Add optional argument "order" to set the order of differentiation

git-svn-id: http://svn.einsteintoolkit.org/cactus/EinsteinUtils/TGRtensor/trunk@38 b716e942-a2de-43ad-8f52-f3dfe468e4e7

2 files changed, 249 insertions, 70 deletions

diff --git a/src/derivs.F90 b/src/derivs.F90
index 95e0fe5..59730ec 100644
--- a/src/derivs.F90
+++ b/src/derivs.F90
@@ -13,61 +13,169 @@ module derivs
   public get_derivs3
 contains
 #endif
-  subroutine get_derivs (a, f, pos, off, dx)
-    CCTK_REAL, intent(in)  :: a(*)
-    CCTK_REAL, intent(out) :: f(3)
-    integer,   intent(in)  :: pos, off(3)
-    CCTK_REAL, intent(in)  :: dx(3)
+  subroutine get_derivs (a, f, pos, off, dx, order)
+    CCTK_REAL, intent(in)            :: a(*)
+    CCTK_REAL, intent(out)           :: f(3)
+    integer,   intent(in)            :: pos, off(3)
+    CCTK_REAL, intent(in)            :: dx(3)
+    integer,   intent(in),  optional :: order
+    integer :: order1
     integer :: i
-    do i=1,3
-       f(i) = (a(pos+off(i)) - a(pos-off(i))) / (2*dx(i))
-    end do
+    order1 = 2
+    if (present(order)) order1 = order
+    select case (order1)
+    case (2)
+       do i=1,3
+          f(i) = (a(pos+off(i)) - a(pos-off(i))) / (2*dx(i))
+       end do
+    case (4)
+       do i=1,3
+          f(i) = (- a(pos+2*off(i)) + 8*a(pos+off(i)) - 8*a(pos-off(i)) + a(pos-2*off(i))) / (12*dx(i))
+       end do
+    case default
+       call CCTK_WARN (0, "Unsupported finite differencing order")
+    end select
   end subroutine get_derivs
-  subroutine get_derivs2 (a, f, pos, off, dx)
-    CCTK_REAL, intent(in)  :: a(*)
-    CCTK_REAL, intent(out) :: f(3,3)
-    integer,   intent(in)  :: pos, off(3)
-    CCTK_REAL, intent(in)  :: dx(3)
+  subroutine get_derivs2 (a, f, pos, off, dx, order)
+    CCTK_REAL, intent(in)            :: a(*)
+    CCTK_REAL, intent(out)           :: f(3,3)
+    integer,   intent(in)            :: pos, off(3)
+    CCTK_REAL, intent(in)            :: dx(3)
+    integer,   intent(in),  optional :: order
+    integer :: order1
     integer :: i
-    do i=1,3
-       f(i,i) = (a(pos+off(i)) - 2*a(pos) + a(pos-off(i))) / dx(i)**2
-    end do
-    f(1,2) = (  a(pos-off(1)-off(2)) - a(pos+off(1)-off(2)) &
-         &    - a(pos-off(1)+off(2)) + a(pos+off(1)+off(2))) / (4*dx(1)*dx(2))
-    f(2,1) = f(1,2)
-    f(1,3) = (  a(pos-off(1)-off(3)) - a(pos+off(1)-off(3)) &
-         &    - a(pos-off(1)+off(3)) + a(pos+off(1)+off(3))) / (4*dx(1)*dx(3))
-    f(3,1) = f(1,3)
-    f(2,3) = (  a(pos-off(2)-off(3)) - a(pos+off(2)-off(3)) &
-         &    - a(pos-off(2)+off(3)) + a(pos+off(2)+off(3))) / (4*dx(2)*dx(3))
-    f(3,2) = f(2,3)
+    order1 = 2
+    if (present(order)) order1 = order
+    select case (order1)
+    case (2)
+       do i=1,3
+          f(i,i) = (a(pos+off(i)) - 2*a(pos) + a(pos-off(i))) / dx(i)**2
+       end do
+       f(1,2) = (  a(pos-off(1)-off(2)) - a(pos+off(1)-off(2)) &
+            &    - a(pos-off(1)+off(2)) + a(pos+off(1)+off(2))) / (4*dx(1)*dx(2))
+       f(2,1) = f(1,2)
+       f(1,3) = (  a(pos-off(1)-off(3)) - a(pos+off(1)-off(3)) &
+            &    - a(pos-off(1)+off(3)) + a(pos+off(1)+off(3))) / (4*dx(1)*dx(3))
+       f(3,1) = f(1,3)
+       f(2,3) = (  a(pos-off(2)-off(3)) - a(pos+off(2)-off(3)) &
+            &    - a(pos-off(2)+off(3)) + a(pos+off(2)+off(3))) / (4*dx(2)*dx(3))
+       f(3,2) = f(2,3)
+    case (4)
+       do i=1,3
+          f(i,i) = (- a(pos-2*off(i)) + 16*a(pos-off(i)) - 30*a(pos) + 16*a(pos+off(i)) - a(pos+2*off(i))) / (12*dx(i)**2)
+       end do
+       f(1,2) = (    a(pos+2*off(1)+2*off(2)) -  8*a(pos+off(1)+2*off(2)) +  8*a(pos-off(1)+2*off(2)) -   a(pos-2*off(1)+2*off(2)) &
+            &    - 8*a(pos+2*off(1)+  off(2)) + 64*a(pos+off(1)+  off(2)) - 64*a(pos-off(1)+  off(2)) + 8*a(pos-2*off(1)+  off(2)) &
+            &    + 8*a(pos+2*off(1)-  off(2)) - 64*a(pos+off(1)-  off(2)) + 64*a(pos-off(1)-  off(2)) - 8*a(pos-2*off(1)-  off(2)) &
+            &    -   a(pos+2*off(1)-2*off(2)) +  8*a(pos+off(1)-2*off(2)) -  8*a(pos-off(1)-2*off(2)) +   a(pos-2*off(1)-2*off(2))) / (144*dx(1)*dx(2))
+       f(2,1) = f(1,2)
+       f(1,3) = (    a(pos+2*off(1)+2*off(3)) -  8*a(pos+off(1)+2*off(3)) +  8*a(pos-off(1)+2*off(3)) -   a(pos-2*off(1)+2*off(3)) &
+            &    - 8*a(pos+2*off(1)+  off(3)) + 64*a(pos+off(1)+  off(3)) - 64*a(pos-off(1)+  off(3)) + 8*a(pos-2*off(1)+  off(3)) &
+            &    + 8*a(pos+2*off(1)-  off(3)) - 64*a(pos+off(1)-  off(3)) + 64*a(pos-off(1)-  off(3)) - 8*a(pos-2*off(1)-  off(3)) &
+            &    -   a(pos+2*off(1)-2*off(3)) +  8*a(pos+off(1)-2*off(3)) -  8*a(pos-off(1)-2*off(3)) +   a(pos-2*off(1)-2*off(3))) / (144*dx(1)*dx(3))
+       f(3,1) = f(1,3)
+       f(2,3) = (    a(pos+2*off(2)+2*off(3)) -  8*a(pos+off(2)+2*off(3)) +  8*a(pos-off(2)+2*off(3)) -   a(pos-2*off(2)+2*off(3)) &
+            &    - 8*a(pos+2*off(2)+  off(3)) + 64*a(pos+off(2)+  off(3)) - 64*a(pos-off(2)+  off(3)) + 8*a(pos-2*off(2)+  off(3)) &
+            &    + 8*a(pos+2*off(2)-  off(3)) - 64*a(pos+off(2)-  off(3)) + 64*a(pos-off(2)-  off(3)) - 8*a(pos-2*off(2)-  off(3)) &
+            &    -   a(pos+2*off(2)-2*off(3)) +  8*a(pos+off(2)-2*off(3)) -  8*a(pos-off(2)-2*off(3)) +   a(pos-2*off(2)-2*off(3))) / (144*dx(2)*dx(3))
+       f(3,2) = f(2,3)
+    case default
+       call CCTK_WARN (0, "Unsupported finite differencing order")
+    end select
   end subroutine get_derivs2
-  subroutine get_derivs3 (a, f, pos, off, dx)
-    CCTK_REAL, intent(in)  :: a(*)
-    CCTK_REAL, intent(out) :: f(3,3,3)
-    integer,   intent(in)  :: pos, off(3)
-    CCTK_REAL, intent(in)  :: dx(3)
-    f(1,1,1) = (a(pos+2*off(1)) - 2*a(pos+off(1)) + 2*a(pos-off(1)) - a(pos-2*off(1))) / (2*dx(1)**3)
-    f(2,1,1) = (a(pos+off(1)+off(2)) - 2*a(pos+off(2)) + a(pos-off(1)+off(2)) - a(pos+off(1)-off(2)) + 2*a(pos-off(2)) - a(pos-off(1)-off(2))) / (2*dx(1)*dx(1)*dx(2))
-    f(3,1,1) = (a(pos+off(1)+off(3)) - 2*a(pos+off(3)) + a(pos-off(1)+off(3)) - a(pos+off(1)-off(3)) + 2*a(pos-off(3)) - a(pos-off(1)-off(3))) / (2*dx(1)*dx(1)*dx(3))
-    f(1,2,1) = f(2,1,1)
-    f(2,2,1) = (a(pos+off(1)+off(2)) - 2*a(pos+off(1)) + a(pos+off(1)-off(2)) - a(pos-off(1)+off(2)) + 2*a(pos-off(1)) - a(pos-off(1)-off(2))) / (2*dx(1)*dx(2)*dx(2))
-    f(3,2,1) = (a(pos+off(1)+off(2)+off(3)) - a(pos-off(1)+off(2)+off(3)) - a(pos+off(1)-off(2)+off(3)) + a(pos-off(1)-off(2)+off(3)) - a(pos+off(1)+off(2)-off(3)) + a(pos-off(1)+off(2)-off(3)) + a(pos+off(1)-off(2)-off(3)) - a(pos-off(1)-off(2)-off(3))) / (8*dx(1)*dx(2)*dx(3))
-    f(1,3,1) = f(3,1,1)
-    f(2,3,1) = f(3,2,1)
-    f(3,3,1) = (a(pos+off(1)+off(3)) - 2*a(pos+off(1)) + a(pos+off(1)-off(3)) - a(pos-off(1)+off(3)) + 2*a(pos-off(1)) - a(pos-off(1)-off(3))) / (2*dx(1)*dx(3)*dx(3))
-    f(:,1,2) = f(:,2,1)
-    f(1,2,2) = f(2,2,1)
-    f(2,2,2) = (a(pos+2*off(2)) - 2*a(pos+off(2)) + 2*a(pos-off(2)) - a(pos-2*off(2))) / (2*dx(2)**3)
-    f(3,2,2) = (a(pos+off(2)+off(3)) - 2*a(pos+off(3)) + a(pos-off(2)+off(3)) - a(pos+off(2)-off(3)) + 2*a(pos-off(3)) - a(pos-off(2)-off(3))) / (2*dx(2)*dx(2)*dx(3))
-    f(1,3,2) = f(3,1,2)
-    f(2,3,2) = f(3,2,2)
-    f(3,3,2) = (a(pos+off(2)+off(3)) - 2*a(pos+off(2)) + a(pos+off(2)-off(3)) - a(pos-off(2)+off(3)) + 2*a(pos-off(2)) - a(pos-off(2)-off(3))) / (2*dx(2)*dx(3)*dx(3))
-    f(:,1,3) = f(:,3,1)
-    f(:,2,3) = f(:,3,2)
-    f(1,3,3) = f(3,1,3)
-    f(2,3,3) = f(3,2,3)
-    f(3,3,3) = (a(pos+2*off(3)) - 2*a(pos+off(3)) + 2*a(pos-off(3)) - a(pos-2*off(3))) / (2*dx(3)**3)
+  subroutine get_derivs3 (a, f, pos, off, dx, order)
+    CCTK_REAL, intent(in)            :: a(*)
+    CCTK_REAL, intent(out)           :: f(3,3,3)
+    integer,   intent(in)            :: pos, off(3)
+    CCTK_REAL, intent(in)            :: dx(3)
+    integer,   intent(in),  optional :: order
+    integer :: order1
+    order1 = 2
+    if (present(order)) order1 = order
+    select case (order1)
+    case (2)
+       f(1,1,1) = (a(pos+2*off(1)) - 2*a(pos+off(1)) + 2*a(pos-off(1)) - a(pos-2*off(1))) / (2*dx(1)**3)
+       f(2,1,1) = (a(pos+off(1)+off(2)) - 2*a(pos+off(2)) + a(pos-off(1)+off(2)) - a(pos+off(1)-off(2)) + 2*a(pos-off(2)) - a(pos-off(1)-off(2))) / (2*dx(1)*dx(1)*dx(2))
+       f(3,1,1) = (a(pos+off(1)+off(3)) - 2*a(pos+off(3)) + a(pos-off(1)+off(3)) - a(pos+off(1)-off(3)) + 2*a(pos-off(3)) - a(pos-off(1)-off(3))) / (2*dx(1)*dx(1)*dx(3))
+       f(1,2,1) = f(2,1,1)
+       f(2,2,1) = (a(pos+off(1)+off(2)) - 2*a(pos+off(1)) + a(pos+off(1)-off(2)) - a(pos-off(1)+off(2)) + 2*a(pos-off(1)) - a(pos-off(1)-off(2))) / (2*dx(1)*dx(2)*dx(2))
+       f(3,2,1) = (a(pos+off(1)+off(2)+off(3)) - a(pos-off(1)+off(2)+off(3)) - a(pos+off(1)-off(2)+off(3)) + a(pos-off(1)-off(2)+off(3)) - a(pos+off(1)+off(2)-off(3)) + a(pos-off(1)+off(2)-off(3)) + a(pos+off(1)-off(2)-off(3)) - a(pos-off(1)-off(2)-off(3))) / (8*dx(1)*dx(2)*dx(3))
+       f(1,3,1) = f(3,1,1)
+       f(2,3,1) = f(3,2,1)
+       f(3,3,1) = (a(pos+off(1)+off(3)) - 2*a(pos+off(1)) + a(pos+off(1)-off(3)) - a(pos-off(1)+off(3)) + 2*a(pos-off(1)) - a(pos-off(1)-off(3))) / (2*dx(1)*dx(3)*dx(3))
+       f(:,1,2) = f(:,2,1)
+       f(1,2,2) = f(2,2,1)
+       f(2,2,2) = (a(pos+2*off(2)) - 2*a(pos+off(2)) + 2*a(pos-off(2)) - a(pos-2*off(2))) / (2*dx(2)**3)
+       f(3,2,2) = (a(pos+off(2)+off(3)) - 2*a(pos+off(3)) + a(pos-off(2)+off(3)) - a(pos+off(2)-off(3)) + 2*a(pos-off(3)) - a(pos-off(2)-off(3))) / (2*dx(2)*dx(2)*dx(3))
+       f(1,3,2) = f(3,1,2)
+       f(2,3,2) = f(3,2,2)
+       f(3,3,2) = (a(pos+off(2)+off(3)) - 2*a(pos+off(2)) + a(pos+off(2)-off(3)) - a(pos-off(2)+off(3)) + 2*a(pos-off(2)) - a(pos-off(2)-off(3))) / (2*dx(2)*dx(3)*dx(3))
+       f(:,1,3) = f(:,3,1)
+       f(:,2,3) = f(:,3,2)
+       f(1,3,3) = f(3,1,3)
+       f(2,3,3) = f(3,2,3)
+       f(3,3,3) = (a(pos+2*off(3)) - 2*a(pos+off(3)) + 2*a(pos-off(3)) - a(pos-2*off(3))) / (2*dx(3)**3)
+    case (4)
+       ! [+1 -8 +13 0 -13 +8 -1] / 8
+       f(1,1,1) = (a(pos-3*off(1)) - 8*a(pos-2*off(1)) + 13*a(pos-off(1)) - 13*a(pos+off(1)) + 8*a(pos+2*off(1)) - a(pos+3*off(1))) / (8*dx(1)**3)
+       ! [-1 +8 0 -8 +1] / 12
+       ! [-1 +16 -30 +16 -1] / 12
+       f(2,1,1) = (+   a(pos-2*off(1)-2*off(2)) -  16*a(pos-off(1)-2*off(2)) +  30*a(pos-2*off(2)) -  16*a(pos+off(1)-2*off(2)) +   a(pos+2*off(1)-2*off(2)) &
+            &      - 8*a(pos-2*off(1)-  off(2)) + 128*a(pos-off(1)-  off(2)) - 240*a(pos-  off(2)) + 128*a(pos+off(1)-  off(2)) - 8*a(pos+2*off(1)-  off(2)) &
+            &      + 8*a(pos-2*off(1)+  off(2)) - 128*a(pos-off(1)+  off(2)) + 240*a(pos+  off(2)) - 128*a(pos+off(1)+  off(2)) + 8*a(pos+2*off(1)+  off(2)) &
+            &      -   a(pos-2*off(1)+2*off(2)) +  16*a(pos-off(1)+2*off(2)) -  30*a(pos+2*off(2)) +  16*a(pos+off(1)+2*off(2)) -   a(pos+2*off(1)+2*off(2))) / (144*dx(1)**2*dx(2))
+       f(3,1,1) = (+   a(pos-2*off(1)-2*off(3)) -  16*a(pos-off(1)-2*off(3)) +  30*a(pos-2*off(3)) -  16*a(pos+off(1)-2*off(3)) +   a(pos+2*off(1)-2*off(3)) &
+            &      - 8*a(pos-2*off(1)-  off(3)) + 128*a(pos-off(1)-  off(3)) - 240*a(pos-  off(3)) + 128*a(pos+off(1)-  off(3)) - 8*a(pos+2*off(1)-  off(3)) &
+            &      + 8*a(pos-2*off(1)+  off(3)) - 128*a(pos-off(1)+  off(3)) + 240*a(pos+  off(3)) - 128*a(pos+off(1)+  off(3)) + 8*a(pos+2*off(1)+  off(3)) &
+            &      -   a(pos-2*off(1)+2*off(3)) +  16*a(pos-off(1)+2*off(3)) -  30*a(pos+2*off(3)) +  16*a(pos+off(1)+2*off(3)) -   a(pos+2*off(1)+2*off(3))) / (144*dx(1)**2*dx(3))
+       f(1,2,1) = f(2,1,1)
+       f(2,2,1) = (+   a(pos-2*off(2)-2*off(1)) -  16*a(pos-off(2)-2*off(1)) +  30*a(pos-2*off(1)) -  16*a(pos+off(2)-2*off(1)) +   a(pos+2*off(2)-2*off(1)) &
+            &      - 8*a(pos-2*off(2)-  off(1)) + 128*a(pos-off(2)-  off(1)) - 240*a(pos-  off(1)) + 128*a(pos+off(2)-  off(1)) - 8*a(pos+2*off(2)-  off(1)) &
+            &      + 8*a(pos-2*off(2)+  off(1)) - 128*a(pos-off(2)+  off(1)) + 240*a(pos+  off(1)) - 128*a(pos+off(2)+  off(1)) + 8*a(pos+2*off(2)+  off(1)) &
+            &      -   a(pos-2*off(2)+2*off(1)) +  16*a(pos-off(2)+2*off(1)) -  30*a(pos+2*off(1)) +  16*a(pos+off(2)+2*off(1)) -   a(pos+2*off(2)+2*off(1))) / (144*dx(2)**2*dx(1))
+       f(3,2,1) = (-     a(pos-2*off(1)-2*off(2)-2*off(3)) +   8*a(pos-off(1)-2*off(2)-2*off(3)) -   8*a(pos+off(1)-2*off(2)-2*off(3)) +     a(pos+2*off(1)-2*off(2)-2*off(3)) &
+            &      +   8*a(pos-2*off(1)-  off(2)-2*off(3)) -  64*a(pos-off(1)-  off(2)-2*off(3)) +  64*a(pos+off(1)-  off(2)-2*off(3)) -   8*a(pos+2*off(1)-  off(2)-2*off(3)) &
+            &      -   8*a(pos-2*off(1)+  off(2)-2*off(3)) +  64*a(pos-off(1)+  off(2)-2*off(3)) -  64*a(pos+off(1)+  off(2)-2*off(3)) +   8*a(pos+2*off(1)+  off(2)-2*off(3)) &
+            &      +     a(pos-2*off(1)+2*off(2)-2*off(3)) -   8*a(pos-off(1)+2*off(2)-2*off(3)) +   8*a(pos+off(1)+2*off(2)-2*off(3)) -     a(pos+2*off(1)+2*off(2)-2*off(3)) &
+            &      +   8*a(pos-2*off(1)-2*off(2)-  off(3)) -  64*a(pos-off(1)-2*off(2)-  off(3)) +  64*a(pos+off(1)-2*off(2)-  off(3)) -   8*a(pos+2*off(1)-2*off(2)-  off(3)) &
+            &      -  64*a(pos-2*off(1)-  off(2)-  off(3)) + 512*a(pos-off(1)-  off(2)-  off(3)) - 512*a(pos+off(1)-  off(2)-  off(3)) +  64*a(pos+2*off(1)-  off(2)-  off(3)) &
+            &      +  64*a(pos-2*off(1)+  off(2)-  off(3)) - 512*a(pos-off(1)+  off(2)-  off(3)) + 512*a(pos+off(1)+  off(2)-  off(3)) -  64*a(pos+2*off(1)+  off(2)-  off(3)) &
+            &      -   8*a(pos-2*off(1)+2*off(2)-  off(3)) +  64*a(pos-off(1)+2*off(2)-  off(3)) -  64*a(pos+off(1)+2*off(2)-  off(3)) +   8*a(pos+2*off(1)+2*off(2)-  off(3)) &
+            &      -   8*a(pos-2*off(1)-2*off(2)+  off(3)) +  64*a(pos-off(1)-2*off(2)+  off(3)) -  64*a(pos+off(1)-2*off(2)+  off(3)) +   8*a(pos+2*off(1)-2*off(2)+  off(3)) &
+            &      +  64*a(pos-2*off(1)-  off(2)+  off(3)) - 512*a(pos-off(1)-  off(2)+  off(3)) + 512*a(pos+off(1)-  off(2)+  off(3)) -  64*a(pos+2*off(1)-  off(2)+  off(3)) &
+            &      -  64*a(pos-2*off(1)+  off(2)+  off(3)) + 512*a(pos-off(1)+  off(2)+  off(3)) - 512*a(pos+off(1)+  off(2)+  off(3)) +  64*a(pos+2*off(1)+  off(2)+  off(3)) &
+            &      +   8*a(pos-2*off(1)+2*off(2)+  off(3)) -  64*a(pos-off(1)+2*off(2)+  off(3)) +  64*a(pos+off(1)+2*off(2)+  off(3)) -   8*a(pos+2*off(1)+2*off(2)+  off(3)) &
+            &      +     a(pos-2*off(1)-2*off(2)+2*off(3)) -   8*a(pos-off(1)-2*off(2)+2*off(3)) +   8*a(pos+off(1)-2*off(2)+2*off(3)) -     a(pos+2*off(1)-2*off(2)+2*off(3)) &
+            &      -   8*a(pos-2*off(1)-  off(2)+2*off(3)) +  64*a(pos-off(1)-  off(2)+2*off(3)) -  64*a(pos+off(1)-  off(2)+2*off(3)) +   8*a(pos+2*off(1)-  off(2)+2*off(3)) &
+            &      +   8*a(pos-2*off(1)+  off(2)+2*off(3)) -  64*a(pos-off(1)+  off(2)+2*off(3)) +  64*a(pos+off(1)+  off(2)+2*off(3)) -   8*a(pos+2*off(1)+  off(2)+2*off(3)) &
+            &      -     a(pos-2*off(1)+2*off(2)+2*off(3)) +   8*a(pos-off(1)+2*off(2)+2*off(3)) -   8*a(pos+off(1)+2*off(2)+2*off(3)) +     a(pos+2*off(1)+2*off(2)+2*off(3))) / (512*dx(1)*dx(2)*dx(3))
+       f(1,3,1) = f(3,1,1)
+       f(2,3,1) = f(3,2,1)
+       f(3,3,1) = (+   a(pos-2*off(3)-2*off(1)) -  16*a(pos-off(3)-2*off(1)) +  30*a(pos-2*off(1)) -  16*a(pos+off(3)-2*off(1)) +   a(pos+2*off(3)-2*off(1)) &
+            &      - 8*a(pos-2*off(3)-  off(1)) + 128*a(pos-off(3)-  off(1)) - 240*a(pos-  off(1)) + 128*a(pos+off(3)-  off(1)) - 8*a(pos+2*off(3)-  off(1)) &
+            &      + 8*a(pos-2*off(3)+  off(1)) - 128*a(pos-off(3)+  off(1)) + 240*a(pos+  off(1)) - 128*a(pos+off(3)+  off(1)) + 8*a(pos+2*off(3)+  off(1)) &
+            &      -   a(pos-2*off(3)+2*off(1)) +  16*a(pos-off(3)+2*off(1)) -  30*a(pos+2*off(1)) +  16*a(pos+off(3)+2*off(1)) -   a(pos+2*off(3)+2*off(1))) / (144*dx(3)**2*dx(1))
+       f(:,1,2) = f(:,2,1)
+       f(1,2,2) = f(2,2,1)
+       f(2,2,2) = (a(pos-3*off(2)) - 8*a(pos-2*off(2)) + 13*a(pos-off(2)) - 13*a(pos+off(2)) + 8*a(pos+2*off(2)) - a(pos+3*off(2))) / (8*dx(2)**3)
+       f(3,2,2) = (+   a(pos-2*off(2)-2*off(3)) -  16*a(pos-off(2)-2*off(3)) +  30*a(pos-2*off(3)) -  16*a(pos+off(2)-2*off(3)) +   a(pos+2*off(2)-2*off(3)) &
+            &      - 8*a(pos-2*off(2)-  off(3)) + 128*a(pos-off(2)-  off(3)) - 240*a(pos-  off(3)) + 128*a(pos+off(2)-  off(3)) - 8*a(pos+2*off(2)-  off(3)) &
+            &      + 8*a(pos-2*off(2)+  off(3)) - 128*a(pos-off(2)+  off(3)) + 240*a(pos+  off(3)) - 128*a(pos+off(2)+  off(3)) + 8*a(pos+2*off(2)+  off(3)) &
+            &      -   a(pos-2*off(2)+2*off(3)) +  16*a(pos-off(2)+2*off(3)) -  30*a(pos+2*off(3)) +  16*a(pos+off(2)+2*off(3)) -   a(pos+2*off(2)+2*off(3))) / (144*dx(2)**2*dx(3))
+       f(1,3,2) = f(3,1,2)
+       f(2,3,2) = f(3,2,2)
+       f(3,3,2) = (+   a(pos-2*off(3)-2*off(2)) -  16*a(pos-off(3)-2*off(2)) +  30*a(pos-2*off(2)) -  16*a(pos+off(3)-2*off(2)) +   a(pos+2*off(3)-2*off(2)) &
+            &      - 8*a(pos-2*off(3)-  off(2)) + 128*a(pos-off(3)-  off(2)) - 240*a(pos-  off(2)) + 128*a(pos+off(3)-  off(2)) - 8*a(pos+2*off(3)-  off(2)) &
+            &      + 8*a(pos-2*off(3)+  off(2)) - 128*a(pos-off(3)+  off(2)) + 240*a(pos+  off(2)) - 128*a(pos+off(3)+  off(2)) + 8*a(pos+2*off(3)+  off(2)) &
+            &      -   a(pos-2*off(3)+2*off(2)) +  16*a(pos-off(3)+2*off(2)) -  30*a(pos+2*off(2)) +  16*a(pos+off(3)+2*off(2)) -   a(pos+2*off(3)+2*off(2))) / (144*dx(3)**2*dx(2))
+       f(:,1,3) = f(:,3,1)
+       f(:,2,3) = f(:,3,2)
+       f(1,3,3) = f(3,1,3)
+       f(2,3,3) = f(3,2,3)
+       f(3,3,3) = (a(pos-3*off(3)) - 8*a(pos-2*off(3)) + 13*a(pos-off(3)) - 13*a(pos+off(3)) + 8*a(pos+2*off(3)) - a(pos+3*off(3))) / (8*dx(3)**3)
+    case default
+       call CCTK_WARN (0, "Unsupported finite differencing order")
+    end select
   end subroutine get_derivs3
 #ifndef TGR_INCLUDED
 end module derivs
diff --git a/src/derivs2.F90 b/src/derivs2.F90
index 4ca51bf..5b7e98a 100644
--- a/src/derivs2.F90
+++ b/src/derivs2.F90
@@ -10,31 +10,102 @@ module derivs2
   private
   public get_2derivs
   public get_2derivs2
+  public get_2derivs3
 contains
 #endif
-  subroutine get_2derivs (a, f, pos, off, dx)
-    CCTK_REAL, intent(in)  :: a(*)
-    CCTK_REAL, intent(out) :: f(2)
-    integer,   intent(in)  :: pos, off(2)
-    CCTK_REAL, intent(in)  :: dx(2)
+  subroutine get_2derivs (a, f, pos, off, dx, order)
+    CCTK_REAL, intent(in)            :: a(*)
+    CCTK_REAL, intent(out)           :: f(2)
+    integer,   intent(in)            :: pos, off(2)
+    CCTK_REAL, intent(in)            :: dx(2)
+    integer,   intent(in),  optional :: order
+    integer :: order1
     integer :: i
-    do i=1,2
-       f(i) = (a(pos+off(i)) - a(pos-off(i))) / (2*dx(i))
-    end do
+    order1 = 2
+    if (present(order)) order1 = order
+    select case (order1)
+    case (2)
+       do i=1,2
+          f(i) = (a(pos+off(i)) - a(pos-off(i))) / (2*dx(i))
+       end do
+    case (4)
+       do i=1,2
+          f(i) = (- a(pos+2*off(i)) + 8*a(pos+off(i)) - 8*a(pos-off(i)) + a(pos-2*off(i))) / (12*dx(i))
+       end do
+    case default
+       call CCTK_WARN (0, "Unsupported finite differencing order")
+    end select
   end subroutine get_2derivs
-  subroutine get_2derivs2 (a, f, pos, off, dx)
-    CCTK_REAL, intent(in)  :: a(*)
-    CCTK_REAL, intent(out) :: f(2,2)
-    integer,   intent(in)  :: pos, off(2)
-    CCTK_REAL, intent(in)  :: dx(2)
+  subroutine get_2derivs2 (a, f, pos, off, dx, order)
+    CCTK_REAL, intent(in)            :: a(*)
+    CCTK_REAL, intent(out)           :: f(2,2)
+    integer,   intent(in)            :: pos, off(2)
+    CCTK_REAL, intent(in)            :: dx(2)
+    integer,   intent(in),  optional :: order
+    integer :: order1
     integer :: i
-    do i=1,2
-       f(i,i) = (a(pos+off(i)) - 2*a(pos) + a(pos-off(i))) / dx(i)**2
-    end do
-    f(1,2) = (  a(pos-off(1)-off(2)) - a(pos+off(1)-off(2)) &
-         &    - a(pos-off(1)+off(2)) + a(pos+off(1)+off(2))) / (4*dx(1)*dx(2))
-    f(2,1) = f(1,2)
+    order1 = 2
+    if (present(order)) order1 = order
+    select case (order1)
+    case (2)
+       do i=1,2
+          f(i,i) = (a(pos+off(i)) - 2*a(pos) + a(pos-off(i))) / dx(i)**2
+       end do
+       f(1,2) = (  a(pos-off(1)-off(2)) - a(pos+off(1)-off(2)) &
+            &    - a(pos-off(1)+off(2)) + a(pos+off(1)+off(2))) / (4*dx(1)*dx(2))
+       f(2,1) = f(1,2)
+    case (4)
+       do i=1,2
+          f(i,i) = (- a(pos-2*off(i)) + 16*a(pos-off(i)) - 30*a(pos) + 16*a(pos+off(i)) - a(pos+2*off(i))) / (12*dx(i)**2)
+       end do
+       f(1,2) = (    a(pos+2*off(1)+2*off(2)) -  8*a(pos+off(1)+2*off(2)) +  8*a(pos-off(1)+2*off(2)) -   a(pos-2*off(1)+2*off(2)) &
+            &    - 8*a(pos+2*off(1)+  off(2)) + 64*a(pos+off(1)+  off(2)) - 64*a(pos-off(1)+  off(2)) + 8*a(pos-2*off(1)+  off(2)) &
+            &    + 8*a(pos+2*off(1)-  off(2)) - 64*a(pos+off(1)-  off(2)) + 64*a(pos-off(1)-  off(2)) - 8*a(pos-2*off(1)-  off(2)) &
+            &    -   a(pos+2*off(1)-2*off(2)) +  8*a(pos+off(1)-2*off(2)) -  8*a(pos-off(1)-2*off(2)) +   a(pos-2*off(1)-2*off(2))) / (144*dx(1)*dx(2))
+       f(2,1) = f(1,2)
+    case default
+       call CCTK_WARN (0, "Unsupported finite differencing order")
+    end select
   end subroutine get_2derivs2
+  subroutine get_2derivs3 (a, f, pos, off, dx, order)
+    CCTK_REAL, intent(in)            :: a(*)
+    CCTK_REAL, intent(out)           :: f(2,2,2)
+    integer,   intent(in)            :: pos, off(2)
+    CCTK_REAL, intent(in)            :: dx(2)
+    integer,   intent(in),  optional :: order
+    integer :: order1
+    order1 = 2
+    if (present(order)) order1 = order
+    select case (order1)
+    case (2)
+       f(1,1,1) = (a(pos+2*off(1)) - 2*a(pos+off(1)) + 2*a(pos-off(1)) - a(pos-2*off(1))) / (2*dx(1)**3)
+       f(2,1,1) = (a(pos+off(1)+off(2)) - 2*a(pos+off(2)) + a(pos-off(1)+off(2)) - a(pos+off(1)-off(2)) + 2*a(pos-off(2)) - a(pos-off(1)-off(2))) / (2*dx(1)*dx(1)*dx(2))
+       f(1,2,1) = f(2,1,1)
+       f(2,2,1) = (a(pos+off(1)+off(2)) - 2*a(pos+off(1)) + a(pos+off(1)-off(2)) - a(pos-off(1)+off(2)) + 2*a(pos-off(1)) - a(pos-off(1)-off(2))) / (2*dx(1)*dx(2)*dx(2))
+       f(:,1,2) = f(:,2,1)
+       f(1,2,2) = f(2,2,1)
+       f(2,2,2) = (a(pos+2*off(2)) - 2*a(pos+off(2)) + 2*a(pos-off(2)) - a(pos-2*off(2))) / (2*dx(2)**3)
+    case (4)
+       ! [+1 -8 +13 0 -13 +8 -1] / 8
+       f(1,1,1) = (a(pos-3*off(1)) - 8*a(pos-2*off(1)) + 13*a(pos-off(1)) - 13*a(pos+off(1)) + 8*a(pos+2*off(1)) - a(pos+3*off(1))) / (8*dx(1)**3)
+       ! [-1 +8 0 -8 +1] / 12
+       ! [-1 +16 -30 +16 -1] / 12
+       f(2,1,1) = (+   a(pos-2*off(1)-2*off(2)) -  16*a(pos-off(1)-2*off(2)) +  30*a(pos-2*off(2)) -  16*a(pos+off(1)-2*off(2)) +   a(pos+2*off(1)-2*off(2)) &
+            &      - 8*a(pos-2*off(1)-  off(2)) + 128*a(pos-off(1)-  off(2)) - 240*a(pos-  off(2)) + 128*a(pos+off(1)-  off(2)) - 8*a(pos+2*off(1)-  off(2)) &
+            &      + 8*a(pos-2*off(1)+  off(2)) - 128*a(pos-off(1)+  off(2)) + 240*a(pos+  off(2)) - 128*a(pos+off(1)+  off(2)) + 8*a(pos+2*off(1)+  off(2)) &
+            &      -   a(pos-2*off(1)+2*off(2)) +  16*a(pos-off(1)+2*off(2)) -  30*a(pos+2*off(2)) +  16*a(pos+off(1)+2*off(2)) -   a(pos+2*off(1)+2*off(2))) / (144*dx(1)**2*dx(2))
+       f(1,2,1) = f(2,1,1)
+       f(2,2,1) = (+   a(pos-2*off(2)-2*off(1)) -  16*a(pos-off(2)-2*off(1)) +  30*a(pos-2*off(1)) -  16*a(pos+off(2)-2*off(1)) +   a(pos+2*off(2)-2*off(1)) &
+            &      - 8*a(pos-2*off(2)-  off(1)) + 128*a(pos-off(2)-  off(1)) - 240*a(pos-  off(1)) + 128*a(pos+off(2)-  off(1)) - 8*a(pos+2*off(2)-  off(1)) &
+            &      + 8*a(pos-2*off(2)+  off(1)) - 128*a(pos-off(2)+  off(1)) + 240*a(pos+  off(1)) - 128*a(pos+off(2)+  off(1)) + 8*a(pos+2*off(2)+  off(1)) &
+            &      -   a(pos-2*off(2)+2*off(1)) +  16*a(pos-off(2)+2*off(1)) -  30*a(pos+2*off(1)) +  16*a(pos+off(2)+2*off(1)) -   a(pos+2*off(2)+2*off(1))) / (144*dx(2)**2*dx(1))
+       f(:,1,2) = f(:,2,1)
+       f(1,2,2) = f(2,2,1)
+       f(2,2,2) = (a(pos-3*off(2)) - 8*a(pos-2*off(2)) + 13*a(pos-off(2)) - 13*a(pos+off(2)) + 8*a(pos+2*off(2)) - a(pos+3*off(2))) / (8*dx(2)**3)
+    case default
+       call CCTK_WARN (0, "Unsupported finite differencing order")
+    end select
+  end subroutine get_2derivs3
 #ifndef TGR_INCLUDED
 end module derivs2
 #endif