Add routines to calculate the time derivatives of the metric from the

extrinsic curvature and the Einstein equations.


git-svn-id: http://svn.einsteintoolkit.org/cactus/EinsteinUtils/TGRtensor/trunk@40 b716e942-a2de-43ad-8f52-f3dfe468e4e7

1 files changed, 75 insertions, 0 deletions

diff --git a/src/adm_metric.F90 b/src/adm_metric.F90
index 3df077e..9e284cd 100644
--- a/src/adm_metric.F90
+++ b/src/adm_metric.F90
@@ -14,6 +14,12 @@ module adm_metric
   
   public calc_3metricdot
   public calc_extcurv
+  
+  public calc_3metricdot_simple
+  public calc_3metricderivdot_simple
+  public calc_extcurvdot_simple
+  public calc_3metricdot2_simple
+  
 contains
   
   subroutine calc_4metric (gg, alfa, beta, g4)
@@ -273,5 +279,74 @@ contains
     end do
     
   end subroutine calc_extcurv
+  
+  
+  
+  subroutine calc_3metricdot_simple (kk, gg_dot)
+    CCTK_REAL, intent(in)  :: kk(3,3)
+    CCTK_REAL, intent(out) :: gg_dot(3,3)
+    integer :: i,j
+    
+    ! d/dt g_ij = -2 K_ij
+    
+    do i=1,3
+       do j=1,3
+          gg_dot(i,j) = -2 * kk(i,j)
+       end do
+    end do
+  end subroutine calc_3metricdot_simple
+  
+  subroutine calc_3metricderivdot_simple (dkk, dgg_dot)
+    CCTK_REAL, intent(in)  :: dkk(3,3,3)
+    CCTK_REAL, intent(out) :: dgg_dot(3,3,3)
+    integer :: i,j,k
     
+    ! d/dt g_ij,k = -2 K_ij,k
+    
+    do i=1,3
+       do j=1,3
+          do k=1,3
+             dgg_dot(i,j,k) = -2 * dkk(i,j,k)
+          end do
+       end do
+    end do
+  end subroutine calc_3metricderivdot_simple
+  
+  subroutine calc_extcurvdot_simple (gu,ri, kk, kk_dot)
+    CCTK_REAL, intent(in)  :: gu(3,3)
+    CCTK_REAL, intent(in)  :: ri(3,3)
+    CCTK_REAL, intent(in)  :: kk(3,3)
+    CCTK_REAL, intent(out) :: kk_dot(3,3)
+    integer :: i,j,l,m
+    
+    ! d/dt K_ij = R_ij - 2 K_il g^lm K_mj + g^lm K_lm K_ij
+    
+    do i=1,3
+       do j=1,3
+          kk_dot(i,j) = ri(i,j)
+          do l=1,3
+             do m=1,3
+                kk_dot(i,j) = kk_dot(i,j) + gu(l,m) &
+                     * (-2 * kk(i,l) * kk(m,j) + kk(l,m) * kk(i,j))
+             end do
+          end do
+       end do
+    end do
+  end subroutine calc_extcurvdot_simple
+  
+  subroutine calc_3metricdot2_simple (kk_dot, gg_dot2)
+    CCTK_REAL, intent(in)  :: kk_dot(3,3)
+    CCTK_REAL, intent(out) :: gg_dot2(3,3)
+    integer :: i,j
+    
+    ! d/dt g_ij = -2 K_ij
+    ! d^2/dt^2 g_ij = -2 d/dt K_ij
+    
+    do i=1,3
+       do j=1,3
+          gg_dot2(i,j) = -2 * kk_dot(i,j)
+       end do
+    end do
+  end subroutine calc_3metricdot2_simple
+  
 end module adm_metric