/[escript]/trunk/paso/src/Solver_AMG.c
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Contents of /trunk/paso/src/Solver_AMG.c

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Revision 2107 - (show annotations)
Fri Nov 28 04:39:07 2008 UTC (10 years, 10 months ago) by artak
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Current version of AMG uses ILU for relaxation, however it is not stable when schur matrix becames more denser. For example it is not stable for -e paramenter is more 400 in 2D for convection problem 
1
2 /*******************************************************
3 *
4 * Copyright (c) 2003-2008 by University of Queensland
5 * Earth Systems Science Computational Center (ESSCC)
6 * http://www.uq.edu.au/esscc
7 *
8 * Primary Business: Queensland, Australia
9 * Licensed under the Open Software License version 3.0
10 * http://www.opensource.org/licenses/osl-3.0.php
11 *
12 *******************************************************/
13
14
15 /**************************************************************/
16
17 /* Paso: AMG preconditioner with reordering */
18
19 /**************************************************************/
20
21 /* Author: artak@access.edu.au */
22
23 /**************************************************************/
24
25 #include "Paso.h"
26 #include "Solver.h"
27 #include "PasoUtil.h"
28 #include "UMFPACK.h"
29 #include "Pattern_coupling.h"
30
31 /**************************************************************/
32
33 /* free all memory used by AMG */
34
35 void Paso_Solver_AMG_free(Paso_Solver_AMG * in) {
36 if (in!=NULL) {
37 Paso_Solver_AMG_free(in->AMG_of_Schur);
38 Paso_Solver_ILU_free(in->GS);
39 MEMFREE(in->inv_A_FF);
40 MEMFREE(in->A_FF_pivot);
41 Paso_SparseMatrix_free(in->A_FC);
42 Paso_SparseMatrix_free(in->A_CF);
43 MEMFREE(in->rows_in_F);
44 MEMFREE(in->rows_in_C);
45 MEMFREE(in->mask_F);
46 MEMFREE(in->mask_C);
47 MEMFREE(in->x_F);
48 MEMFREE(in->b_F);
49 MEMFREE(in->x_C);
50 MEMFREE(in->b_C);
51 MEMFREE(in);
52 }
53 }
54
55 /**************************************************************/
56
57 /* constructs the block-block factorization of
58
59 [ A_FF A_FC ]
60 A_p=
61 [ A_CF A_FF ]
62
63 to
64
65 [ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FF ]
66 [ A_CF*invA_FF I ] [ 0 S ] [ 0 I ]
67
68
69 where S=A_FF-ACF*invA_FF*A_FC within the shape of S
70
71 then AMG is applied to S again until S becomes empty
72
73 */
74 Paso_Solver_AMG* Paso_Solver_getAMG(Paso_SparseMatrix *A_p,bool_t verbose,dim_t level) {
75 Paso_Solver_AMG* out=NULL;
76 dim_t n=A_p->numRows;
77 dim_t n_block=A_p->row_block_size;
78 index_t* mis_marker=NULL;
79 index_t* counter=NULL;
80 index_t iPtr,*index, *where_p, iPtr_s;
81 dim_t i,k,j;
82 Paso_SparseMatrix * schur=NULL;
83 Paso_SparseMatrix * schur_withFillIn=NULL;
84 double time0=0,time1=0,time2=0,S=0;
85 /*Paso_Pattern* test;*/
86
87 /* identify independend set of rows/columns */
88 mis_marker=TMPMEMALLOC(n,index_t);
89 counter=TMPMEMALLOC(n,index_t);
90 out=MEMALLOC(1,Paso_Solver_AMG);
91 out->AMG_of_Schur=NULL;
92 out->inv_A_FF=NULL;
93 out->A_FF_pivot=NULL;
94 out->A_FC=NULL;
95 out->A_CF=NULL;
96 out->rows_in_F=NULL;
97 out->rows_in_C=NULL;
98 out->mask_F=NULL;
99 out->mask_C=NULL;
100 out->x_F=NULL;
101 out->b_F=NULL;
102 out->x_C=NULL;
103 out->b_C=NULL;
104 out->GS=NULL;
105 out->A=Paso_SparseMatrix_getReference(A_p);
106 out->GS=Paso_Solver_getILU(A_p,verbose);
107 /*out->GS=Paso_Solver_getJacobi(A_p);*/
108 /*out->GS->sweeps=2;*/
109 out->level=level;
110
111 if ( !(Paso_checkPtr(mis_marker) || Paso_checkPtr(out) || Paso_checkPtr(counter) ) ) {
112 /* identify independend set of rows/columns */
113 #pragma omp parallel for private(i) schedule(static)
114 for (i=0;i<n;++i) mis_marker[i]=-1;
115 /*Paso_Pattern_RS(A_p,mis_marker,0.25);*/
116 /*Paso_Pattern_Aggregiation(A_p,mis_marker,0.5);*/
117 Paso_Pattern_coup(A_p,mis_marker,0.05);
118 if (Paso_noError()) {
119 #pragma omp parallel for private(i) schedule(static)
120 for (i = 0; i < n; ++i) counter[i]=mis_marker[i];
121 out->n=n;
122 out->n_block=n_block;
123 out->n_F=Paso_Util_cumsum(n,counter);
124 out->mask_F=MEMALLOC(n,index_t);
125 out->rows_in_F=MEMALLOC(out->n_F,index_t);
126 out->inv_A_FF=MEMALLOC(n_block*n_block*out->n_F,double);
127 out->A_FF_pivot=NULL; /* later use for block size>3 */
128 if (! (Paso_checkPtr(out->mask_F) || Paso_checkPtr(out->inv_A_FF) || Paso_checkPtr(out->rows_in_F) ) ) {
129 /* creates an index for F from mask */
130 #pragma omp parallel for private(i) schedule(static)
131 for (i = 0; i < out->n_F; ++i) out->rows_in_F[i]=-1;
132 #pragma omp parallel for private(i) schedule(static)
133 for (i = 0; i < n; ++i) {
134 if (mis_marker[i]) {
135 out->rows_in_F[counter[i]]=i;
136 out->mask_F[i]=counter[i];
137 } else {
138 out->mask_F[i]=-1;
139 }
140 }
141
142 /* Compute row-sum for getting rs(A_FF)^-1*/
143 #pragma omp parallel for private(i,iPtr,j) schedule(static)
144 for (i = 0; i < out->n_F; ++i) {
145 S=0;
146 for (iPtr=A_p->pattern->ptr[out->rows_in_F[i]];iPtr<A_p->pattern->ptr[out->rows_in_F[i] + 1]; ++iPtr) {
147 j=A_p->pattern->index[iPtr];
148 if (mis_marker[j])
149 S+=A_p->val[iPtr];
150 }
151 if (ABS(S)>0)
152 out->inv_A_FF[i]=1./S;
153 }
154
155 if( Paso_noError()) {
156 /* if there are no nodes in the coarse level there is no more work to do */
157 out->n_C=n-out->n_F;
158 /*if (level<5) {*/
159 if (out->n_F>50) {
160 out->rows_in_C=MEMALLOC(out->n_C,index_t);
161 out->mask_C=MEMALLOC(n,index_t);
162 if (! (Paso_checkPtr(out->mask_C) || Paso_checkPtr(out->rows_in_C) ) ) {
163 /* creates an index for C from mask */
164 #pragma omp parallel for private(i) schedule(static)
165 for (i = 0; i < n; ++i) counter[i]=! mis_marker[i];
166 Paso_Util_cumsum(n,counter);
167 #pragma omp parallel for private(i) schedule(static)
168 for (i = 0; i < out->n_C; ++i) out->rows_in_C[i]=-1;
169 #pragma omp parallel for private(i) schedule(static)
170 for (i = 0; i < n; ++i) {
171 if (! mis_marker[i]) {
172 out->rows_in_C[counter[i]]=i;
173 out->mask_C[i]=counter[i];
174 } else {
175 out->mask_C[i]=-1;
176 }
177 }
178 /* get A_CF block: */
179 out->A_CF=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_F,out->rows_in_C,out->mask_F);
180 if (Paso_noError()) {
181 /* get A_FC block: */
182 out->A_FC=Paso_SparseMatrix_getSubmatrix(A_p,out->n_F,out->n_C,out->rows_in_F,out->mask_C);
183 /* get A_CC block: */
184 if (Paso_noError()) {
185 schur=Paso_SparseMatrix_getSubmatrix(A_p,out->n_C,out->n_C,out->rows_in_C,out->mask_C);
186 /*find the pattern of the schur complement with fill in*/
187
188 schur_withFillIn=Paso_SparseMatrix_alloc(A_p->type,Paso_Pattern_binop(PATTERN_FORMAT_DEFAULT, schur->pattern, Paso_Pattern_multiply(PATTERN_FORMAT_DEFAULT,out->A_CF->pattern,out->A_FC->pattern)),1,1);
189
190 fprintf(stderr,"Sparsity of Schure: %dx%d LEN %d Percentage %f\n",schur_withFillIn->pattern->numOutput,schur_withFillIn->pattern->numInput,schur_withFillIn->len,schur_withFillIn->len/(1.*schur_withFillIn->pattern->numOutput*schur_withFillIn->pattern->numInput));
191
192 /* copy values over*/
193 #pragma omp parallel for private(i,iPtr,j,iPtr_s,index,where_p) schedule(static)
194 for (i = 0; i < schur_withFillIn->numRows; ++i) {
195 for (iPtr=schur_withFillIn->pattern->ptr[i];iPtr<schur_withFillIn->pattern->ptr[i + 1]; ++iPtr) {
196 j=schur_withFillIn->pattern->index[iPtr];
197 iPtr_s=schur->pattern->ptr[i];
198 schur_withFillIn->val[iPtr]=0.;
199 index=&(schur->pattern->index[iPtr_s]);
200 where_p=(index_t*)bsearch(&j,
201 index,
202 schur->pattern->ptr[i + 1]-schur->pattern->ptr[i],
203 sizeof(index_t),
204 Paso_comparIndex);
205 if (where_p!=NULL) {
206 schur_withFillIn->val[iPtr]=schur->val[iPtr_s+(index_t)(where_p-index)];
207 }
208 }
209 }
210
211 if (Paso_noError()) {
212 Paso_Solver_updateIncompleteSchurComplement(schur_withFillIn,out->A_CF,out->inv_A_FF,out->A_FF_pivot,out->A_FC);
213 out->AMG_of_Schur=Paso_Solver_getAMG(schur_withFillIn,verbose,level+1);
214 Paso_SparseMatrix_free(schur);
215 }
216 /* allocate work arrays for AMG application */
217 if (Paso_noError()) {
218 out->x_F=MEMALLOC(n_block*out->n_F,double);
219 out->b_F=MEMALLOC(n_block*out->n_F,double);
220 out->x_C=MEMALLOC(n_block*out->n_C,double);
221 out->b_C=MEMALLOC(n_block*out->n_C,double);
222
223 if (! (Paso_checkPtr(out->x_F) || Paso_checkPtr(out->b_F) || Paso_checkPtr(out->x_C) || Paso_checkPtr(out->b_C) ) ) {
224 #pragma omp parallel for private(i,k) schedule(static)
225 for (i = 0; i < out->n_F; ++i) {
226 for (k=0; k<n_block;++k) {
227 out->x_F[i*n_block+k]=0.;
228 out->b_F[i*n_block+k]=0.;
229 }
230 }
231 #pragma omp parallel for private(i,k) schedule(static)
232 for (i = 0; i < out->n_C; ++i) {
233 for (k=0; k<n_block;++k) {
234 out->x_C[i*n_block+k]=0.;
235 out->b_C[i*n_block+k]=0.;
236 }
237 }
238 }
239 }
240 }
241 }
242 }
243 }
244 }
245 }
246 }
247 }
248 TMPMEMFREE(mis_marker);
249 TMPMEMFREE(counter);
250 if (Paso_noError()) {
251 if (verbose) {
252 printf("AMG: %d unknowns eliminated. %d left.\n",out->n_F,n-out->n_F);
253 /*if (level<5) {*/
254 if (out->n_F<50) {
255 printf("timing: AMG: MIS/reordering/elemination : %e/%e/%e\n",time2,time0,time1);
256 } else {
257 printf("timing: AMG: MIS: %e\n",time2);
258 }
259 }
260 return out;
261 } else {
262 Paso_Solver_AMG_free(out);
263 return NULL;
264 }
265 }
266
267 /**************************************************************/
268
269 /* apply AMG precondition b-> x
270
271 in fact it solves
272
273 [ I 0 ] [ A_FF 0 ] [ I invA_FF*A_FF ] [ x_F ] = [b_F]
274 [ A_CF*invA_FF I ] [ 0 S ] [ 0 I ] [ x_C ] = [b_C]
275
276 in the form
277
278 b->[b_F,b_C]
279 x_F=invA_FF*b_F
280 b_C=b_C-A_CF*x_F
281 x_C=AMG(b_C)
282 b_F=b_F-A_FC*x_C
283 x_F=invA_FF*b_F
284 x<-[x_F,x_C]
285
286 should be called within a parallel region
287 barrier synconization should be performed to make sure that the input vector available
288
289 */
290
291 void Paso_Solver_solveAMG(Paso_Solver_AMG * amg, double * x, double * b) {
292 dim_t i;
293 double *r=MEMALLOC(amg->n,double);
294 /*Paso_Solver_GS* GS=NULL;*/
295 double *x0=MEMALLOC(amg->n,double);
296 double time0=0;
297
298 /*if (amg->level==5) {*/
299 if (amg->n_F<=50) {
300 time0=Paso_timer();
301
302 /*Paso_Solver_solveJacobi(amg->GS,x,b);*/
303
304 /* #pragma omp parallel for private(i) schedule(static)
305 for (i=0;i<amg->n;++i) r[i]=b[i];
306 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
307 Paso_Solver_solveGS(amg->GS,x0,r);
308 #pragma omp parallel for private(i) schedule(static)
309 for (i=0;i<amg->n;++i) {
310 x[i]+=x0[i];
311 }
312 */
313 Paso_UMFPACK1(amg->A,x,b,0);
314
315 time0=Paso_timer()-time0;
316 /*fprintf(stderr,"timing: DIRECT SOLVER: %e/\n",time0);*/
317 } else {
318
319 /* presmoothing */
320 Paso_Solver_solveILU(amg->GS,x,b);
321 /*
322 #pragma omp parallel for private(i) schedule(static)
323 for (i=0;i<amg->n;++i) r[i]=b[i];
324
325 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
326 Paso_Solver_solveGS(amg->GS,x0,r);
327
328 #pragma omp parallel for private(i) schedule(static)
329 for (i=0;i<amg->n;++i) {
330 x[i]+=x0[i];
331 }
332 */
333 /* end of presmoothing */
334
335 #pragma omp parallel for private(i) schedule(static)
336 for (i=0;i<amg->n;++i) r[i]=b[i];
337
338 /*r=b-Ax*/
339 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
340
341 /* b->[b_F,b_C] */
342 #pragma omp parallel for private(i) schedule(static)
343 for (i=0;i<amg->n_F;++i) amg->b_F[i]=r[amg->rows_in_F[i]];
344
345 #pragma omp parallel for private(i) schedule(static)
346 for (i=0;i<amg->n_C;++i) amg->b_C[i]=r[amg->rows_in_C[i]];
347
348 /* x_F=invA_FF*b_F */
349 Paso_Solver_applyBlockDiagonalMatrix(1,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
350
351 /* b_C=b_C-A_CF*x_F */
352 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_CF,amg->x_F,1.,amg->b_C);
353
354 /* x_C=AMG(b_C) */
355 Paso_Solver_solveAMG(amg->AMG_of_Schur,amg->x_C,amg->b_C);
356
357 /* b_F=b_F-A_FC*x_C */
358 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A_FC,amg->x_C,1.,amg->b_F);
359 /* x_F=invA_FF*b_F */
360 Paso_Solver_applyBlockDiagonalMatrix(1,amg->n_F,amg->inv_A_FF,amg->A_FF_pivot,amg->x_F,amg->b_F);
361 /* x<-[x_F,x_C] */
362
363 #pragma omp parallel for private(i) schedule(static)
364 for (i=0;i<amg->n;++i) {
365 if (amg->mask_C[i]>-1) {
366 x[i]=amg->x_C[amg->mask_C[i]];
367 } else {
368 x[i]=amg->x_F[amg->mask_F[i]];
369 }
370 }
371
372
373 /*postsmoothing*/
374
375 #pragma omp parallel for private(i) schedule(static)
376 for (i=0;i<amg->n;++i) r[i]=b[i];
377
378 /*r=b-Ax*/
379 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
380 Paso_Solver_solveILU(amg->GS,x0,r);
381
382 #pragma omp parallel for private(i) schedule(static)
383 for (i=0;i<amg->n;++i) x[i]+=x0[i];
384
385
386 /*#pragma omp parallel for private(i) schedule(static)
387 for (i=0;i<amg->n;++i) r[i]=b[i];
388
389 Paso_SparseMatrix_MatrixVector_CSR_OFFSET0(-1.,amg->A,x,1.,r);
390 Paso_Solver_solveGS(amg->GS,x0,r);
391
392 #pragma omp parallel for private(i) schedule(static)
393 for (i=0;i<amg->n;++i) {
394 x[i]+=x0[i];
395 }
396 */
397 /*end of postsmoothing*/
398
399
400 }
401
402 MEMFREE(r);
403 MEMFREE(x0);
404 return;
405 }
406
407 /*
408 * $Log$
409 *
410 */

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