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
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
|
subroutine rbicgst3d(cc,ce,cw,cn,cs,ct,cb,u,rhs,
& eps,rmax,ier,im,jm,km)
c
c This routine was lifted from stab.f. Minor modifications have
c been made.
c
implicit none
c
integer,intent(in) :: im,jm,km
real*8,intent(inout) :: cc(im,jm,km),cn(im,jm,km),cs(im,jm,km),
$ ce(im,jm,km),cw(im,jm,km),ct(im,jm,km),cb(im,jm,km)
real*8,intent(out) :: eps
real*8,intent(out) :: rmax
real*8,intent(inout) :: u(im,jm,km),rhs(im,jm,km)
c Local variable
integer ncyc
integer iscale,i,j,k,ier
c
c******************************************************************************
c
ncyc = (im-2)*(jm-2)*(km-2)
ier=0
*
* Determine whether we can diagonally scale the problem to speed
* convergence. Can only be done if there are no zeros on the main
* diagonal (ie. central difference coefficient).
*
iscale=1
do k = 2,km-1
do j = 2,jm-1
do i = 2,im-1
if (cc(i,j,k).eq.0.) iscale = 0
enddo
enddo
enddo
*
* Do the diagonal scaling if we can.
*
if (iscale.eq.1) then
do k = 2,km-1
do j = 2,jm-1
do i = 2,im-1
rhs(i,j,k)=rhs(i,j,k)/cc(i,j,k)
cb(i,j,k)=cb(i,j,k)/cc(i,j,k)
ct(i,j,k)=ct(i,j,k)/cc(i,j,k)
cw(i,j,k)=cw(i,j,k)/cc(i,j,k)
ce(i,j,k)=ce(i,j,k)/cc(i,j,k)
cs(i,j,k)=cs(i,j,k)/cc(i,j,k)
cn(i,j,k)=cn(i,j,k)/cc(i,j,k)
cc(i,j,k)=1.
enddo
enddo
enddo
endif
*
* Now call the bicgstab routine
*
call rbicgstab (cc,cn,cs,ce,cw,ct,cb,u,rhs,eps,ncyc,rmax,ier,
& im,jm,km)
if (rmax.gt.eps) then
ier = -1
print*,'Did not converge'
print*,' maximum residual = ',rmax
print*,' tolerance = ',eps
endif
return
end
c
c******************************************************************
c
subroutine rbicgstab (cc,cn,cs,ce,cw,ct,cb,x,r,tol,ncyc,rnorm,
$ ier,im,jm,km)
c
c This routine was lifted from stab.f. Minor modifications have
c been made.
c
implicit none
c
integer,intent(in) :: im,jm,km
integer,intent(in) :: ncyc
real*8,intent(in) :: cc(im*jm*km),cn(im*jm*km)
real*8,intent(in) :: cs(im*jm*km),ce(im*jm*km)
real*8,intent(in) :: cw(im*jm*km),ct(im*jm*km)
real*8,intent(in) :: cb(im*jm*km)
real*8,intent(in) :: tol
real*8,intent(out) :: rnorm
integer,intent(out) :: ier
real*8,intent(inout) :: x(im*jm*km),r(im*jm*km)
c Local variables
integer :: i,j,k,kk
real*8, allocatable :: p(:),Ap(:),w(:),As(:)
real*8 :: omega, chi,chi1,chi2, delta, deltap, pp
*
***********************************************************************
*
allocate(p(im*jm*km),Ap(im*jm*km),w(im*jm*km),As(im*jm*km))
do i = 1,im*jm*km
p(i) = 0.
Ap(i) = 0.
w(i) = 0.
As(i) = 0.
enddo
kk = 0
10 call rusermv(cc,cn,cs,ce,cw,ct,cb,x,Ap,im,jm,km)
do i = 1,im*jm*km
r(i) = r(i)-Ap(i)
p(i) = r(i)
enddo
c delta = sum(r)
delta = 0.
do i = 1,im*jm*km
delta = delta+r(i)
enddo
if (delta.eq.0.) then
ier=-1
return
endif
call rusermv(cc,cn,cs,ce,cw,ct,cb,p,Ap,im,jm,km)
c phi = sum(Ap)
pp = 0.
do i = 1,im*jm*km
pp = pp+Ap(i)
enddo
pp = pp/delta
if (pp.eq.0.) then
ier=-1
return
endif
c rnorm = sum(r**2)
rnorm = 0.
do i = 1,im*jm*km
rnorm = rnorm + r(i)**2
enddo
rnorm=sqrt(rnorm)
c Test if initial guess is great (residual less than tolerance)
if (rnorm .lt. tol) return
1 continue
kk = kk + 1
omega = 1./pp
do i = 1,im*jm*km
w(i) = r(i) - omega*Ap(i)
enddo
call rusermv(cc,cn,cs,ce,cw,ct,cb,w,As,im,jm,km)
c chi1 = sum(As*w)
chi1 = 0.
do i = 1,im*jm*km
chi1 = chi1+As(i)*w(i)
enddo
c chi2 = sum(As**2)
chi2 = 0.
do i = 1,im*jm*km
chi2 = chi2+As(i)**2
enddo
chi = chi1/chi2
do i = 1,im*jm*km
r(i) = w(i) - chi*As(i)
x(i) = x(i) + omega*p(i) + chi*w(i)
enddo
deltap = delta
c delta = sum(r)
delta = 0.
do i = 1,im*jm*km
delta = delta+r(i)
enddo
if (delta.eq.0.) then
goto 10
endif
do i = 1,im*jm*km
p(i) = r(i) + (p(i)-chi*Ap(i))*omega*
& delta/(deltap*chi)
enddo
call rusermv(cc,cn,cs,ce,cw,ct,cb,p,Ap,im,jm,km)
c phi = sum(Ap)
pp = 0.
do i = 1,im*jm*km
pp = pp+Ap(i)
enddo
pp=pp/delta
if (pp.eq.0.) then
goto 10
endif
if (kk.gt.ncyc) then
print*,' BI-CGStab solver reached maximum nuber of iterations.'
ier=-1
return
endif
c rnorm = sum(r**2)
rnorm = 0.
do i = 1,im*jm*km
rnorm = rnorm+r(i)**2
enddo
rnorm=sqrt(rnorm)
if (rnorm .gt. tol) goto 1
c
deallocate(p,Ap,w,As)
c
return
end
c
c******************************************************************
c
subroutine rusermv(cc,cn,cs,ce,cw,ct,cb,x,y,im,jm,km)
c
c This routine was lifted from stab.f. Minor modifications have
c been made.
c
c Be careful that the cs are zero on their outer boundary!!
c
implicit none
c
integer,intent(in) :: im,jm,km
real*8,intent(in) :: cc(im*jm*km),cn(im*jm*km)
real*8,intent(in) :: cs(im*jm*km),ce(im*jm*km)
real*8,intent(in) :: cw(im*jm*km),ct(im*jm*km)
real*8,intent(in) :: cb(im*jm*km)
real*8,intent(inout) :: x(im*jm*km), y(im*jm*km)
c Local variables
integer :: i, j, k
*
***********************************************************************
*
*
do i = im*jm+im+1,im*(jm*km-jm-1)
y(i) = cw(i)*x(i-1)
& +cc(i)*x(i)
& +ce(i)*x(i+1)
& +cn(i)*x(i+im)
& +cs(i)*x(i-im)
& +ct(i)*x(i+im*jm)
& +cb(i)*x(i-im*jm)
enddo
c
return
end
|