Add routines for third derivatives

git-svn-id: http://svn.einsteintoolkit.org/cactus/EinsteinUtils/TGRtensor/trunk@22 b716e942-a2de-43ad-8f52-f3dfe468e4e7

2 files changed, 75 insertions, 0 deletions

diff --git a/src/derivs.F90 b/src/derivs.F90
index 1d425c8..1413f7d 100644
--- a/src/derivs.F90
+++ b/src/derivs.F90
@@ -10,6 +10,7 @@ module derivs
   private
   public get_derivs
   public get_derivs2
+  public get_derivs3
 contains
 #endif
   subroutine get_derivs (a, f, pos, off, dx)
@@ -41,6 +42,34 @@ contains
          &    - a(pos-off(2)+off(3)) + a(pos+off(2)+off(3))) / (4*dx(2)*dx(3))
     f(3,2) = f(2,3)
   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)
+    integer :: i
+    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)+1) - a(pos-off(1)+off(2)+1) - a(pos+off(1)-off(2)+1) + a(pos-off(1)-off(2)+1) - a(pos+off(1)+off(2)-1) + a(pos-off(1)+off(2)-1) + a(pos+off(1)-off(2)-1) - a(pos-off(1)-off(2)-1)) * (8*dx(1)*dx(2)*dx(3))
+    f(1,3,1) = f(3,3,1)
+    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)+1) - 2*a(pos+off(3)) + a(pos-off(2)+1) - a(pos+off(2)-1) + 2*a(pos-off(3)) - a(pos-off(2)-1)) / (2*dx(2)*dx(2)*dx(3))
+    f(1,3,2) = f(3,2,1)
+    f(2,3,2) = f(3,2,2)
+    f(3,3,2) = (a(pos+off(2)+1) - 2*a(pos+off(2)) + a(pos+off(2)-1) - a(pos-off(2)+1) + 2*a(pos-off(2)) - a(pos-off(2)-1)) / (2*dx(2)*dx(3)*dx(3))
+    f(:,1,3) = f(:,3,1)
+    f(:,2,3) = f(:,3,2)
+    f(1,3,3) = f(3,3,1)
+    f(2,3,3) = f(3,3,2)
+    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)
+  end subroutine get_derivs3
 #ifndef TGR_INCLUDED
 end module derivs
 #endif
diff --git a/src/pointwise.F90 b/src/pointwise.F90
index 80c8bc6..6f435cb 100644
--- a/src/pointwise.F90
+++ b/src/pointwise.F90
@@ -22,6 +22,9 @@ module pointwise
   public get_scalarderivs2
   public get_vectorderivs2
   public get_tensorderivs2
+  public get_scalarderivs3
+  public get_vectorderivs3
+  public get_tensorderivs3
 contains
 #define TGR_INCLUDED
 #include "derivs.F90"
@@ -247,4 +250,47 @@ contains
     f(3,2,:,:) = fyz
     f(3,3,:,:) = fzz
   end subroutine get_tensorderivs2
+  subroutine get_scalarderivs3 (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)
+    call get_derivs3 (a, f, pos, off, dx)
+  end subroutine get_scalarderivs3
+  subroutine get_vectorderivs3 (ax,ay,az, f, pos, off, dx)
+    CCTK_REAL, intent(in)  :: ax(*),ay(*),az(*)
+    CCTK_REAL, intent(out) :: f(3,3,3,3)
+    integer,   intent(in)  :: pos, off(3)
+    CCTK_REAL, intent(in)  :: dx(3)
+    CCTK_REAL :: fx(3,3,3),fy(3,3,3),fz(3,3,3)
+    call get_derivs3 (ax, fx, pos, off, dx)
+    call get_derivs3 (ay, fy, pos, off, dx)
+    call get_derivs3 (az, fz, pos, off, dx)
+    f(1,:,:,:) = fx
+    f(2,:,:,:) = fy
+    f(3,:,:,:) = fz
+  end subroutine get_vectorderivs3
+  subroutine get_tensorderivs3 (axx,axy,axz,ayy,ayz,azz, f, pos, off, dx)
+    CCTK_REAL, intent(in)  :: axx(*),axy(*),axz(*),ayy(*),ayz(*),azz(*)
+    CCTK_REAL, intent(out) :: f(3,3,3,3,3)
+    integer,   intent(in)  :: pos, off(3)
+    CCTK_REAL, intent(in)  :: dx(3)
+    CCTK_REAL :: fxx(3,3,3),fxy(3,3,3),fxz(3,3,3),&
+         &       fyy(3,3,3),fyz(3,3,3),fzz(3,3,3)
+    call get_derivs3 (axx, fxx, pos, off, dx)
+    call get_derivs3 (axy, fxy, pos, off, dx)
+    call get_derivs3 (axz, fxz, pos, off, dx)
+    call get_derivs3 (ayy, fyy, pos, off, dx)
+    call get_derivs3 (ayz, fyz, pos, off, dx)
+    call get_derivs3 (azz, fzz, pos, off, dx)
+    f(1,1,:,:,:) = fxx
+    f(1,2,:,:,:) = fxy
+    f(1,3,:,:,:) = fxz
+    f(2,1,:,:,:) = fxy
+    f(2,2,:,:,:) = fyy
+    f(2,3,:,:,:) = fyz
+    f(3,1,:,:,:) = fxz
+    f(3,2,:,:,:) = fyz
+    f(3,3,:,:,:) = fzz
+  end subroutine get_tensorderivs3
 end module pointwise