1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
|
! $Header$
#include "cctk.h"
#include "cctk_Arguments.h"
#include "cctk_Functions.h"
#include "cctk_Parameters.h"
subroutine CalcK (CCTK_ARGUMENTS)
implicit none
DECLARE_CCTK_ARGUMENTS
DECLARE_CCTK_FUNCTIONS
DECLARE_CCTK_PARAMETERS
CCTK_INT, parameter :: idummy=0
integer, parameter :: ik=kind(idummy)
CCTK_INT, parameter :: bndwidth = 1
CCTK_INT :: len_boundary, len_options
character(1000) :: str_boundary, str_options
integer :: options
CCTK_REAL :: dt, dx(3)
CCTK_REAL :: gama(3,3), gama_dot(3,3), dgama(3,3,3)
CCTK_REAL :: alfa
CCTK_REAL :: beta(3), dbeta(3,3)
CCTK_REAL :: kk(3,3)
integer :: imin(3), imax(3)
integer :: i, j, k
integer :: a, b, c
integer :: ierr
dt = CCTK_DELTA_TIME
dx(:) = CCTK_DELTA_SPACE(:)
call CCTK_FortranString &
(len_boundary, int(extcurv_boundary,ik), str_boundary)
call CCTK_FortranString &
(len_options, int(extcurv_boundary_options,ik), str_options)
call Util_TableCreateFromString (options, str_options)
if (options<0) then
call CCTK_WARN (0, "Parameter ""extcurv_boundary_options"" has an illegal syntax")
end if
imin(:) = 1+cctk_nghostzones(:)
imax(:) = cctk_lsh(:)-cctk_nghostzones(:)
where (cctk_bbox(1::2)/=0) imin(:) = 1+bndwidth
where (cctk_bbox(2::2)/=0) imax(:) = cctk_lsh(:)-bndwidth
! Convert to physical metric, if necessary
if (CCTK_EQUALS(metric_type, "static conformal")) then
call ConfToPhysInPlace &
(int(cctk_lsh(1),ik), int(cctk_lsh(2),ik), int(cctk_lsh(3),ik), &
psi, gxx, gxy, gxz, gyy, gyz, gzz)
call ConfToPhysInPlace &
(int(cctk_lsh(1),ik), int(cctk_lsh(2),ik), int(cctk_lsh(3),ik), &
psi, gxx_prev, gxy_prev, gxz_prev, gyy_prev, gyz_prev, gzz_prev)
#if 0
call ConfToPhysInPlace &
(int(cctk_lsh(1),ik), int(cctk_lsh(2),ik), int(cctk_lsh(3),ik), &
psi, gxx_prev2, gxy_prev2, gxz_prev2, gyy_prev2, gyz_prev2, gzz_prev2)
#else
call ConfToPhysInPlace &
(int(cctk_lsh(1),ik), int(cctk_lsh(2),ik), int(cctk_lsh(3),ik), &
psi, gxx_next, gxy_next, gxz_next, gyy_next, gyz_next, gzz_next)
#endif
end if
do k = imin(3), imax(3)
do j = imin(2), imax(2)
do i = imin(1), imax(1)
gama(1,1) = gxx(i,j,k)
gama(1,2) = gxy(i,j,k)
gama(1,3) = gxz(i,j,k)
gama(2,2) = gyy(i,j,k)
gama(2,3) = gyz(i,j,k)
gama(3,3) = gzz(i,j,k)
gama(2,1) = gama(1,2)
gama(3,1) = gama(1,3)
gama(3,2) = gama(2,3)
#if 0
gama_dot(1,1) = (-3*gxx(i,j,k) + 4*gxx_prev(i,j,k) - gxx_prev2(i,j,k)) / (2*dt)
gama_dot(1,2) = (-3*gxy(i,j,k) + 4*gxy_prev(i,j,k) - gxy_prev2(i,j,k)) / (2*dt)
gama_dot(1,3) = (-3*gxz(i,j,k) + 4*gxz_prev(i,j,k) - gxz_prev2(i,j,k)) / (2*dt)
gama_dot(2,2) = (-3*gyy(i,j,k) + 4*gyy_prev(i,j,k) - gyy_prev2(i,j,k)) / (2*dt)
gama_dot(2,3) = (-3*gyz(i,j,k) + 4*gyz_prev(i,j,k) - gyz_prev2(i,j,k)) / (2*dt)
gama_dot(3,3) = (-3*gzz(i,j,k) + 4*gzz_prev(i,j,k) - gzz_prev2(i,j,k)) / (2*dt)
#else
gama_dot(1,1) = (gxx_next(i,j,k) - gxx_prev(i,j,k)) / (2*dt)
gama_dot(1,2) = (gxy_next(i,j,k) - gxy_prev(i,j,k)) / (2*dt)
gama_dot(1,3) = (gxz_next(i,j,k) - gxz_prev(i,j,k)) / (2*dt)
gama_dot(2,2) = (gyy_next(i,j,k) - gyy_prev(i,j,k)) / (2*dt)
gama_dot(2,3) = (gyz_next(i,j,k) - gyz_prev(i,j,k)) / (2*dt)
gama_dot(3,3) = (gzz_next(i,j,k) - gzz_prev(i,j,k)) / (2*dt)
#endif
gama_dot(2,1) = gama_dot(1,2)
gama_dot(3,1) = gama_dot(1,3)
gama_dot(3,2) = gama_dot(2,3)
dgama(1,1,1) = (gxx(i+1,j,k) - gxx(i-1,j,k)) / (2*dx(1))
dgama(1,2,1) = (gxy(i+1,j,k) - gxy(i-1,j,k)) / (2*dx(1))
dgama(1,3,1) = (gxz(i+1,j,k) - gxz(i-1,j,k)) / (2*dx(1))
dgama(2,2,1) = (gyy(i+1,j,k) - gyy(i-1,j,k)) / (2*dx(1))
dgama(2,3,1) = (gyz(i+1,j,k) - gyz(i-1,j,k)) / (2*dx(1))
dgama(3,3,1) = (gzz(i+1,j,k) - gzz(i-1,j,k)) / (2*dx(1))
dgama(1,1,2) = (gxx(i,j+1,k) - gxx(i,j-1,k)) / (2*dx(2))
dgama(1,2,2) = (gxy(i,j+1,k) - gxy(i,j-1,k)) / (2*dx(2))
dgama(1,3,2) = (gxz(i,j+1,k) - gxz(i,j-1,k)) / (2*dx(2))
dgama(2,2,2) = (gyy(i,j+1,k) - gyy(i,j-1,k)) / (2*dx(2))
dgama(2,3,2) = (gyz(i,j+1,k) - gyz(i,j-1,k)) / (2*dx(2))
dgama(3,3,2) = (gzz(i,j+1,k) - gzz(i,j-1,k)) / (2*dx(2))
dgama(1,1,3) = (gxx(i,j,k+1) - gxx(i,j,k-1)) / (2*dx(3))
dgama(1,2,3) = (gxy(i,j,k+1) - gxy(i,j,k-1)) / (2*dx(3))
dgama(1,3,3) = (gxz(i,j,k+1) - gxz(i,j,k-1)) / (2*dx(3))
dgama(2,2,3) = (gyy(i,j,k+1) - gyy(i,j,k-1)) / (2*dx(3))
dgama(2,3,3) = (gyz(i,j,k+1) - gyz(i,j,k-1)) / (2*dx(3))
dgama(3,3,3) = (gzz(i,j,k+1) - gzz(i,j,k-1)) / (2*dx(3))
dgama(2,1,:) = dgama(1,2,:)
dgama(3,1,:) = dgama(1,3,:)
dgama(3,2,:) = dgama(2,3,:)
alfa = alp(i,j,k)
beta(1) = betax(i,j,k)
beta(2) = betay(i,j,k)
beta(3) = betaz(i,j,k)
dbeta(1,1) = (betax(i+1,j,k) - betax(i-1,j,k)) / (2*dx(1))
dbeta(2,1) = (betay(i+1,j,k) - betay(i-1,j,k)) / (2*dx(1))
dbeta(3,1) = (betaz(i+1,j,k) - betaz(i-1,j,k)) / (2*dx(1))
dbeta(1,2) = (betax(i,j+1,k) - betax(i,j-1,k)) / (2*dx(2))
dbeta(2,2) = (betay(i,j+1,k) - betay(i,j-1,k)) / (2*dx(2))
dbeta(3,2) = (betaz(i,j+1,k) - betaz(i,j-1,k)) / (2*dx(2))
dbeta(1,3) = (betax(i,j,k+1) - betax(i,j,k-1)) / (2*dx(3))
dbeta(2,3) = (betay(i,j,k+1) - betay(i,j,k-1)) / (2*dx(3))
dbeta(3,3) = (betaz(i,j,k+1) - betaz(i,j,k-1)) / (2*dx(3))
! d/dt gamma_ij = - 2 alpha K_ij
! + gamma_kj d_i beta^k
! + gamma_kj d_i beta^k
! + beta^k d_k gamma_ij
do a=1,3
do b=1,3
kk(a,b) = - gama_dot(a,b)
do c=1,3
kk(a,b) = kk(a,b) + gama(c,b) * dbeta(c,a) &
& + gama(a,c) * dbeta(c,b) &
& + beta(c) * dgama(a,b,c)
end do
kk(a,b) = kk(a,b) / (2*alfa)
end do
end do
kxx(i,j,k) = kk(1,1)
kxy(i,j,k) = kk(1,2)
kxz(i,j,k) = kk(1,3)
kyy(i,j,k) = kk(2,2)
kyz(i,j,k) = kk(2,3)
kzz(i,j,k) = kk(3,3)
end do
end do
end do
call CartSymGN (ierr, cctkGH, "ADMBase::curv")
if (ierr /= 0) call CCTK_WARN (0, "internal error")
ierr = Boundary_SelectGroupForBC (cctkGH, CCTK_ALL_FACES, bndwidth, &
int(options,ik), "ADMBase::curv", str_boundary)
if (ierr /= 0) call CCTK_WARN (0, "internal error")
! Convert back to conformal metric, if necessary
if (CCTK_EQUALS(metric_type, "static conformal")) then
call PhysToConfInPlace &
(int(cctk_lsh(1),ik), int(cctk_lsh(2),ik), int(cctk_lsh(3),ik), &
psi, gxx, gxy, gxz, gyy, gyz, gzz)
call PhysToConfInPlace &
(int(cctk_lsh(1),ik), int(cctk_lsh(2),ik), int(cctk_lsh(3),ik), &
psi, gxx_prev, gxy_prev, gxz_prev, gyy_prev, gyz_prev, gzz_prev)
#if 0
call PhysToConfInPlace &
(int(cctk_lsh(1),ik), int(cctk_lsh(2),ik), int(cctk_lsh(3),ik), &
psi, gxx_prev2, gxy_prev2, gxz_prev2, gyy_prev2, gyz_prev2, gzz_prev2)
#else
call PhysToConfInPlace &
(int(cctk_lsh(1),ik), int(cctk_lsh(2),ik), int(cctk_lsh(3),ik), &
psi, gxx_next, gxy_next, gxz_next, gyy_next, gyz_next, gzz_next)
#endif
end if
end subroutine CalcK
|
