Dissipation operator for the optimized 4-3 restricted full norm case. Testing

still in progress, but it looks like the convergence order is right.


git-svn-id: https://svn.cct.lsu.edu/repos/numrel/LSUThorns/SummationByParts/trunk@33 f69c4107-0314-4c4f-9ad4-17e986b73f4a

4 files changed, 519 insertions, 0 deletions

diff --git a/param.ccl b/param.ccl
index 0866282..ebbe4d4 100644
--- a/param.ccl
+++ b/param.ccl
@@ -27,6 +27,11 @@ REAL epsdis "Dissipation strength" STEERABLE=always
   *:* :: "Values typical between 0 and 1"
 } 0.2
 
+REAL diss_fraction "Fractional size of the transition region for the full restricted dissipation operator"
+{
+  0:0.5 :: ""
+} 0.2
+
 STRING vars "List of evolved grid functions that should have dissipation added" STEERABLE=always
 {
   .* :: "Must be a valid list of grid functions"
diff --git a/src/Dissipation_4_3_min_err_coeff.F90 b/src/Dissipation_4_3_min_err_coeff.F90
new file mode 100644
index 0000000..eefbecf
--- /dev/null
+++ b/src/Dissipation_4_3_min_err_coeff.F90
@@ -0,0 +1,497 @@
+! $Header$
+
+#include "cctk.h"
+#include "cctk_Parameters.h"
+
+
+subroutine dissipation_4_3_opt (var, lsh, gsh, lbnd, bb, gsize, delta, epsdisl, dfl, rhs)
+
+  implicit none
+
+  DECLARE_CCTK_PARAMETERS
+
+  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
+  CCTK_REAL, dimension(:,:), allocatable :: a, d, b, h
+  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) )
+  a = zero; d = zero; b = zero; h = zero;
+
+  call set_dmatrix ( d, bb(1:2) )
+
+  call set_bmatrix ( b, bb(1:2), lsh(1), gsh(1), lbnd(1), delta(1), dfl )
+  
+  call set_hmatrix ( h, bb(1:2) )
+
+  a = - transpose ( matmul ( h, matmul ( transpose(d), matmul ( b, d ) ) ) )
+
+  idel = epsdisl /  16.0_wp
+
+  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,:,:) + &
+                   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,:,:) ) * 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(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,:,:) ) * idel
+    il = 6
+  end if
+  if ( bb(2) == 0 ) then
+    ir = ni - gsize(1)
+  else
+    rhs(ni-4,:,:) = rhs(ni-4,:,:) + &
+                    ( 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-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-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-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-2,ni) * var(ni-2,:,:) + &
+                      a(ni-1,ni) * var(ni-1,:,:) + &
+                      a(ni,ni) * var(ni,:,:) ) * idel
+    ir = ni - 5
+  end if
+  do i = il, ir
+    rhs(i,:,:) = rhs(i,:,:) + &
+                   ( 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,:,:) ) * idel
+  end do
+
+  deallocate ( a, d, b, h )
+
+  allocate ( a(nj,nj), d(nj,nj), b(nj,nj), h(nj,nj) )
+  a = zero; d = zero; b = zero; h = zero;
+
+  call set_dmatrix ( d, bb(3:4) )
+
+  call set_bmatrix ( b, bb(3:4), lsh(2), gsh(2), lbnd(2), delta(2), dfl )
+  
+  call set_hmatrix ( h, bb(3:4) )
+
+  a = - transpose ( matmul ( h, matmul ( transpose(d), matmul ( b, d ) ) ) )
+
+  idel = epsdisl /  16.0_wp
+
+  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,:) + &
+                   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,:) ) * 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(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,:) ) * idel
+    jl = 6
+  end if
+  if ( bb(4) == 0 ) then
+    jr = nj - gsize(2)
+  else
+    rhs(:,nj-4,:) = rhs(:,nj-4,:) + &
+                    ( 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-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-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-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-2,nj) * var(:,nj-2,:) + &
+                      a(nj-1,nj) * var(:,nj-1,:) + &
+                      a(nj,nj) * var(:,nj,:) ) * idel
+    jr = nj - 5
+  end if
+
+  do j = jl, jr
+    rhs(:,j,:) = rhs(:,j,:) + &
+                   ( 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,:) ) * idel
+  end do
+
+  deallocate ( a, d, b, h )
+
+  allocate ( a(nk,nk), d(nk,nk), b(nk,nk), h(nk,nk) )
+  a = zero; d = zero; b = zero; h = zero;
+
+  call set_dmatrix ( d, bb(5:6) )
+
+  call set_bmatrix ( b, bb(5:6), lsh(3), gsh(3), lbnd(3), delta(3), dfl )
+
+  call set_hmatrix ( h, bb(5:6) )
+
+  a = - transpose ( matmul ( h, matmul ( transpose(d), matmul ( b, d ) ) ) )
+
+    idel = epsdisl /  16.0_wp
+
+
+  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) + &
+                   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) ) * 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(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) ) * idel
+    kl = 6
+  end if
+  if ( bb(6) == 0 ) then
+    kr = nk - gsize(3)
+  else
+    rhs(:,:,nk-4) = rhs(:,:,nk-4) + &
+                    ( 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-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-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-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-2,nk) * var(:,:,nk-2) + &
+                      a(nk-1,nk) * var(:,:,nk-1) + &
+                      a(nk,nk) * var(:,:,nk) ) * idel
+    kr = nk - 5
+  end if
+
+  do k = kl, kr
+    rhs(:,:,k) = rhs(:,:,k) + &
+                   ( 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) ) * idel
+  end do
+
+  deallocate ( a, d, b, h )
+
+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(3), save :: ac = (/ 1.0_wp, -2.0_wp, 1.0_wp /)
+    CCTK_INT :: i
+
+    n = size(d,1)
+    if ( bb(1) == 0 ) then
+      d(1,1:2) = ac(2:3)
+    else
+      d(1,1:3) = ac
+    end if
+    if ( bb(2) == 0 ) then
+      d(n,n-1:n) = ac(1:2)
+    else
+      d(n,n-2:n) = ac
+    end if
+    do i = 2, n-1
+      d(i,i-1:i+1) = 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(d,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)
+    do i = 1, n
+      h(i,i) = 1.0_wp
+    end do
+    if ( bb(1) /= 0 ) then
+      h(1:5,1:5) = sigma ( )
+    end if
+    if ( bb(2) /= 0 ) then
+      h(n:n-4:-1,n:n-4:-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 :: zero = 0.0
+    integer, parameter :: wp = kind(zero)
+
+    if ( x < xp ) then
+      bf = ( 1.0_wp - h ) / xp * x + h
+    else if ( x > xmax - xp ) then
+      bf = ( h - 1.0_wp ) / xp * ( x + xp - xmax ) + 1
+    else
+      bf = 1.0_wp
+    end if
+
+  end function bf
+
+  function sigma ( )
+
+    implicit none
+
+    CCTK_REAL, dimension(5,5) :: sigma
+
+    CCTK_REAL :: zero = 0.0
+    integer, parameter :: wp = kind(zero)
+
+    sigma(1,1) = 4.186595370392226897362216859769846226369_wp
+    sigma(2,1) = 0_wp
+    sigma(3,1) = 0_wp
+    sigma(4,1) = 0_wp
+    sigma(5,1) = 0_wp
+    sigma(1,2) = 0_wp
+    sigma(2,2) = 0.6725191921225620731888714836983116420871_wp
+    sigma(3,2) = 0.3613418181134949259370502966736306984367_wp
+    sigma(4,2) = -0.2021316117293899791481674539631879662707_wp
+    sigma(5,2) = 0.03455320708729270824077678274955265350304_wp
+    sigma(1,3) = 0_wp
+    sigma(2,3) = 0.3613418181134949259370502966736306984367_wp
+    sigma(3,3) = 0.7206133711630147057720442098623847362950_wp
+    sigma(4,3) = 0.1376472340546569368321616389764958792591_wp
+    sigma(5,3) = -0.04136405531324488624637892257286207044784_wp
+    sigma(1,4) = 0_wp
+    sigma(2,4) = -0.2021316117293899791481674539631879662707_wp
+    sigma(3,4) = 0.1376472340546569368321616389764958792591_wp
+    sigma(4,4) = 0.9578653607931026822074133441449909689509_wp
+    sigma(5,4) = 0.02069353627247161734563597102894256809696_wp
+    sigma(1,5) = 0_wp
+    sigma(2,5) = 0.03455320708729270824077678274955265350304_wp
+    sigma(3,5) = -0.04136405531324488624637892257286207044784_wp
+    sigma(4,5) = 0.02069353627247161734563597102894256809696_wp
+    sigma(5,5) = 0.9908272703370861473007798925906968380654_wp
+
+  end function sigma
+
+  subroutine set_coeff ( a, dx )
+
+    implicit none
+
+    CCTK_REAL, dimension(7,5), intent(OUT) :: a
+    CCTK_REAL, intent(in) :: dx
+    CCTK_REAL :: zero = 0.0
+    integer, parameter :: wp = kind(zero)
+    CCTK_REAL, dimension(4) :: b
+
+    b(1) = dx
+    b(2) = ( 1 + 3*b(1) ) / 4
+    b(3) = ( 1 + b(1) ) / 2
+    b(4) = ( 3 + b(1) )/4
+
+    a(1,1) = -2.001729494283060564327579028280434295231079652820_wp*b(1)-2.001729494283060564327579028280434295231079652820_wp*b(2)
+    a(2,1) = 4.0034589885661211286551580565608685904621593056401_wp*b(1)+4.0034589885661211286551580565608685904621593056401_wp*b(2)
+    a(3,1) = -2.001729494283060564327579028280434295231079652820_wp*b(1)-2.001729494283060564327579028280434295231079652820_wp*b(2)
+    a(4,1) = 0.0_wp
+    a(5,1) = 0.0_wp
+    a(6,1) = 0.0_wp
+    a(7,1) = 0.0_wp
+    a(1,2) = 33.349009885955840248954469595024528895341083236112_wp*b(1)+33.349009885955840248954469595024528895341083236112_wp*b(2)
+    a(2,2) = -66.698019771911680497908939190049057790682166472223_wp*b(1)-66.698019771911680497908939190049057790682166472223_wp*b(2)-14.236744515267393430983451831106076148131079582685_wp*b(3)
+    a(3,2) = 33.349009885955840248954469595024528895341083236112_wp*b(1)+33.349009885955840248954469595024528895341083236112_wp*b(2)+28.473489030534786861966903662212152296262159165371_wp*b(3)-5.0440331538485788446043928053469767557227163958272_wp*b(4)
+    a(4,2) = -1.3951356569032137488502820136180622005437534045293_wp-14.236744515267393430983451831106076148131079582685_wp*b(3)+10.088066307697157689208785610693953511445432791654_wp*b(4)
+    a(5,2) = 5.9576955605539351261459121347762848951403545560302_wp-5.0440331538485788446043928053469767557227163958272_wp*b(4)
+    a(6,2) = -7.7299841503982290057409782286983831886494488984724_wp
+    a(7,2) = 3.1674242467475076284453481075401604940528477469716_wp
+    a(1,3) = -3.9903407976170909924931618645027940552738274990905_wp*b(1)-3.9903407976170909924931618645027940552738274990905_wp*b(2)
+    a(2,3) = 7.9806815952341819849863237290055881105476549981809_wp*b(1)+7.9806815952341819849863237290055881105476549981809_wp*b(2)+2.0281925060753259562659269077917853627407035645458_wp*b(3)
+    a(3,3) = -3.9903407976170909924931618645027940552738274990905_wp*b(1)-3.9903407976170909924931618645027940552738274990905_wp*b(2)-4.0563850121506519125318538155835707254814071290916_wp*b(3)+0.85749863949531149345224149788443686605331530370993_wp*b(4)
+    a(4,3) = -0.17805296968581960088505371131995522597503148483988_wp+2.0281925060753259562659269077917853627407035645458_wp*b(3)-1.7149972789906229869044829957688737321066306074199_wp*b(4)
+    a(5,3) = -0.029159711483604197600932897250942820943416950674515_wp+0.85749863949531149345224149788443686605331530370993_wp*b(4)
+    a(6,3) = 0.59247833202466719785702692846175131981192835586867_wp
+    a(7,3) = -0.38526565085524339937104031989085327289347992035428_wp
+    a(1,4) = -10.828009944579909415707962754026179346885875504376_wp*b(1)-10.828009944579909415707962754026179346885875504376_wp*b(2)
+    a(2,4) = 21.656019889159818831415925508052358693771751008752_wp*b(1)+21.656019889159818831415925508052358693771751008752_wp*b(2)+4.8030111910833762941985823652201696605573253856589_wp*b(3)
+    a(3,4) = -10.828009944579909415707962754026179346885875504376_wp*b(1)-10.828009944579909415707962754026179346885875504376_wp*b(2)-9.6060223821667525883971647304403393211146507713177_wp*b(3)+1.8413742894937777907392755981492717093567250921496_wp*b(4)
+    a(4,4) = 0.52169344312294565855548171683437104934836522915934_wp+4.8030111910833762941985823652201696605573253856589_wp*b(3)-3.6827485789875555814785511962985434187134501842992_wp*b(4)
+    a(5,4) = -2.3211687019578831529367545613086339586352127503243_wp+1.8413742894937777907392755981492717093567250921496_wp*b(4)
+    a(6,4) = 3.0772570745469293302070639721141547692253298131705_wp
+    a(7,4) = -1.2777818157119918358257911276398918599384822920056_wp
+    a(1,5) = -6.7201141443502586562617365349711742609991754142974_wp*b(1)-6.7201141443502586562617365349711742609991754142974_wp*b(2)
+    a(2,5) = 13.440228288700517312523473069942348521998350828595_wp*b(1)+13.440228288700517312523473069942348521998350828595_wp*b(2)+2.6601737327460025913616376196819751799013252956745_wp*b(3)
+    a(3,5) = -6.7201141443502586562617365349711742609991754142974_wp*b(1)-6.7201141443502586562617365349711742609991754142974_wp*b(2)-5.3203474654920051827232752393639503598026505913491_wp*b(3)+0.68697583481584777698277591803888262651185956794776_wp*b(4)
+    a(4,5) = 1.6888624757937931547697409070602037810047678994127_wp+2.6601737327460025913616376196819751799013252956745_wp*b(3)-1.3739516696316955539655518360777652530237191358955_wp*b(4)
+    a(5,5) = -4.8610470973404788048372478314704553824811608945344_wp+0.68697583481584777698277591803888262651185956794776_wp*b(4)
+    a(6,5) = 4.6555067672995781453652729417602994219480180908309_wp
+    a(7,5) = -1.4833221457528924952977660173500478204716250957091_wp
+
+  end subroutine set_coeff
+end subroutine dissipation_4_3_opt
diff --git a/src/dissipation.c b/src/dissipation.c
index 638a47a..59daa23 100644
--- a/src/dissipation.c
+++ b/src/dissipation.c
@@ -7,6 +7,16 @@
 #include "cctk_Arguments.h"
 #include "cctk_Parameters.h"
 
+void CCTK_FCALL CCTK_FNAME(dissipation_4_3_opt) (const CCTK_REAL *var,
+                                             const CCTK_INT *lsh,
+                                             const CCTK_INT *gsh,
+                                             const CCTK_INT *lbnd,
+                                             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_6_5) (const CCTK_REAL *var,
                                              const CCTK_INT *ni,
                                              const CCTK_INT *nj,
@@ -124,6 +134,12 @@ apply (int const varindex, char const * const optstring, void * const arg)
     }
   } else {
     switch(order) {
+    case 4: {
+      CCTK_FNAME(dissipation_4_3_opt)
+        (varptr, cctk_lsh, cctk_gsh, cctk_lbnd,
+                            bbox, gsize, dx, &epsdis, &diss_fraction, rhsptr);
+      break;
+    }
     case 6: {
       CCTK_FNAME(dissipation_6_5)
         (varptr, &cctk_lsh[0], &cctk_lsh[1], &cctk_lsh[2],
diff --git a/src/make.code.defn b/src/make.code.defn
index 040c89d..171c48f 100644
--- a/src/make.code.defn
+++ b/src/make.code.defn
@@ -17,6 +17,7 @@ SRCS =  call_derivs.c \
         set_norm_mask.F90 \
         CheckGridSizes.F90 \
         dissipation.c \
+        Dissipation_4_3_min_err_coeff.F90 \
         Dissipation_8_4.F90 \
         Dissipation_6_5.F90 \
         get_coeffs.c \