,1) = 0.1042956382142412661862395105494407610836_wp
+    q(6,1) = 0.03662604404499391209045870736276191879693_wp
+    q(7,1) = 0_wp
+    q(8,1) = 0_wp
+    q(9,1) = 0_wp
+    q(1,2) = -0.4620701275035953590186631853846278325646_wp
+    q(2,2) = 0_wp
+    q(3,2) = 0.2873679417026202568532985205129449923126_wp
+    q(4,2) = 0.2585974499280928196267362923074433487080_wp
+    q(5,2) = -0.06894808744606961472005221923058251153103_wp
+    q(6,2) = -0.01494717668104810274131940820517799692506_wp
+    q(7,2) = 0_wp
+    q(8,2) = 0_wp
+    q(9,2) = 0_wp
+    q(1,3) = 0.07134398748360337973038301686379010397038_wp
+    q(2,3) = -0.6366933020423417826592908754928085932593_wp
+    q(3,3) = 0_wp
+    q(4,3) = 0.6067199374180168986519150843189505198519_wp
+    q(5,3) = -0.02338660408468356531858175098561718651857_wp
+    q(6,3) = -0.01798401877459493040442547470431484404443_wp
+    q(7,3) = 0_wp
+    q(8,3) = 0_wp
+    q(9,3) = 0_wp
+    q(1,4) = 0.1146397975178068401430112823144985150596_wp
+    q(2,4) = -0.2898424301162697370942324201800071793273_wp
+    q(3,4) = -0.3069262456316931913128086944558079603132_wp
+    q(4,4) = 0_wp
+    q(5,4) = 0.5203848121857539166740071338174418292578_wp
+    q(6,4) = -0.05169127637022742348368508279860701098408_wp
+    q(7,4) = 0.01343534241462959507370778130248180630715_wp
+    q(8,4) = 0_wp
+    q(9,4) = 0_wp
+    q(1,5) = -0.03614399304268576976452921364705641609825_wp
+    q(2,5) = 0.1051508663818248421520867474440761344449_wp
+    q(3,5) = 0.01609777419666805778308369351834662756172_wp
+    q(4,5) = -0.7080721616106272031118456849378369336023_wp
+    q(5,5) = 0_wp
+    q(6,5) = 0.7692160858661111736140494493705980473867_wp
+    q(7,5) = -0.1645296432652024882569506157166433921544_wp
+    q(8,5) = 0.01828107147391138758410562396851593246160_wp
+    q(9,5) = 0_wp
+    q(1,6) = -0.01141318406360863692889821914555232596651_wp
+    q(2,6) = 0.02049729840293952857599941220163960606616_wp
+    q(3,6) = 0.01113095018331244864875173213474522093204_wp
+    q(4,6) = 0.06324365883611076515355091406993789453750_wp
+    q(5,6) = -0.6916640154753724474963890679085181638850_wp
+    q(6,6) = 0_wp
+    q(7,6) = 0.7397091390607520376247117645715851236273_wp
+    q(8,6) = -0.1479418278121504075249423529143170247255_wp
+    q(9,6) = 0.01643798086801671194721581699047966941394_wp
+
+    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,:,:) + &
+                      q(5,1) * var(5,:,:) + q(6,1) * var(6,:,:) ) * idel
+      dvar(2,:,:) = ( q(1,2) * var(1,:,:) + 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(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(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(6,5) * var(6,:,:) + q(7,5) * var(7,:,:) + &
+                      q(8,5) * var(8,:,:) ) * idel
+      dvar(6,:,:) = ( q(1,6) * var(1,:,:) + q(2,6) * var(2,:,:) + &
+                      q(3,6) * var(3,:,:) + q(4,6) * var(4,:,:) + &
+                      q(5,6) * var(5,:,:) + q(7,6) * var(7,:,:) + &
+                      q(8,6) * var(8,:,:) + q(9,6) * var(9,:,:) ) * idel
+
+      il = 7
+    end if
+    if ( bb(2) == 0 ) then
+      ir = ni - gsize
+    else
+      dvar(ni-5,:,:) = - ( q(1,6) * var(ni,:,:) + q(2,6) * var(ni-1,:,:) + &
+                           q(3,6) * var(ni-2,:,:) + q(4,6) * var(ni-3,:,:) + &
+                           q(5,6) * var(ni-4,:,:) + q(7,6) * var(ni-6,:,:) + &
+                           q(8,6) * var(ni-7,:,:) + &
+                           q(9,6) * var(ni-8,:,:) ) * idel
+      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(6,5) * var(ni-5,:,:) + q(7,5) * var(ni-6,:,:) + &
+                           q(8,5) * var(ni-7,:,:) ) * idel
+      dvar(ni-3,:,:) = - ( q(1,4) * var(ni,:,:) + q(2,4) * var(ni-1,:,:) + &
+                           q(3,4) * var(ni-2,:,:) + 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(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(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,:,:) + &
+                           q(5,1) * var(ni-4,:,:) + &
+                           q(6,1) * var(ni-5,:,:) ) * idel
+
+      ir = ni - 6
+    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,:,:) ) + &
+                        a(3) * ( var(il+3:ir+3,:,:) - &
+                                 var(il-3:ir-3,:,:) ) ) * 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,:) + &
+                      q(5,1) * var(:,5,:) + q(6,1) * var(:,6,:) ) * idel
+      dvar(:,2,:) = ( q(1,2) * var(:,1,:) + 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(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(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(6,5) * var(:,6,:) + q(7,5) * var(:,7,:) + &
+                      q(8,5) * var(:,8,:) ) * idel
+      dvar(:,6,:) = ( q(1,6) * var(:,1,:) + q(2,6) * var(:,2,:) + &
+                      q(3,6) * var(:,3,:) + q(4,6) * var(:,4,:) + &
+                      q(5,6) * var(:,5,:) + q(7,6) * var(:,7,:) + &
+                      q(8,6) * var(:,8,:) + q(9,6) * var(:,9,:) ) * idel
+
+      jl = 7
+    end if
+    if ( bb(2) == 0 ) then
+      jr = nj - gsize
+    else
+      dvar(:,nj-5,:) = - ( q(1,6) * var(:,nj,:) + q(2,6) * var(:,nj-1,:) + &
+                           q(3,6) * var(:,nj-2,:) + q(4,6) * var(:,nj-3,:) + &
+                           q(5,6) * var(:,nj-4,:) + q(7,6) * var(:,nj-6,:) + &
+                           q(8,6) * var(:,nj-7,:) + &
+                           q(9,6) * var(:,nj-8,:) ) * idel
+      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(6,5) * var(:,nj-5,:) + q(7,5) * var(:,nj-6,:) + &
+                           q(8,5) * var(:,nj-7,:) ) * idel
+      dvar(:,nj-3,:) = - ( q(1,4) * var(:,nj,:) + q(2,4) * var(:,nj-1,:) + &
+                           q(3,4) * var(:,nj-2,:) + 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(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(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,:) + &
+                           q(5,1) * var(:,nj-4,:) + &
+                           q(6,1) * var(:,nj-5,:) ) * idel
+
+      jr = nj - 6
+    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,:) ) + &
+                        a(3) * ( var(:,jl+3:jr+3,:) - &
+                                 var(:,jl-3:jr-3,:) ) ) * 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) + &
+                      q(5,1) * var(:,:,5) + q(6,1) * var(:,:,6) ) * idel
+      dvar(:,:,2) = ( q(1,2) * var(:,:,1) + 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(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(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(6,5) * var(:,:,6) + q(7,5) * var(:,:,7) + &
+                      q(8,5) * var(:,:,8) ) * idel
+      dvar(:,:,6) = ( q(1,6) * var(:,:,1) + q(2,6) * var(:,:,2) + &
+                      q(3,6) * var(:,:,3) + q(4,6) * var(:,:,4) + &
+                      q(5,6) * var(:,:,5) + q(7,6) * var(:,:,7) + &
+                      q(8,6) * var(:,:,8) + q(9,6) * var(:,:,9) ) * idel
+
+      kl = 7
+    end if
+    if ( bb(2) == 0 ) then
+      kr = nk - gsize
+    else 
+      dvar(:,:,nk-5) = - ( q(1,6) * var(:,:,nk) + q(2,6) * var(:,:,nk-1) + &
+                           q(3,6) * var(:,:,nk-2) + q(4,6) * var(:,:,nk-3) + &
+                           q(5,6) * var(:,:,nk-4) + q(7,6) * var(:,:,nk-6) + &
+                           q(8,6) * var(:,:,nk-7) + &
+                           q(9,6) * var(:,:,nk-8) ) * idel
+      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(6,5) * var(:,:,nk-5) + q(7,5) * var(:,:,nk-6) + &
+                           q(8,5) * var(:,:,nk-7) ) * idel
+      dvar(:,:,nk-3) = - ( q(1,4) * var(:,:,nk) + q(2,4) * var(:,:,nk-1) + &
+                           q(3,4) * var(:,:,nk-2) + 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(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(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) + &
+                           q(5,1) * var(:,:,nk-4) + &
+                           q(6,1) * var(:,:,nk-5) ) * idel
+
+      kr = nk - 6
+    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) ) + &
+                        a(3) * ( var(:,:,kl+3:kr+3) - &
+                                 var(:,:,kl-3:kr-3) ) ) * idel
+  end select direction
+end subroutine deriv_gf_6_3_opt
diff --git a/src/Dissipation_2_1.F90 b/src/Dissipation_2_1.F90
new file mode 100644
index 0000000..62ba030
--- /dev/null
+++ b/src/Dissipation_2_1.F90
@@ -0,0 +1,137 @@
+! $Header$
+
+#include "cctk.h"
+
+subroutine dissipation_2_1 (var, ni, nj, nk, bb, gsize, delta, epsdis, rhs)
+
+  implicit none
+
+  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) :: epsdis 
+
+  CCTK_REAL :: zero = 0.0
+  integer, parameter :: wp = kind(zero)
+  integer :: i, j, k
+  CCTK_REAL, dimension(3,2) :: a
+  CCTK_REAL :: idel
+
+  CCTK_INT :: il, ir, jl, jr, kl, kr
+
+  call set_coeff ( a )
+
+  idel = epsdis / 4
+
+  if ( bb(1) == 0 ) then
+    il = 1 + gsize(1)
+  else
+    rhs(1,:,:) = rhs(1,:,:) + &
+                 ( a(1,1) * var(1,:,:) + a(2,1) * var(2,:,:) ) * idel
+    rhs(2,:,:) = rhs(2,:,:) + &
+                 ( a(1,2) * var(1,:,:) + a(2,2) * var(2,:,:) + &
+                   a(3,2) * var(3,:,:) ) * idel
+
+    il = 3
+  end if
+  if ( bb(2) == 0 ) then
+    ir = ni - gsize(1)
+  else
+    rhs(ni-1,:,:) = rhs(ni-1,:,:) + &
+                 ( a(1,2) * var(ni,:,:) + a(2,2) * var(ni-1,:,:) + &
+                   a(3,2) * var(ni-2,:,:) ) * idel
+    rhs(ni,:,:)   = rhs(ni,:,:) + &
+                 ( a(1,1) * var(ni,:,:) + a(2,1) * var(ni-1,:,:) ) * idel
+
+    ir = ni - 2
+  end if
+  rhs(il:ir,:,:) = rhs(il:ir,:,:) + &
+                   ( -2.0_wp * var(il:ir,:,:) + &
+                             ( var(il-1:ir-1,:,:) + &
+                               var(il+1:ir+1,:,:) ) ) * idel
+
+  call set_coeff ( a )
+
+  idel = epsdis / 4
+
+  if ( bb(3) == 0 ) then
+    jl = 1 + gsize(2)
+  else
+    rhs(:,1,:) = rhs(:,1,:) + &
+                 ( a(1,1) * var(:,1,:) + a(2,1) * var(:,2,:) ) * idel
+    rhs(:,2,:) = rhs(:,2,:) + &
+                 ( a(1,2) * var(:,1,:) + a(2,2) * var(:,2,:) + &
+                   a(3,2) * var(:,3,:) ) * idel
+
+    jl = 3
+  end if
+  if ( bb(4) == 0 ) then
+    jr = nj - gsize(2)
+  else
+    rhs(:,nj-1,:) = rhs(:,nj-1,:) + &
+                 ( a(1,2) * var(:,nj,:) + a(2,2) * var(:,nj-1,:) + &
+                   a(3,2) * var(:,nj-2,:) ) * idel
+    rhs(:,nj,:)   = rhs(:,nj,:) + &
+                 ( a(1,1) * var(:,nj,:) + a(2,1) * var(:,nj-1,:) ) * idel
+
+    jr = nj - 2
+  end if
+  rhs(:,jl:jr,:) = rhs(:,jl:jr,:) + &
+                   ( -2.0_wp * var(:,jl:jr,:) + &
+                             ( var(:,jl-1:jr-1,:) + &
+                               var(:,jl+1:jr+1,:) ) ) * idel
+
+  call set_coeff ( a )
+
+  idel = epsdis / 4
+
+  if ( bb(5) == 0 ) then
+    kl = 1 + gsize(3)
+  else
+    rhs(:,:,1) = rhs(:,:,1) + &
+                 ( a(1,1) * var(:,:,1) + a(2,1) * var(:,:,2) ) * idel
+    rhs(:,:,2) = rhs(:,:,2) + &
+                 ( a(1,2) * var(:,:,1) + a(2,2) * var(:,:,2) + &
+                   a(3,2) * var(:,:,3) ) * idel
+
+    kl = 3
+  end if
+  if ( bb(6) == 0 ) then
+    kr = nk - gsize(3)
+  else
+    rhs(:,:,nk-1) = rhs(:,:,nk-1) + &
+                 ( a(1,2) * var(:,:,nk) + a(2,2) * var(:,:,nk-1) + &
+                   a(3,2) * var(:,:,nk-2) ) * idel
+    rhs(:,:,nk)   = rhs(:,:,nk) + &
+                 ( a(1,1) * var(:,:,nk) + a(2,1) * var(:,:,nk-1) ) * idel
+
+    kr = nk - 2
+  end if
+  rhs(:,:,kl:kr) = rhs(:,:,kl:kr) + &
+                   ( -2.0_wp * var(:,:,kl:kr) + &
+                             ( var(:,:,kl-1:kr-1) + &
+                               var(:,:,kl+1:kr+1) ) ) * idel
+
+contains
+
+  subroutine set_coeff ( a )
+
+    implicit none
+
+    CCTK_REAL, dimension(3,2), intent(OUT) :: a
+    CCTK_REAL :: zero = 0.0
+    integer, parameter :: wp = kind(zero)
+
+    a(1,1) = -2.0_wp
+    a(2,1) = 2.0_wp
+    a(3,1) = 0.0_wp
+    a(1,2) = 1.0_wp
+    a(2,2) = -2.0_wp
+    a(3,2) = 1.0_wp
+
+  end subroutine set_coeff
+
+end subroutine dissipation_2_1
diff --git a/src/Dissipation_4_2.F90 b/src/Dissipation_4_2.F90
new file mode 100644
index 0000000..16a870d
--- /dev/null
+++ b/src/Dissipation_4_2.F90
@@ -0,0 +1,215 @@
+! $Header$
+
+#include "cctk.h"
+
+subroutine dissipation_4_2 (var, ni, nj, nk, bb, gsize, delta, epsdis, rhs)
+
+  implicit none
+
+  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) :: epsdis 
+
+  CCTK_REAL :: zero = 0.0
+  integer, parameter :: wp = kind(zero)
+  integer :: i, j, k
+  CCTK_REAL, dimension(6,4) :: a
+  CCTK_REAL :: idel
+
+  CCTK_INT :: il, ir, jl, jr, kl, kr
+
+  call set_coeff ( a )
+
+  idel = epsdis / 16
+
+  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,:,:) ) * 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,:,:) ) * 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,:,:) ) * idel
+    rhs(4,:,:) = rhs(4,:,:) + &
+                 ( 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,:,:) ) * idel
+
+    il = 5
+  end if
+  if ( bb(2) == 0 ) then
+    ir = ni - gsize(1)
+  else
+    rhs(ni-3,:,:) = rhs(ni-3,:,:) + &
+                 ( 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,:,:) ) * 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,:,:) ) * 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,:,:) ) * idel
+    rhs(ni,:,:)   = rhs(ni,:,:) + &
+                 ( a(1,1) * var(ni,:,:) + a(2,1) * var(ni-1,:,:) + &
+                   a(3,1) * var(ni-2,:,:) ) * idel
+
+    ir = ni - 4
+  end if
+  rhs(il:ir,:,:) = rhs(il:ir,:,:) + &
+                   ( -6.0_wp * var(il:ir,:,:) + &
+                      4.0_wp * ( var(il-1:ir-1,:,:) + &
+                                 var(il+1:ir+1,:,:) ) - &
+                               ( var(il-2:ir-2,:,:) + &
+                                 var(il+2:ir+2,:,:) ) ) * idel
+
+  call set_coeff ( a )
+
+  idel = epsdis / 16
+
+  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,:) ) * 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,:) ) * 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,:) ) * idel
+    rhs(:,4,:) = rhs(:,4,:) + &
+                 ( 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,:) ) * idel
+
+    jl = 5
+  end if
+  if ( bb(4) == 0 ) then
+    jr = nj - gsize(2)
+  else
+    rhs(:,nj-3,:) = rhs(:,nj-3,:) + &
+                 ( 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,:) ) * 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,:) ) * 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,:) ) * idel
+    rhs(:,nj,:)   = rhs(:,nj,:) + &
+                 ( a(1,1) * var(:,nj,:) + a(2,1) * var(:,nj-1,:) + &
+                   a(3,1) * var(:,nj-2,:) ) * idel
+
+    jr = nj - 4
+  end if
+  rhs(:,jl:jr,:) = rhs(:,jl:jr,:) + &
+                   ( -6.0_wp * var(:,jl:jr,:) + &
+                      4.0_wp * ( var(:,jl-1:jr-1,:) + &
+                                 var(:,jl+1:jr+1,:) ) - &
+                               ( var(:,jl-2:jr-2,:) + &
+                                 var(:,jl+2:jr+2,:) ) ) * idel
+
+  call set_coeff ( a )
+
+  idel = epsdis / 16
+
+  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) ) * 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) ) * 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) ) * idel
+    rhs(:,:,4) = rhs(:,:,4) + &
+                 ( 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) ) * idel
+
+    kl = 5
+  end if
+  if ( bb(6) == 0 ) then
+    kr = nk - gsize(3)
+  else
+    rhs(:,:,nk-3) = rhs(:,:,nk-3) + &
+                 ( 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) ) * 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) ) * 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) ) * idel
+    rhs(:,:,nk)   = rhs(:,:,nk) + &
+                 ( a(1,1) * var(:,:,nk) + a(2,1) * var(:,:,nk-1) + &
+                   a(3,1) * var(:,:,nk-2) ) * idel
+
+    kr = nk - 4
+  end if
+  rhs(:,:,kl:kr) = rhs(:,:,kl:kr) + &
+                   ( -6.0_wp * var(:,:,kl:kr) + &
+                      4.0_wp * ( var(:,:,kl-1:kr-1) + &
+                                 var(:,:,kl+1:kr+1) ) - &
+                               ( var(:,:,kl-2:kr-2) + &
+                                 var(:,:,kl+2:kr+2) ) ) * idel
+
+contains
+
+  subroutine set_coeff ( a )
+
+    implicit none
+
+    CCTK_REAL, dimension(6,4), intent(OUT) :: a
+    CCTK_REAL :: zero = 0.0
+    integer, parameter :: wp = kind(zero)
+
+    a(1,1) = -2.8235294117647058823529411764705882352941176470588_wp
+    a(2,1) = 5.6470588235294117647058823529411764705882352941176_wp
+    a(3,1) = -2.8235294117647058823529411764705882352941176470588_wp
+    a(4,1) = 0.0_wp
+    a(5,1) = 0.0_wp
+    a(6,1) = 0.0_wp
+    a(1,2) = 1.6271186440677966101694915254237288135593220338983_wp
+    a(2,2) = -4.0677966101694915254237288135593220338983050847458_wp
+    a(3,2) = 3.2542372881355932203389830508474576271186440677966_wp
+    a(4,2) = -0.81355932203389830508474576271186440677966101694915_wp
+    a(5,2) = 0.0_wp
+    a(6,2) = 0.0_wp
+    a(1,3) = -1.1162790697674418604651162790697674418604651162791_wp
+    a(2,3) = 4.4651162790697674418604651162790697674418604651163_wp
+    a(3,3) = -6.6976744186046511627906976744186046511627906976744_wp
+    a(4,3) = 4.4651162790697674418604651162790697674418604651163_wp
+    a(5,3) = -1.1162790697674418604651162790697674418604651162791_wp
+    a(6,3) = 0.0_wp
+    a(1,4) = 0.0_wp
+    a(2,4) = -0.97959183673469387755102040816326530612244897959184_wp
+    a(3,4) = 3.9183673469387755102040816326530612244897959183673_wp
+    a(4,4) = -5.8775510204081632653061224489795918367346938775510_wp
+    a(5,4) = 3.9183673469387755102040816326530612244897959183673_wp
+    a(6,4) = -0.97959183673469387755102040816326530612244897959184_wp
+
+  end subroutine set_coeff
+
+end subroutine dissipation_4_2
diff --git a/src/Dissipation_6_3.F90 b/src/Dissipation_6_3.F90
new file mode 100644
index 0000000..4f35eec
--- /dev/null
+++ b/src/Dissipation_6_3.F90
@@ -0,0 +1,323 @@
+! $Header$
+
+#include "cctk.h"
+
+subroutine dissipation_6_3 (var, ni, nj, nk, bb, gsize, delta, epsdis, rhs)
+
+  implicit none
+
+  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) :: epsdis 
+
+  CCTK_REAL :: zero = 0.0
+  integer, parameter :: wp = kind(zero)
+  integer :: i, j, k
+  CCTK_REAL, dimension(9,6) :: a
+  CCTK_REAL :: idel
+
+  CCTK_INT :: il, ir, jl, jr, kl, kr
+
+  call set_coeff ( a )
+
+  idel = epsdis / 64
+
+  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,:,:) ) * 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,:,:) ) * 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,:,:) ) * 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,:,:) ) * idel
+    rhs(5,:,:) = rhs(5,:,:) + &
+                 ( 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,:,:) ) * idel
+    rhs(6,:,:) = rhs(6,:,:) + &
+                 ( 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,:,:) ) * idel
+
+    il = 7
+  end if
+  if ( bb(2) == 0 ) then
+    ir = ni - gsize(1)
+  else
+    rhs(ni-5,:,:) = rhs(ni-5,:,:) + &
+                 ( 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,:,:) ) * idel
+    rhs(ni-4,:,:) = rhs(ni-4,:,:) + &
+                 ( 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,:,:) ) * 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,:,:) ) * 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,:,:) ) * 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,:,:) ) * 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,:,:) ) * idel
+
+    ir = ni - 6
+  end if
+  rhs(il:ir,:,:) = rhs(il:ir,:,:) + &
+                   ( -20.0_wp * var(il:ir,:,:) + &
+                      15.0_wp * ( var(il-1:ir-1,:,:) + &
+                                  var(il+1:ir+1,:,:) ) - &
+                       6.0_wp * ( var(il-2:ir-2,:,:) + &
+                                  var(il+2:ir+2,:,:) ) + &
+                                ( var(il-3:ir-3,:,:) + &
+                                  var(il+3:ir+3,:,:) ) ) * idel
+
+  call set_coeff ( a )
+
+  idel = epsdis / 64
+
+  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,:) ) * 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,:) ) * 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,:) ) * 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,:) ) * idel
+    rhs(:,5,:) = rhs(:,5,:) + &
+                 ( 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,:) ) * idel
+    rhs(:,6,:) = rhs(:,6,:) + &
+                 ( 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,:) ) * idel
+
+    jl = 7
+  end if
+  if ( bb(4) == 0 ) then
+    jr = nj - gsize(2)
+  else
+    rhs(:,nj-5,:) = rhs(:,nj-5,:) + &
+                 ( 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,:) ) * idel
+    rhs(:,nj-4,:) = rhs(:,nj-4,:) + &
+                 ( 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,:) ) * 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,:) ) * 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,:) ) * 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,:) ) * 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,:) ) * idel
+
+    jr = nj - 6
+  end if
+  rhs(:,jl:jr,:) = rhs(:,jl:jr,:) + &
+                   ( -20.0_wp * var(:,jl:jr,:) + &
+                      15.0_wp * ( var(:,jl-1:jr-1,:) + &
+                                  var(:,jl+1:jr+1,:) ) - &
+                       6.0_wp * ( var(:,jl-2:jr-2,:) + &
+                                  var(:,jl+2:jr+2,:) ) + &
+                                ( var(:,jl-3:jr-3,:) + &
+                                  var(:,jl+3:jr+3,:) ) ) * idel
+
+  call set_coeff ( a )
+
+  idel = epsdis / 64
+
+  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) ) * 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) ) * 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) ) * 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) ) * idel
+    rhs(:,:,5) = rhs(:,:,5) + &
+                 ( 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) ) * idel
+    rhs(:,:,6) = rhs(:,:,6) + &
+                 ( 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) ) * idel
+
+    kl = 7
+  end if
+  if ( bb(6) == 0 ) then
+    kr = nk - gsize(3)
+  else
+    rhs(:,:,nk-5) = rhs(:,:,nk-5) + &
+                 ( 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) ) * idel
+    rhs(:,:,nk-4) = rhs(:,:,nk-4) + &
+                 ( 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) ) * 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) ) * 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) ) * 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) ) * 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) ) * idel
+
+    kr = nk - 6
+  end if
+  rhs(:,:,kl:kr) = rhs(:,:,kl:kr) + &
+                   ( -20.0_wp * var(:,:,kl:kr) + &
+                      15.0_wp * ( var(:,:,kl-1:kr-1) + &
+                                  var(:,:,kl+1:kr+1) ) - &
+                       6.0_wp * ( var(:,:,kl-2:kr-2) + &
+                                  var(:,:,kl+2:kr+2) ) + &
+                                ( var(:,:,kl-3:kr-3) + &
+                                  var(:,:,kl+3:kr+3) ) ) * idel
+
+contains
+
+  subroutine set_coeff ( a )
+
+    implicit none
+
+    CCTK_REAL, dimension(9,6), intent(OUT) :: a
+    CCTK_REAL :: zero = 0.0
+    integer, parameter :: wp = kind(zero)
+
+    a(1,1) = -3.1650670378782328375705179866656897941241116565316_wp
+    a(2,1) = 9.4952011136346985127115539599970693823723349695948_wp
+    a(3,1) = -9.4952011136346985127115539599970693823723349695948_wp
+    a(4,1) = 3.1650670378782328375705179866656897941241116565316_wp
+    a(5,1) = 0.0_wp
+    a(6,1) = 0.0_wp
+    a(7,1) = 0.0_wp
+    a(8,1) = 0.0_wp
+    a(9,1) = 0.0_wp
+    a(1,2) = 2.1576625322567218846249895946058436693581952884375_wp
+    a(2,2) = -7.1922084408557396154166319820194788978606509614584_wp
+    a(3,2) = 8.6306501290268875384999583784233746774327811537501_wp
+    a(4,2) = -4.3153250645134437692499791892116873387163905768751_wp
+    a(5,2) = 0.71922084408557396154166319820194788978606509614584_wp
+    a(6,2) = 0.0_wp
+    a(7,2) = 0.0_wp
+    a(8,2) = 0.0_wp
+    a(9,2) = 0.0_wp
+    a(1,3) = -4.7805237919586868314275175212098856510512725931391_wp
+    a(2,3) = 19.122095167834747325710070084839542604205090372556_wp
+    a(3,3) = -30.276650682405016599040944300995942456658059756547_wp
+    a(4,3) = 23.902618959793434157137587606049428255256362965695_wp
+    a(5,3) = -9.5610475839173736628550350424197713021025451862781_wp
+    a(6,3) = 1.5935079306528956104758391737366285503504241977130_wp
+    a(7,3) = 0.0_wp
+    a(8,3) = 0.0_wp
+    a(9,3) = 0.0_wp
+    a(1,4) = 0.80612054487777570442246687814890837842881134540026_wp
+    a(2,4) = -4.8367232692666542265348012688934502705728680724016_wp
+    a(3,4) = 12.091808173166635566337003172233625676432170181004_wp
+    a(4,4) = -16.122410897555514088449337562978167568576226908005_wp
+    a(5,4) = 12.091808173166635566337003172233625676432170181004_wp
+    a(6,4) = -4.8367232692666542265348012688934502705728680724016_wp
+    a(7,4) = 0.80612054487777570442246687814890837842881134540026_wp
+    a(8,4) = 0.0_wp
+    a(9,4) = 0.0_wp
+    a(1,5) = 0.0_wp
+    a(2,5) = 1.0968642884346832550463374381109559476958232829758_wp
+    a(3,5) = -6.5811857306080995302780246286657356861749396978545_wp
+    a(4,5) = 16.452964326520248825695061571664339215437349244636_wp
+    a(5,5) = -21.937285768693665100926748762219118953916465659515_wp
+    a(6,5) = 16.452964326520248825695061571664339215437349244636_wp
+    a(7,5) = -6.5811857306080995302780246286657356861749396978545_wp
+    a(8,5) = 1.0968642884346832550463374381109559476958232829758_wp
+    a(9,5) = 0.0_wp
+    a(1,6) = 0.0_wp
+    a(2,6) = 0.0_wp
+    a(3,6) = 0.98627885208100271683294901942878016483641925983425_wp
+    a(4,6) = -5.9176731124860163009976941165726809890185155590055_wp
+    a(5,6) = 14.794182781215040752494235291431702472546288897514_wp
+    a(6,6) = -19.725577041620054336658980388575603296728385196685_wp
+    a(7,6) = 14.794182781215040752494235291431702472546288897514_wp
+    a(8,6) = -5.9176731124860163009976941165726809890185155590055_wp
+    a(9,6) = 0.98627885208100271683294901942878016483641925983425_wp
+
+  end subroutine set_coeff
+
+end subroutine dissipation_6_3
diff --git a/src/call_derivs.c b/src/call_derivs.c
index 7d69c6d..25db68e 100644
--- a/src/call_derivs.c
+++ b/src/call_derivs.c
@@ -63,6 +63,15 @@ void DiffGv ( const CCTK_POINTER_TO_CONST cctkGH_, const CCTK_INT dir,
                                        const CCTK_INT *gsize,
                                        const CCTK_REAL *delta,
                                        CCTK_REAL *dvar);
+  void CCTK_FCALL CCTK_FNAME(deriv_gf_6_3_opt)(const CCTK_REAL *var,
+                                       const CCTK_INT *ni,
+                                       const CCTK_INT *nj,
+                                       const CCTK_INT *nk,
+                                       const CCTK_INT *dir,
+                                       const CCTK_INT *bb,
+                                       const CCTK_INT *gsize,
+                                       const CCTK_REAL *delta,
+                                       CCTK_REAL *dvar);
   void CCTK_FCALL CCTK_FNAME(deriv_gf_6_5)(const CCTK_REAL *var,
                                        const CCTK_INT *ni,
                                        const CCTK_INT *nj,
@@ -161,6 +170,10 @@ void DiffGv ( const CCTK_POINTER_TO_CONST cctkGH_, const CCTK_INT dir,
       }
     } else {
       switch(loc_order) {
+      case 6: {
+        CCTK_FNAME(deriv_gf_6_3_opt)(var,&ni,&nj,&nk,&dir,bb,&gsize,&delta,dvar);
+        break;
+      }
       case 8: {
         CCTK_FNAME(deriv_gf_8_4_opt)(var,&ni,&nj,&nk,&dir,bb,&gsize,&delta,dvar);
         break;
diff --git a/src/dissipation.c b/src/dissipation.c
index 2b28950..6426431 100644
--- a/src/dissipation.c
+++ b/src/dissipation.c
@@ -27,6 +27,33 @@ 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_2_1) (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);
+void CCTK_FCALL CCTK_FNAME(dissipation_4_2) (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);
+void CCTK_FCALL CCTK_FNAME(dissipation_6_3) (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);
 void CCTK_FCALL CCTK_FNAME(dissipation_8_4) (const CCTK_REAL *var,
                                              const CCTK_INT *ni,
                                              const CCTK_INT *nj,
@@ -124,6 +151,24 @@ apply (int const varindex, char const * const optstring, void * const arg)
   
   if ( CCTK_Equals(norm_type,"Diagonal") ) {
     switch(order) {
+    case 2: {
+      CCTK_FNAME(dissipation_2_1)
+        (varptr, &cctk_lsh[0], &cctk_lsh[1], &cctk_lsh[2],
+                            bbox, gsize, dx, &epsdis, rhsptr);
+      break;
+    }
+    case 4: {
+      CCTK_FNAME(dissipation_4_2)
+        (varptr, &cctk_lsh[0], &cctk_lsh[1], &cctk_lsh[2],
+                            bbox, gsize, dx, &epsdis, rhsptr);
+      break;
+    }
+    case 6: {
+      CCTK_FNAME(dissipation_6_3)
+        (varptr, &cctk_lsh[0], &cctk_lsh[1], &cctk_lsh[2],
+                            bbox, gsize, dx, &epsdis, rhsptr);
+      break;
+    }
     case 8: {
       CCTK_FNAME(dissipation_8_4)
         (varptr, &cctk_lsh[0], &cctk_lsh[1], &cctk_lsh[2],
diff --git a/src/make.code.defn b/src/make.code.defn
index c113cfe..cad8b2e 100644
--- a/src/make.code.defn
+++ b/src/make.code.defn
@@ -7,6 +7,7 @@ SRCS =  call_derivs.c \
         Derivatives_2_1.F90 \
         Derivatives_4_2.F90 \
         Derivatives_6_3.F90 \
+        Derivatives_6_3_min_err_coeff.F90 \
         Derivatives_8_4.F90 \
         Derivatives_8_4_min_err_coeff.F90 \
         Derivatives_4_3.F90 \
@@ -17,8 +18,11 @@ SRCS =  call_derivs.c \
         set_norm_mask.F90 \
         CheckGridSizes.F90 \
         dissipation.c \
-        Dissipation_4_3_min_err_coeff.F90 \
+        Dissipation_2_1.F90 \
+        Dissipation_4_2.F90 \
+        Dissipation_6_3.F90 \
         Dissipation_8_4.F90 \
+        Dissipation_4_3_min_err_coeff.F90 \
         Dissipation_6_5.F90 \
         Dissipation_6_5_min_err_coeff.F90 \
         get_coeffs.c \