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#include "cctk.h"
#include "cctk_Arguments.h"
#include "cctk_Functions.h"
#include "cctk_Parameters.h"
subroutine qlm_calc_tetrad (CCTK_ARGUMENTS, hn)
use adm_metric_simple
use cctk
use classify
use matinv
use pointwise2
use qlm_boundary
use qlm_derivs
use qlm_gram_schmidt
use qlm_variables
use ricci4
use tensor
use tensor4
implicit none
DECLARE_CCTK_ARGUMENTS
DECLARE_CCTK_FUNCTIONS
DECLARE_CCTK_PARAMETERS
integer :: hn
CCTK_REAL, parameter :: one=1, two=2
CCTK_REAL, parameter :: gg4(0:3,0:3,0:3) = 0
CCTK_REAL :: gg(3,3), dgg(3,3,3), gg_dot(3,3)
CCTK_REAL :: kk(3,3)
CCTK_REAL :: g4(0:3,0:3), gu4(0:3,0:3), dg4(0:3,0:3,0:3)
CCTK_REAL :: gamma4(0:3,0:3,0:3)
CCTK_REAL :: ee(0:3,0:3), ee_p(0:3,1:3), ee_p_p(0:3,1:3)
CCTK_REAL :: dee_spher(1:3,1:3,1:3), ee_inv(1:3,1:3)
CCTK_REAL :: dee(0:3,0:3,0:3), gee(0:3,0:3,0:3)
CCTK_REAL :: m1(0:3), m2(0:3) ! temporary variables to calculate mm
CCTK_REAL :: ss(0:3) ! spacelike outward normal to horizon
CCTK_REAL :: tt(0:3) ! timelike unit normal to hypersurface
CCTK_REAL :: ll(0:3) ! future null vector on the horizon
CCTK_REAL :: nn(0:3) ! future inward null vector
CCTK_COMPLEX :: mm(0:3) ! vector on horizon within the hypersurface
CCTK_REAL :: gtt(0:3,0:3), gss(0:3,0:3)
CCTK_REAL :: gm1(0:3,0:3), gm2(0:3,0:3)
CCTK_REAL :: gll(0:3,0:3), gnn(0:3,0:3)
CCTK_COMPLEX :: gmm(0:3,0:3)
CCTK_REAL :: nabla_ll(0:3,0:3), nabla_nn(0:3,0:3)
CCTK_COMPLEX :: nabla_mm(0:3,0:3)
!CCTK_REAL :: t0, t1, t2
!logical :: ce0, ce1, ce2
CCTK_REAL :: delta_space(2)
CCTK_REAL :: count, accuracy
integer :: lsh(2)
integer :: i, j
integer :: a, b, c, d
CCTK_REAL :: theta, phi
logical :: lerr
character*2, parameter :: crlf = achar(13) // achar(10)
character :: msg*1000
if (veryverbose/=0) then
call CCTK_INFO ("Setting tetrad")
end if
lsh(:) = (/ qlm_ntheta(hn), qlm_nphi(hn) /)
delta_space(:) = (/ qlm_delta_theta(hn), qlm_delta_phi(hn) /)
count = 0
accuracy = 0
! Calculate the coordinates
do j = 1+qlm_nghostsphi(hn), qlm_nphi(hn)-qlm_nghostsphi(hn)
do i = 1+qlm_nghoststheta(hn), qlm_ntheta(hn)-qlm_nghoststheta(hn)
theta = qlm_origin_theta(hn) + (i-1)*qlm_delta_theta(hn)
phi = qlm_origin_phi(hn) + (j-1)*qlm_delta_phi(hn)
! Get the variables from the arrays
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(2,1,1) = dgg(1,2,1)
dgg(3,1,1) = dgg(1,3,1)
dgg(3,2,1) = dgg(2,3,1)
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(2,1,2) = dgg(1,2,2)
dgg(3,1,2) = dgg(1,3,2)
dgg(3,2,2) = dgg(2,3,2)
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(2,1,3) = dgg(1,2,3)
dgg(3,1,3) = dgg(1,3,3)
dgg(3,2,3) = dgg(2,3,3)
kk(1,1) = qlm_kxx(i,j)
kk(1,2) = qlm_kxy(i,j)
kk(1,3) = qlm_kxz(i,j)
kk(2,2) = qlm_kyy(i,j)
kk(2,3) = qlm_kyz(i,j)
kk(3,3) = qlm_kzz(i,j)
kk(2,1) = kk(1,2)
kk(3,1) = kk(1,3)
kk(3,2) = kk(2,3)
! Calculate 4-metric
call calc_3metricdot_simple (kk, gg_dot)
call calc_4metricderivs_simple (gg,dgg,gg_dot, g4,dg4)
call calc_4inv (g4, gu4)
call calc_4connections (gu4,dg4, gamma4)
! The following must be consistent with qlm_tetrad.F90
ee = TAT_nan()
dee_spher = TAT_nan()
dee = TAT_nan()
ee(0,:) = 0
dee(0,:,:) = 0
ee(1,0) = 0
ee(1,1) = qlm_x(i,j,hn) - qlm_origin_x(hn)
ee(1,2) = qlm_y(i,j,hn) - qlm_origin_y(hn)
ee(1,3) = qlm_z(i,j,hn) - qlm_origin_z(hn)
!ee_p(1,1) = qlm_x_p(i,j,hn) - qlm_origin_x_p(hn)
!ee_p(1,2) = qlm_y_p(i,j,hn) - qlm_origin_y_p(hn)
!ee_p(1,3) = qlm_z_p(i,j,hn) - qlm_origin_z_p(hn)
!ee_p_p(1,1) = qlm_x_p_p(i,j,hn) - qlm_origin_x_p_p(hn)
!ee_p_p(1,2) = qlm_y_p_p(i,j,hn) - qlm_origin_y_p_p(hn)
!ee_p_p(1,3) = qlm_z_p_p(i,j,hn) - qlm_origin_z_p_p(hn)
dee(1,0,:) = 0
!dee(1,1:3,0) = timederiv (ee(1,1:3), ee_p(1,1:3), ee_p_p(1,1:3), t0,t1,t2, ce0,ce1,ce2)
dee(1,1:3,0) = 0
dee_spher(1,:,1) = 0 ! this is a choice
dee_spher(1,1,2:3) = deriv (qlm_x(:,:,hn), i,j, delta_space)
dee_spher(1,2,2:3) = deriv (qlm_y(:,:,hn), i,j, delta_space)
dee_spher(1,3,2:3) = deriv (qlm_z(:,:,hn), i,j, delta_space)
ee(2:3,0) = 0
ee(2:3,1) = deriv (qlm_x(:,:,hn), i,j, delta_space)
ee(2:3,2) = deriv (qlm_y(:,:,hn), i,j, delta_space)
ee(2:3,3) = deriv (qlm_z(:,:,hn), i,j, delta_space)
ee_p(2:3,1) = deriv (qlm_x_p(:,:,hn), i,j, delta_space)
ee_p(2:3,2) = deriv (qlm_y_p(:,:,hn), i,j, delta_space)
ee_p(2:3,3) = deriv (qlm_z_p(:,:,hn), i,j, delta_space)
ee_p_p(2:3,1) = deriv (qlm_x_p_p(:,:,hn), i,j, delta_space)
ee_p_p(2:3,2) = deriv (qlm_y_p_p(:,:,hn), i,j, delta_space)
ee_p_p(2:3,3) = deriv (qlm_z_p_p(:,:,hn), i,j, delta_space)
dee(2:3,0,:) = 0
!dee(2:3,1:3,0) = timederiv (ee(2:3,1:3), ee_p(2:3,1:3), ee_p_p(2:3,1:3), t0,t1,t2, ce0,ce1,ce2)
dee(2:3,1:3,0) = 0
dee_spher(2:3,:,1) = 0 ! this is a choice
dee_spher(2:3,1,2:3) = deriv2 (qlm_x(:,:,hn), i,j, delta_space)
dee_spher(2:3,2,2:3) = deriv2 (qlm_y(:,:,hn), i,j, delta_space)
dee_spher(2:3,3,2:3) = deriv2 (qlm_z(:,:,hn), i,j, delta_space)
! ee_a^i
! dee_spher_a^i,b
! dee_a^i,j = ee_j^b dee_spher_a^i,b
call calc_inv3 (ee(1:3,1:3), ee_inv, lerr)
if (lerr) then
call CCTK_WARN (3, "Could not invert matrix")
end if
do a=1,3
do b=1,3
do c=1,3
dee(a,b,c) = 0
do d=1,3
dee(a,b,c) = dee(a,b,c) + ee_inv(c,d) * dee_spher(a,b,d)
end do
end do
end do
end do
do a=0,3
do b=0,3
gee(:,a,b) = dee(:,a,b)
do c=0,3
gee(:,a,b) = gee(:,a,b) + ee(:,c) * gamma4(a,c,b)
end do
end do
end do
! tt
tt(:) = ee(0,:)
gtt(:,:) = gee(0,:,:)
! m1 = ep
m1(:) = ee(3,:)
gm1(:,:) = gee(3,:,:)
call gram_schmidt_normalise (g4,gg4, m1,gm1, one)
! m2 = et
m2(:) = ee(2,:)
gm2(:,:) = gee(2,:,:)
call gram_schmidt_project (g4,gg4, m1,gm1, one, m2,gm2)
call gram_schmidt_normalise (g4,gg4, m2,gm2, one)
! ss = er
ss(:) = ee(1,:)
gss(:,:) = gee(1,:,:)
call gram_schmidt_project (g4,gg4, m1,gm1, one, ss,gss)
call gram_schmidt_project (g4,gg4, m2,gm2, one, ss,gss)
call gram_schmidt_normalise (g4,gg4, ss,gss, one)
! ll = (tt + ss) / sqrt(two)
ll = (tt + ss) / sqrt(two)
gll = (gtt + gss) / sqrt(two)
! nn = (tt - ss) / sqrt(two)
nn = (tt - ss) / sqrt(two)
gnn = (gtt - gss) / sqrt(two)
! mm = cmplx(m1, m2, kind(mm)) / sqrt(two)
mm = cmplx(m1, m2, kind(mm)) / sqrt(two)
gmm = cmplx(gm1, gm2, kind(gmm)) / sqrt(two)
! Store the stuff into the arrays
do a=0,3
do b=0,3
nabla_ll(a,b) = 0
nabla_nn(a,b) = 0
nabla_mm(a,b) = 0
do c=0,3
nabla_ll(a,b) = nabla_ll(a,b) + g4(a,c) * gll(c,b)
nabla_nn(a,b) = nabla_nn(a,b) + g4(a,c) * gnn(c,b)
nabla_mm(a,b) = nabla_mm(a,b) + g4(a,c) * gmm(c,b)
end do
qlm_tetrad_derivs(i,j)%nabla_ll(a,b) = nabla_ll(a,b)
qlm_tetrad_derivs(i,j)%nabla_nn(a,b) = nabla_nn(a,b)
qlm_tetrad_derivs(i,j)%nabla_mm(a,b) = nabla_mm(a,b)
end do
end do
qlm_l0(i,j,hn) = ll(0)
qlm_l1(i,j,hn) = ll(1)
qlm_l2(i,j,hn) = ll(2)
qlm_l3(i,j,hn) = ll(3)
qlm_n0(i,j,hn) = nn(0)
qlm_n1(i,j,hn) = nn(1)
qlm_n2(i,j,hn) = nn(2)
qlm_n3(i,j,hn) = nn(3)
qlm_m0(i,j,hn) = mm(0)
qlm_m1(i,j,hn) = mm(1)
qlm_m2(i,j,hn) = mm(2)
qlm_m3(i,j,hn) = mm(3)
end do
end do
if (count > 0) then
accuracy = sqrt(accuracy / count)
end if
if (veryverbose/=0) then
write (msg, '("Tetrad accuracy L2 norm: ",g12.4)') accuracy
call CCTK_INFO (msg)
end if
!!$ if (accuracy > 1.0d-12) then
if (accuracy > 1.0d-8) then
call CCTK_WARN (1, "Tetrad is not accurate")
end if
call set_boundary (CCTK_PASS_FTOF, hn, qlm_l0(:,:,hn), +1)
call set_boundary (CCTK_PASS_FTOF, hn, qlm_l1(:,:,hn), +1)
call set_boundary (CCTK_PASS_FTOF, hn, qlm_l2(:,:,hn), +1)
call set_boundary (CCTK_PASS_FTOF, hn, qlm_l3(:,:,hn), +1)
call set_boundary (CCTK_PASS_FTOF, hn, qlm_n0(:,:,hn), +1)
call set_boundary (CCTK_PASS_FTOF, hn, qlm_n1(:,:,hn), +1)
call set_boundary (CCTK_PASS_FTOF, hn, qlm_n2(:,:,hn), +1)
call set_boundary (CCTK_PASS_FTOF, hn, qlm_n3(:,:,hn), +1)
call set_boundary (CCTK_PASS_FTOF, hn, qlm_m0(:,:,hn), +1)
call set_boundary (CCTK_PASS_FTOF, hn, qlm_m1(:,:,hn), +1)
call set_boundary (CCTK_PASS_FTOF, hn, qlm_m2(:,:,hn), +1)
call set_boundary (CCTK_PASS_FTOF, hn, qlm_m3(:,:,hn), +1)
end subroutine qlm_calc_tetrad
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