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! $Header$
#include "cctk.h"
module adm_metric_simple
! This module assumes that alpha=1 and beta^i=0
use tensor
implicit none
private
public calc_4metric_simple
public calc_4metricderivs_simple
public calc_4metricderivs2_simple
public calc_3metric_simple
public calc_3metricderivs_simple
public calc_3metricdot_simple
public calc_extcurv_simple
public calc_3metricderivdot_simple
public calc_extcurvdot_simple
public calc_3metricdot2_simple
contains
subroutine calc_4metric_simple (gg, g4)
CCTK_REAL, intent(in) :: gg(3,3)
CCTK_REAL, intent(out) :: g4(0:3,0:3)
! ds^2 = - dt^2 + g_ij dx^i dx^j
g4(0 ,0 ) = -1
g4(1:3,0 ) = 0
g4(0 ,1:3) = 0
g4(1:3,1:3) = gg
end subroutine calc_4metric_simple
subroutine calc_4metricderivs_simple (gg, dgg, gg_dot, g4,dg4)
CCTK_REAL, intent(in) :: gg(3,3)
CCTK_REAL, intent(in) :: dgg(3,3,3)
CCTK_REAL, intent(in) :: gg_dot(3,3)
CCTK_REAL, intent(out) :: g4(0:3,0:3),dg4(0:3,0:3,0:3)
CCTK_REAL :: d4gg(3,3,0:3)
integer :: i
! 4-metric
g4(0 ,0 ) = -1
g4(1:3,0 ) = 0
g4(0 ,1:3) = 0
g4(1:3,1:3) = gg
! derivatives
d4gg (:,:,0 ) = gg_dot(:,:)
d4gg (:,:,1:3) = dgg(:,:,:)
forall (i=0:3)
dg4(0 ,0 ,i) = 0
dg4(1:3,0 ,i) = 0
dg4(0 ,1:3,i) = 0
dg4(1:3,1:3,i) = d4gg(:,:,i)
end forall
end subroutine calc_4metricderivs_simple
subroutine calc_4metricderivs2_simple (gg, dgg, ddgg, gg_dot, gg_dot2, dgg_dot, &
g4,dg4,ddg4)
CCTK_REAL, intent(in) :: gg(3,3)
CCTK_REAL, intent(in) :: dgg(3,3,3)
CCTK_REAL, intent(in) :: ddgg(3,3,3,3)
CCTK_REAL, intent(in) :: gg_dot(3,3)
CCTK_REAL, intent(in) :: gg_dot2(3,3)
CCTK_REAL, intent(in) :: dgg_dot(3,3,3)
CCTK_REAL, intent(out) :: g4(0:3,0:3),dg4(0:3,0:3,0:3)
CCTK_REAL, intent(out) :: ddg4(0:3,0:3,0:3,0:3)
CCTK_REAL :: d4gg(3,3,0:3)
CCTK_REAL :: dd4gg(3,3,0:3,0:3)
integer :: i,j,k
! 4-metric
g4(0 ,0 ) = -1
g4(1:3,0 ) = 0
g4(0 ,1:3) = 0
g4(1:3,1:3) = gg
! first derivatives
d4gg (:,:,0 ) = gg_dot(:,:)
d4gg (:,:,1:3) = dgg(:,:,:)
forall (i=0:3)
dg4(0 ,0 ,i) = 0
dg4(1:3,0 ,i) = 0
dg4(0 ,1:3,i) = 0
dg4(1:3,1:3,i) = d4gg(:,:,i)
end forall
! second derivatives
dd4gg (:,:,0 ,0 ) = gg_dot2(:,:)
dd4gg (:,:,1:3,0 ) = dgg_dot(:,:,:)
dd4gg (:,:,0 ,1:3) = dgg_dot(:,:,:)
dd4gg (:,:,1:3,1:3) = ddgg(:,:,:,:)
! g4(0 ,0 ) = -1
! g4(1:3,0 ) = 0
! g4(0 ,1:3) = 0
! g4(1:3,1:3) = gg
! dg4(0 ,0 ,i) = 0
! dg4(1:3,0 ,i) = 0
! dg4(0 ,1:3,i) = 0
! dg4(1:3,1:3,i) = d4gg(:,:,i)
forall (i=0:3, j=0:3)
ddg4(0 ,0 ,i,j) = 0
ddg4(1:3,0 ,i,j) = 0
ddg4(0 ,1:3,i,j) = 0
ddg4(1:3,1:3,i,j) = dd4gg(:,:,i,j)
end forall
end subroutine calc_4metricderivs2_simple
subroutine calc_3metric_simple (g4, gg)
CCTK_REAL, intent(in) :: g4(0:3,0:3)
CCTK_REAL, intent(out) :: gg(3,3)
CCTK_REAL :: dtg, gu(3,3)
! ds^2 = -alpha^2 dt^2 + g_ij (dx^i + beta^i dt) (dx^j + beta^j dt)
gg = g4(1:3,1:3)
end subroutine calc_3metric_simple
subroutine calc_3metricderivs_simple (g4,dg4, gg, dgg, gg_dot)
CCTK_REAL, intent(in) :: g4(0:3,0:3),dg4(0:3,0:3,0:3)
CCTK_REAL, intent(out) :: gg(3,3)
CCTK_REAL, intent(out) :: dgg(3,3,3)
CCTK_REAL, intent(out) :: gg_dot(3,3)
CCTK_REAL :: d4gg(3,3,0:3)
integer :: i,j
! ds^2 = -alpha^2 dt^2 + g_ij (dx^i + beta^i dt) (dx^j + beta^j dt)
gg = g4(1:3,1:3)
forall (i=0:3)
d4gg(:,:,i) = dg4(1:3,1:3,i)
end forall
gg_dot = d4gg(:,:,0)
dgg = d4gg(:,:,1:3)
end subroutine calc_3metricderivs_simple
subroutine calc_extcurv_simple (gg, dgg, gg_dot, kk)
CCTK_REAL, intent(in) :: gg(3,3), dgg(3,3,3), gg_dot(3,3)
CCTK_REAL, intent(out) :: kk(3,3)
integer :: i,j
! d/dt g_ij = -2 alpha K_ij + g_kj beta^k,i + g_ik beta^k,j + beta^k g_ij,k
do i=1,3
do j=1,3
kk(i,j) = - gg_dot(i,j) / 2
end do
end do
end subroutine calc_extcurv_simple
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_simple
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