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
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
|
/*@@
@file sor.F
@date Thu Mar 13 07:46:55 1997
@author Joan Masso + Paul Walker
@desc
The SOR solver
@enddesc
@@*/
#include "cctk.h"
#include "cctk_arguments.h"
#include "cctk_parameters.h"
/*@@
@routine sor
@date Thu Apr 24 13:29:52 1997
@author Joan Masso
@desc
This is a standalone sor solver which does all the MPI itself.
It is a pretty good example of doing pugh-based communications
in FORTRAN.
@enddesc
@@*/
subroutine sor_flat_core3d(_CCTK_FARGUMENTS,
$ Mlinear_lsh,Mlinear,
$ Nsource_lsh,Nsource,
$ var,var_idx,
$ abstol,reltol)
implicit none
_DECLARE_CCTK_FARGUMENTS
DECLARE_CCTK_PARAMETERS
INTEGER CCTK_Equals
INTEGER Mlinear_lsh(3)
CCTK_REAL Mlinear(Mlinear_lsh(1),Mlinear_lsh(2),Mlinear_lsh(3))
INTEGER Nsource_lsh(3)
CCTK_REAL Nsource(Nsource_lsh(1),Nsource_lsh(2),Nsource_lsh(3))
CCTK_REAL var(cctk_lsh(1),cctk_lsh(2),cctk_lsh(3))
INTEGER var_idx
CCTK_REAL abstol(3),reltol(3)
CCTK_REAL tol
INTEGER toltype
CCTK_REAL dx,dy,dz
c Temporaries
INTEGER sor_iteration
CCTK_REAL tmp
c Numbers...
CCTK_REAL two, four
c Total residual
CCTK_REAL resnorm, residual
c Stencil
CCTK_REAL a(-1:1,-1:1,-1:1)
c Loopers
INTEGER i,j,k
c Acceleration factor
CCTK_REAL omega, rjacobian
c conformal test
logical conformal
logical octant
c Loop bounds. Starts, Ends, and deltas (steps)
INTEGER is, js, ks, ie, je, ke, di, dj, dk, kstep
c Coeeficients for the solver: 19 point stencil...
CCTK_REAL ac,ac_orig,aw,ae,an,as,at,ab
CCTK_REAL ane,anw,ase,asw,ate,atw
CCTK_REAL abe,abw,atn,ats,abn,asb
CCTK_REAL finf
CCTK_INT npow
logical cheb, const, none, verb
integer Mlinear_storage,Nsource_storage
INTEGER sum_handle,ierr
c stencil size
INTEGER sw(3)
tol = AbsTol(1)
c Get the reduction handel for the sum operation
call CCTK_ReductionArrayHandle(sum_handle,"sum");
if (sum_handle.lt.0) then
call CCTK_WARN(1,"Cannot get reduction handle.")
endif
c Set boundary related variables
if (CCTK_EQUALS(sor_bound,"robin")) then
sw(1)=1
sw(2)=1
sw(3)=1
call Ell_GetRealKey(ierr, finf, "EllLinFlat::Bnd::Robin::inf")
call Ell_GetIntKey (ierr, npow, "EllLinFlat::Bnd::Robin::falloff")
end if
c We have no storage for M/N if they are of size one in each direction
if ((Mlinear_lsh(1).eq.1).and.(Mlinear_lsh(2).eq.1).and.(Mlinear_lsh(3).eq.1)) then
Mlinear_storage=0
else
Mlinear_storage=1
endif
if ((Nsource_lsh(1).eq.1).and.(Nsource_lsh(2).eq.1).and.(Nsource_lsh(3).eq.1)) then
Nsource_storage=0
else
Nsource_storage=1
endif
c Set up shorthand for the grid spacings
dx=cctk_delta_space(1)
dy=cctk_delta_space(2)
dz=cctk_delta_space(3)
verb = CCTK_Equals(elliptic_verbose,"yes").eq.1
octant = CCTK_Equals(domain,"octant").eq.1
c cheb = contains("sor_accel","cheb").ne.0
c const = contains("sor_accel","const").ne.0
c none = contains("sor_accel","none").ne.0
verb = .true.
cheb = .false.
none = .false.
const = .false.
if (verb .and. cheb)
$ print *,"Chebyshev Acceleration with radius of 1"
if (verb .and. const)
$ print *,"SOR with omega = 1.8"
if (verb .and. none)
$ print *,"Un-accelearted relaxation (omega = 1)"
two = 2.0D0
four = 4.0D0
resnorm = 0
ae = 1.0d0/dx**2.
aw = 1.0d0/dx**2.
an = 1.0d0/dy**2.
as = 1.0d0/dy**2.
at = 1.0d0/dz**2.
ab = 1.0d0/dz**2.
ac_orig = -2.0d0/dx**2. - 2.0d0/dy**2. - 2.0d0/dz**2.
do sor_iteration=1,maxit
c We do not know the spectral radius of the Jacobi iteration,
c so we will take it to be one which empirically seems to be pretty good
rjacobian = 1.0D0
c Set up the omega factor
omega = 1.0D0
if (cheb) then
do i=2,sor_iteration
omega = 1.0D0/(1.0D0 - .25D0*rjacobian**2*omega)
enddo
endif
if (const) then
omega = 1.8
endif
c Total norm of the residual zero
resnorm = 0.
c Start loop with Red Black
ks = mod(sor_iteration,2)+2
if (cctk_lsh(3) .eq. 3) then
ks = 2
endif
kstep = 2
do k=ks,cctk_lsh(3)-1,kstep
do j=2,cctk_lsh(2)-1
do i=2,cctk_lsh(1)-1
ac = ac_orig
if (Mlinear_storage.eq.1) then
ac = ac - Mlinear(i,j,k)
endif
residual = ac*var(i,j,k)
& + ae*var(i+1,j,k) + aw*var(i-1,j,k)
& + an*var(i,j+1,k) + as*var(i,j-1,k)
& + at*var(i,j,k+1) + ab*var(i,j,k-1)
if (Nsource_storage.eq.1) then
residual = residual - Nsource(i,j,k)
endif
c Accumulate to the total Norm of the residual
resnorm = resnorm + abs(residual)
c Update
var(i,j,k) = var(i,j,k) - omega*residual/ac
end do
end do
end do
c Reduce the norm
call CCTK_ReduceLocalScalar(ierr, cctkGH, -1, sum_handle,
$ resnorm, residual, CCTK_VARIABLE_REAL)
if (ierr.ne.0) then
call CCTK_WARN(1,"Reduction of norm failed!");
endif
residual = residual / (cctk_gsh(1)*cctk_gsh(2)*cctk_gsh(3))
c write (*,*) "Iteration/Norm",sor_iteration,residual
c Synchronize the variables
call CCTK_SyncGroupWithVarI(cctkGH, var_idx)
if (residual .lt. tol) then
goto 123
endif
c Apply boundary conditions
c call Ell_GetStringKey(nchar, mybound,"EllLinFlat::Bnd")
if (CCTK_EQUALS(sor_bound,"robin")) then
call RobinBCVarI(ierr, cctkGH, finf, npow, sw, var_idx);
if (ierr.ne.0) then
call CCTK_WARN(1,"Could not apply Robin BC !")
endif
endif
c Apply octant Symmetries
call CartSymBCVarI(ierr, cctkGH, var_idx)
enddo
write (*,*) "!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"
write (*,*) "!! WARNING: SOR SOLVER DID NOT CONVERGE !!"
write (*,*) "!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"
123 continue
if (verb) write (*,*) "Iteration/Norm",sor_iteration,residual
return
end
|
