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#include "cctk.h"
#include "cctk_Arguments.h"
#include "cctk_Functions.h"
#include "cctk_Parameters.h"
subroutine qlm_calc_twometric (CCTK_ARGUMENTS, hn)
use adm_metric
use cctk
use qlm_boundary
use qlm_derivs
use qlm_variables
use ricci
use ricci2
use tensor
use tensor2
use tensor4
implicit none
DECLARE_CCTK_ARGUMENTS
DECLARE_CCTK_FUNCTIONS
DECLARE_CCTK_PARAMETERS
integer :: hn
CCTK_REAL, parameter :: two = 2, half = 1d0/2d0
CCTK_REAL :: gg(3,3), dgg(3,3,3), ddgg(3,3,3,3)
CCTK_REAL :: gamma(3,3,3), dgamma(3,3,3,3), ri(3,3), rsc
CCTK_REAL :: ee(3,2), dee(3,2,2), ddee(3,2,2,2)
CCTK_REAL :: qq(2,2), dqq(2,2,2), ddqq(2,2,2,2)
CCTK_REAL :: dtq, qu(2,2), dqu(2,2,2)
CCTK_REAL :: delta_space(2)
integer :: i, j
integer :: a, b, c, d, e, f, g, h
if (veryverbose/=0) then
call CCTK_INFO ("Calculating two-metric")
end if
delta_space(:) = (/ qlm_delta_theta(hn), qlm_delta_phi(hn) /)
! Calculate the two-metric
do j = 1+qlm_nghostsphi(hn), qlm_nphi(hn)-qlm_nghostsphi(hn)
do i = 1+qlm_nghoststheta(hn), qlm_ntheta(hn)-qlm_nghoststheta(hn)
gg(1,1) = qlm_gxx(i,j)
gg(1,2) = qlm_gxy(i,j)
gg(1,3) = qlm_gxz(i,j)
gg(2,2) = qlm_gyy(i,j)
gg(2,3) = qlm_gyz(i,j)
gg(3,3) = qlm_gzz(i,j)
gg(2,1) = gg(1,2)
gg(3,1) = gg(1,3)
gg(3,2) = gg(2,3)
dgg(1,1,1) = qlm_dgxxx(i,j)
dgg(1,2,1) = qlm_dgxyx(i,j)
dgg(1,3,1) = qlm_dgxzx(i,j)
dgg(2,2,1) = qlm_dgyyx(i,j)
dgg(2,3,1) = qlm_dgyzx(i,j)
dgg(3,3,1) = qlm_dgzzx(i,j)
dgg(1,1,2) = qlm_dgxxy(i,j)
dgg(1,2,2) = qlm_dgxyy(i,j)
dgg(1,3,2) = qlm_dgxzy(i,j)
dgg(2,2,2) = qlm_dgyyy(i,j)
dgg(2,3,2) = qlm_dgyzy(i,j)
dgg(3,3,2) = qlm_dgzzy(i,j)
dgg(1,1,3) = qlm_dgxxz(i,j)
dgg(1,2,3) = qlm_dgxyz(i,j)
dgg(1,3,3) = qlm_dgxzz(i,j)
dgg(2,2,3) = qlm_dgyyz(i,j)
dgg(2,3,3) = qlm_dgyzz(i,j)
dgg(3,3,3) = qlm_dgzzz(i,j)
dgg(2,1,:) = dgg(1,2,:)
dgg(3,1,:) = dgg(1,3,:)
dgg(3,2,:) = dgg(2,3,:)
ddgg(1,1,1,1) = qlm_ddgxxxx(i,j)
ddgg(1,2,1,1) = qlm_ddgxyxx(i,j)
ddgg(1,3,1,1) = qlm_ddgxzxx(i,j)
ddgg(2,2,1,1) = qlm_ddgyyxx(i,j)
ddgg(2,3,1,1) = qlm_ddgyzxx(i,j)
ddgg(3,3,1,1) = qlm_ddgzzxx(i,j)
ddgg(1,1,1,2) = qlm_ddgxxxy(i,j)
ddgg(1,2,1,2) = qlm_ddgxyxy(i,j)
ddgg(1,3,1,2) = qlm_ddgxzxy(i,j)
ddgg(2,2,1,2) = qlm_ddgyyxy(i,j)
ddgg(2,3,1,2) = qlm_ddgyzxy(i,j)
ddgg(3,3,1,2) = qlm_ddgzzxy(i,j)
ddgg(1,1,1,3) = qlm_ddgxxxz(i,j)
ddgg(1,2,1,3) = qlm_ddgxyxz(i,j)
ddgg(1,3,1,3) = qlm_ddgxzxz(i,j)
ddgg(2,2,1,3) = qlm_ddgyyxz(i,j)
ddgg(2,3,1,3) = qlm_ddgyzxz(i,j)
ddgg(3,3,1,3) = qlm_ddgzzxz(i,j)
ddgg(1,1,2,2) = qlm_ddgxxyy(i,j)
ddgg(1,2,2,2) = qlm_ddgxyyy(i,j)
ddgg(1,3,2,2) = qlm_ddgxzyy(i,j)
ddgg(2,2,2,2) = qlm_ddgyyyy(i,j)
ddgg(2,3,2,2) = qlm_ddgyzyy(i,j)
ddgg(3,3,2,2) = qlm_ddgzzyy(i,j)
ddgg(1,1,2,3) = qlm_ddgxxyz(i,j)
ddgg(1,2,2,3) = qlm_ddgxyyz(i,j)
ddgg(1,3,2,3) = qlm_ddgxzyz(i,j)
ddgg(2,2,2,3) = qlm_ddgyyyz(i,j)
ddgg(2,3,2,3) = qlm_ddgyzyz(i,j)
ddgg(3,3,2,3) = qlm_ddgzzyz(i,j)
ddgg(1,1,3,3) = qlm_ddgxxzz(i,j)
ddgg(1,2,3,3) = qlm_ddgxyzz(i,j)
ddgg(1,3,3,3) = qlm_ddgxzzz(i,j)
ddgg(2,2,3,3) = qlm_ddgyyzz(i,j)
ddgg(2,3,3,3) = qlm_ddgyzzz(i,j)
ddgg(3,3,3,3) = qlm_ddgzzzz(i,j)
ddgg(2,1,:,:) = ddgg(1,2,:,:)
ddgg(3,1,:,:) = ddgg(1,3,:,:)
ddgg(3,2,:,:) = ddgg(2,3,:,:)
ddgg(:,:,2,1) = ddgg(:,:,1,2)
ddgg(:,:,3,1) = ddgg(:,:,1,3)
ddgg(:,:,3,2) = ddgg(:,:,2,3)
ee(1,1:2) = deriv (qlm_x(:,:,hn), i, j, delta_space)
ee(2,1:2) = deriv (qlm_y(:,:,hn), i, j, delta_space)
ee(3,1:2) = deriv (qlm_z(:,:,hn), i, j, delta_space)
dee(1,1:2,1:2) = deriv2 (qlm_x(:,:,hn), i, j, delta_space)
dee(2,1:2,1:2) = deriv2 (qlm_y(:,:,hn), i, j, delta_space)
dee(3,1:2,1:2) = deriv2 (qlm_z(:,:,hn), i, j, delta_space)
ddee(1,1:2,1:2,1:2) = deriv3 (qlm_x(:,:,hn), i, j, delta_space)
ddee(2,1:2,1:2,1:2) = deriv3 (qlm_y(:,:,hn), i, j, delta_space)
ddee(3,1:2,1:2,1:2) = deriv3 (qlm_z(:,:,hn), i, j, delta_space)
do a=1,2
do b=1,2
qq(a,b) = 0
do c=1,3
do d=1,3
qq(a,b) = qq(a,b) + gg(c,d) * ee(c,a) * ee(d,b)
end do
end do
end do
end do
do a=1,2
do b=1,2
do c=1,2
dqq(a,b,c) = 0
do d=1,3
do e=1,3
do f=1,3
dqq(a,b,c) = dqq(a,b,c) + dgg(d,e,f) * ee(d,a) * ee(e,b) * ee(f,c)
end do
dqq(a,b,c) = dqq(a,b,c) + gg(d,e) * dee(d,a,c) * ee(e,b)
dqq(a,b,c) = dqq(a,b,c) + gg(d,e) * ee(d,a) * dee(e,b,c)
end do
end do
end do
end do
end do
do a=1,2
do b=1,2
do c=1,2
do d=1,2
ddqq(a,b,c,d) = 0
do e=1,3
do f=1,3
do g=1,3
do h=1,3
ddqq(a,b,c,d) = ddqq(a,b,c,d) + ddgg(e,f,g,h) * ee(e,a) * ee(f,b) * ee(g,c) * ee(h,d)
end do
ddqq(a,b,c,d) = ddqq(a,b,c,d) + dgg(e,f,g) * dee(e,a,d) * ee(f,b) * ee(g,c)
ddqq(a,b,c,d) = ddqq(a,b,c,d) + dgg(e,f,g) * ee(e,a) * dee(f,b,d) * ee(g,c)
ddqq(a,b,c,d) = ddqq(a,b,c,d) + dgg(e,f,g) * ee(e,a) * ee(f,b) * dee(g,c,d)
ddqq(a,b,c,d) = ddqq(a,b,c,d) + dgg(e,f,g) * dee(e,a,c) * ee(f,b) * ee(g,d)
ddqq(a,b,c,d) = ddqq(a,b,c,d) + dgg(e,f,g) * ee(e,a) * dee(f,b,c) * ee(g,d)
end do
ddqq(a,b,c,d) = ddqq(a,b,c,d) + gg(e,f) * ddee(e,a,c,d) * ee(f,b)
ddqq(a,b,c,d) = ddqq(a,b,c,d) + gg(e,f) * dee(e,a,c) * dee(f,b,d)
ddqq(a,b,c,d) = ddqq(a,b,c,d) + gg(e,f) * dee(e,a,d) * dee(f,b,c)
ddqq(a,b,c,d) = ddqq(a,b,c,d) + gg(e,f) * ee(e,a) * ddee(f,b,c,d)
end do
end do
end do
end do
end do
end do
call calc_2det (qq, dtq)
call calc_2inv (qq, dtq, qu)
call calc_2invderiv (qu, dqq, dqu)
call calc_2connections (qu, dqq, gamma)
call calc_2connectionderivs (qu, dqq, dqu, ddqq, dgamma)
call calc_2ricci (gamma, dgamma, ri)
call calc_2trace (qu, ri, rsc)
! Could also calculate this as:
! q^ab = m^a mbar^b + mbar^a m^b
qlm_qtt(i,j,hn) = qq(1,1)
qlm_qtp(i,j,hn) = qq(1,2)
qlm_qpp(i,j,hn) = qq(2,2)
! Could also calculate this from NP coefficients alpha and
! beta (and epsilon and gamma?)
qlm_dqttt(i,j,hn) = dqq(1,1,1)
qlm_dqtpt(i,j,hn) = dqq(1,2,1)
qlm_dqppt(i,j,hn) = dqq(2,2,1)
qlm_dqttp(i,j,hn) = dqq(1,1,2)
qlm_dqtpp(i,j,hn) = dqq(1,2,2)
qlm_dqppp(i,j,hn) = dqq(2,2,2)
! Could also calculate this from 3Rsc and extrinsic curvature
qlm_rsc(i,j,hn) = rsc
end do
end do
call set_boundary (CCTK_PASS_FTOF, hn, qlm_qtt(:,:,hn), +1)
call set_boundary (CCTK_PASS_FTOF, hn, qlm_qtp(:,:,hn), +1)
call set_boundary (CCTK_PASS_FTOF, hn, qlm_qpp(:,:,hn), +1)
call set_boundary (CCTK_PASS_FTOF, hn, qlm_dqttt(:,:,hn), -1)
call set_boundary (CCTK_PASS_FTOF, hn, qlm_dqtpt(:,:,hn), -1)
call set_boundary (CCTK_PASS_FTOF, hn, qlm_dqppt(:,:,hn), -1)
call set_boundary (CCTK_PASS_FTOF, hn, qlm_dqttp(:,:,hn), -1)
call set_boundary (CCTK_PASS_FTOF, hn, qlm_dqtpp(:,:,hn), -1)
call set_boundary (CCTK_PASS_FTOF, hn, qlm_dqppp(:,:,hn), -1)
call set_boundary (CCTK_PASS_FTOF, hn, qlm_rsc(:,:,hn), +1)
end subroutine qlm_calc_twometric
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