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

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Revision 3014 - (show annotations)
Wed Apr 28 04:05:21 2010 UTC (9 years, 5 months ago) by gross
File MIME type: text/plain
File size: 14672 byte(s)
a more stable handling of divergence in the CN or BE
1
2 /*******************************************************
3 *
4 * Copyright (c) 2003-2010 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: Transport solver with flux corretion (L is row sum zero)
18 *
19 * - Mv_t=Lv v(0)=u
20 *
21 * to return v(dt)
22 *
23 */
24 /**************************************************************/
25
26 /* Author: l.gross@uq.edu.au */
27
28 /**************************************************************/
29
30 #include "FCTSolver.h"
31 #include "Solver.h"
32 #include "PasoUtil.h"
33
34 Paso_Function* Paso_FCTSolver_Function_alloc(Paso_TransportProblem *fctp, Paso_Options* options)
35 {
36 const dim_t n=Paso_SystemMatrix_getTotalNumRows(fctp->transport_matrix);
37 const dim_t blockSize=Paso_TransportProblem_getBlockSize(fctp);
38 Paso_Function * out=NULL;
39 Paso_FCTSolver *more=NULL;
40 out=MEMALLOC(1,Paso_Function);
41 if (! Paso_checkPtr(out)) {
42 out->kind=FCT;
43 out->mpi_info=Paso_MPIInfo_getReference(fctp->mpi_info);
44 out->n=n;
45 out->b=TMPMEMALLOC(n,double); /*b_m */
46 Paso_checkPtr(out->b);
47 out->tmp=TMPMEMALLOC(n,double); /* z_m */
48 Paso_checkPtr(out->tmp);
49
50 more=MEMALLOC(1,Paso_FCTSolver);
51 out->more=(void*) more;
52 if (! Paso_checkPtr(more)) {
53 more->transportproblem=Paso_TransportProblem_getReference(fctp);
54 more->uTilde_n=TMPMEMALLOC(n,double);
55 Paso_checkPtr(more->uTilde_n);
56 more->QN_n=TMPMEMALLOC(n,double);
57 Paso_checkPtr(more->QN_n);
58 more->QP_n=TMPMEMALLOC(n,double);
59 Paso_checkPtr(more->QP_n);
60 more->RN_m=TMPMEMALLOC(n,double);
61 Paso_checkPtr(more->RN_m);
62 more->RP_m=TMPMEMALLOC(n,double);
63 Paso_checkPtr(more->RP_m);
64 more->QN_n_coupler=Paso_Coupler_alloc(Paso_TransportProblem_borrowConnector(fctp),blockSize);
65 more->QP_n_coupler=Paso_Coupler_alloc(Paso_TransportProblem_borrowConnector(fctp),blockSize);
66 more->RN_m_coupler=Paso_Coupler_alloc(Paso_TransportProblem_borrowConnector(fctp),blockSize);
67 more->RP_m_coupler=Paso_Coupler_alloc(Paso_TransportProblem_borrowConnector(fctp),blockSize);
68 more->uTilde_n_coupler=Paso_Coupler_alloc(Paso_TransportProblem_borrowConnector(fctp),blockSize);
69 more->u_m_coupler=Paso_Coupler_alloc(Paso_TransportProblem_borrowConnector(fctp),blockSize);
70 more->flux_matrix_m=Paso_SystemMatrix_alloc(fctp->transport_matrix->type,
71 fctp->transport_matrix->pattern,
72 fctp->transport_matrix->row_block_size,
73 fctp->transport_matrix->col_block_size, TRUE);
74
75 }
76 }
77 if (Paso_noError()) {
78 return out;
79 } else {
80 Paso_FCTSolver_Function_free(out);
81 return NULL;
82 }
83 }
84
85 void Paso_FCTSolver_Function_free(Paso_Function * in)
86 {
87 Paso_FCTSolver *more=NULL;
88 if (in!=NULL) {
89 Paso_MPIInfo_free(in->mpi_info);
90 MEMFREE(in->tmp);
91 MEMFREE(in->b);
92 more=(Paso_FCTSolver *) (in->more);
93 if (NULL !=more) {
94 Paso_TransportProblem_free(more->transportproblem);
95 Paso_SystemMatrix_free(more->flux_matrix_m);
96 TMPMEMFREE(more->uTilde_n);
97 TMPMEMFREE(more->QN_n);
98 TMPMEMFREE(more->QP_n);
99 TMPMEMFREE(more->RN_m);
100 TMPMEMFREE(more->RP_m);
101 Paso_Coupler_free(more->QN_n_coupler);
102 Paso_Coupler_free(more->QP_n_coupler);
103 Paso_Coupler_free(more->RN_m_coupler);
104 Paso_Coupler_free(more->RP_m_coupler);
105 Paso_Coupler_free(more->uTilde_n_coupler);
106 Paso_Coupler_free(more->u_m_coupler);
107 }
108 MEMFREE(in);
109 }
110 }
111 double Paso_FCTSolver_getSafeTimeStepSize(Paso_TransportProblem* fctp)
112 {
113 dim_t i, n;
114 double dt_max=LARGE_POSITIVE_FLOAT, dt_max_loc;
115 register double l_ii,m;
116 n=Paso_SystemMatrix_getTotalNumRows(fctp->transport_matrix);
117
118
119 /* set low order transport operator */
120 Paso_FCTSolver_setLowOrderOperator(fctp);
121
122 if (Paso_noError()) {
123 /*
124 * calculate time step size:
125 */
126 dt_max=LARGE_POSITIVE_FLOAT;
127 #pragma omp parallel private(dt_max_loc)
128 {
129 dt_max_loc=LARGE_POSITIVE_FLOAT;
130 #pragma omp for schedule(static) private(i,l_ii,m)
131 for (i=0;i<n;++i) {
132 l_ii=fctp->main_diagonal_low_order_transport_matrix[i];
133 m=fctp->lumped_mass_matrix[i];
134 if ( (l_ii<0 && m>0.) || (l_ii>0 && m<0) ) {
135 dt_max_loc=MIN(dt_max_loc,-m/l_ii);
136 }
137 }
138 #pragma omp critical
139 {
140 dt_max=MIN(dt_max,dt_max_loc);
141 }
142 }
143 #ifdef PASO_MPI
144 dt_max_loc = dt_max;
145 MPI_Allreduce(&dt_max_loc, &dt_max, 1, MPI_DOUBLE, MPI_MIN, fctp->mpi_info->comm);
146 #endif
147 if (dt_max<LARGE_POSITIVE_FLOAT) dt_max*=fctp->dt_factor;
148 }
149 return dt_max;
150 }
151 /*
152 * evaluates F as
153 * (m_i*omega - l_ij)*(F_j/omega)
154 * =(m u^n[i] + dt*(1-theta) sum_{j <> i} l_{ij}*(u^n[j]-u^n[i]))-(m_i*u[i] - dt*theta*sum_{j<>i} l_{ij} (u[j]-u[i]) )- antidiffusion
155 *
156 */
157 err_t Paso_FCTSolver_Function_call(Paso_Function * F,double* value, const double* arg, Paso_Performance *pp)
158 {
159 Paso_Options options;
160 Paso_FCTSolver *more=(Paso_FCTSolver *) (F->more);
161 Paso_Options_setDefaults(&options);
162 options.verbose=TRUE;
163
164 /* set z_m in tmp */
165 Paso_FCTSolver_setUpRightHandSide(more->transportproblem,more->dt,arg,more->u_m_coupler,F->tmp,more->flux_matrix_m,
166 more->uTilde_n_coupler,F->b,
167 more->QN_n_coupler,more->QP_n_coupler,more->RN_m,
168 more->RN_m_coupler,more->RP_m,more->RP_m_coupler,pp);
169 /* apply preconditoner do get du = */
170 /* Paso_Solver(more->transportproblem->iteration_matrix,value,F->tmp,&options,pp); */
171
172
173 Paso_Solver_solvePreconditioner(more->transportproblem->iteration_matrix,value,F->tmp);
174 return NO_ERROR;
175 }
176
177 err_t Paso_FCTSolver_solve(Paso_Function* F, double* u, double dt, Paso_Options* options, Paso_Performance *pp)
178 {
179 const dim_t num_critical_rates_max=3; /* number of rates >=critical_rate accepted before divergence is triggered */
180 const double critical_rate=0.6; /* expected value of convergence rate */
181
182 double norm_u_tilde, ATOL, norm_u, norm_du=LARGE_POSITIVE_FLOAT, norm_du_old, *du=NULL, rate;
183 err_t errorCode=SOLVER_NO_ERROR;
184 Paso_FCTSolver *more=(Paso_FCTSolver *) (F->more);
185 const double omega=1./(dt*Paso_Transport_getTheta(more->transportproblem));
186 Paso_TransportProblem* fctp=more->transportproblem;
187 const dim_t n=Paso_SystemMatrix_getTotalNumRows(fctp->transport_matrix);
188 const double atol=options->absolute_tolerance;
189 const double rtol=options->tolerance;
190 const dim_t max_m=options->iter_max;
191 dim_t m=0, num_critical_rates=0 ;
192 bool_t converged=FALSE, max_m_reached=FALSE,diverged=FALSE;
193
194 /* tolerance? */
195 more->dt=dt;
196 Paso_FCTSolver_setUp(fctp,dt,u, F->b,more->uTilde_n,more->uTilde_n_coupler,more->QN_n,more->QN_n_coupler,more->QP_n,more->QP_n_coupler,
197 options,pp);
198
199
200 norm_u_tilde=Paso_lsup(n,more->uTilde_n,F->mpi_info);
201 ATOL= rtol * norm_u_tilde + atol ;
202 if (options->verbose) printf("Paso_FCTSolver_solve: iteration starts u_tilda lsup = %e (abs. tol = %e)\n",norm_u_tilde,ATOL);
203 if (more->transportproblem->useBackwardEuler && FALSE ) {
204 options->absolute_tolerance = ATOL/omega;
205 options->tolerance=0;
206 errorCode=Paso_Solver_NewtonGMRES(F,u,options,pp);
207 options->absolute_tolerance=atol;
208 options->tolerance=rtol;
209 } else {
210 m=0;
211 du=MEMALLOC(n,double);
212 if (Paso_checkPtr(du)) {
213 errorCode=SOLVER_MEMORY_ERROR;
214 } else {
215 /* tolerance? */
216
217 while ( (!converged) && (!diverged) && (! max_m_reached) && Paso_noError()) {
218 errorCode=Paso_FCTSolver_Function_call(F,du, u, pp);
219 Paso_Update(n,1.,u,omega,du);
220 norm_u=Paso_lsup(n,u, fctp->mpi_info);
221 norm_du_old=norm_du;
222 norm_du=Paso_lsup(n,du, fctp->mpi_info);
223 if (m ==0) {
224 if (options->verbose) printf("Paso_FCTSolver_solve: step %d: increment= %e\n",m+1, norm_du*omega);
225
226 } else {
227 if (norm_du_old > 0.) {
228 rate=norm_du/norm_du_old;
229 } else if (norm_du <= 0.) {
230 rate=0.;
231 } else {
232 rate=LARGE_POSITIVE_FLOAT;
233 }
234 if (options->verbose) printf("Paso_FCTSolver_solve: step %d: increment= %e (rate = %e)\n",m+1, norm_du*omega, rate);
235 num_critical_rates+=( rate<critical_rate ? 0 : 1);
236 }
237
238 max_m_reached=(m>max_m);
239 diverged = (num_critical_rates >= num_critical_rates_max);
240 converged=(norm_du*omega <= ATOL) ;
241 m++;
242 }
243 }
244 MEMFREE(du);
245 if (errorCode == SOLVER_NO_ERROR) {
246 if (converged) {
247 if (options->verbose) printf("Paso_FCTSolver_solve: iteration is completed.\n");
248 errorCode=SOLVER_NO_ERROR;
249 } else if (diverged) {
250 if (options->verbose) printf("Paso_FCTSolver_solve: divergence.\n");
251 errorCode=SOLVER_DIVERGENCE;
252 } else if (max_m_reached) {
253 if (options->verbose) printf("Paso_FCTSolver_solve: maximum number of iteration steps reached.\n");
254 errorCode=SOLVER_MAXITER_REACHED;
255 }
256 }
257 }
258 return errorCode;
259 }
260
261
262
263 err_t Paso_FCTSolver_setUpRightHandSide(Paso_TransportProblem* fctp, const double dt, const double *u_m,
264 Paso_Coupler* u_m_coupler, double * z_m,
265 Paso_SystemMatrix* flux_matrix, Paso_Coupler* uTilde_coupler, const double *b,
266 Paso_Coupler* QN_coupler, Paso_Coupler* QP_coupler,
267 double *RN_m, Paso_Coupler* RN_m_coupler, double* RP_m, Paso_Coupler* RP_m_coupler,
268 Paso_Performance* pp)
269 {
270 const double omega=dt* Paso_Transport_getTheta(fctp);
271 const dim_t n=Paso_SystemMatrix_getTotalNumRows(fctp->transport_matrix);
272 /* distribute u */
273 Paso_Coupler_startCollect(u_m_coupler,u_m);
274 Paso_Coupler_finishCollect(u_m_coupler);
275 /*
276 * set the ant diffusion fluxes:
277 *
278 */
279 Paso_FCTSolver_setAntiDiffusionFlux(dt,fctp,flux_matrix,u_m_coupler);
280 /*
281 * apply pre flux-correction: f_{ij}:=0 if f_{ij}*(\tilde{u}[i]- \tilde{u}[j])<=0
282 *
283 */
284 Paso_FCTSolver_applyPreAntiDiffusionCorrection(flux_matrix,uTilde_coupler);
285 /*
286 * set flux limiters RN_m,RP_m
287 *
288 */
289 Paso_FCTSolver_setRs(flux_matrix,fctp->lumped_mass_matrix,QN_coupler,QP_coupler,RN_m,RP_m);
290 Paso_Coupler_startCollect(RN_m_coupler,RN_m);
291 Paso_Coupler_startCollect(RP_m_coupler,RP_m);
292 /*
293 * z_m[i]=b[i] - (m_i*u_m[i] - dt*theta*sum_{j<>i} l_{ij} (u_m[j]-u_m[i]) )
294 *
295 * note that iteration_matrix stores the negative values of the
296 * low order transport matrix l therefore a=dt*theta is used.
297 */
298 Paso_FCTSolver_setMuPaLu(z_m, fctp->lumped_mass_matrix, u_m_coupler, omega, fctp->iteration_matrix);
299 /*{
300 int kk;
301 for (kk=0;kk<n;kk++) printf("z_m %d : %e %e -> %e\n",kk,z_m[kk], b[kk],z_m[kk]-b[kk]);
302 }
303 */
304 /* z_m=b-z_m */
305 Paso_Update(n,-1.,z_m,1.,b);
306
307 Paso_Coupler_finishCollect(RN_m_coupler);
308 Paso_Coupler_finishCollect(RP_m_coupler);
309 /* add corrected fluxes into z_m */
310 Paso_FCTSolver_addCorrectedFluxes(z_m,flux_matrix,RN_m_coupler,RP_m_coupler);
311 return SOLVER_NO_ERROR;
312 }
313
314 void Paso_FCTSolver_Function_initialize(const double dt, Paso_TransportProblem* fctp, Paso_Options* options, Paso_Performance* pp)
315 {
316 dim_t i;
317 const index_t* main_iptr=Paso_TransportProblem_borrowMainDiagonalPointer(fctp);
318 const dim_t n=Paso_SystemMatrix_getTotalNumRows(fctp->transport_matrix);
319 const double theta = Paso_Transport_getTheta(fctp);
320 const double omega=1./(dt* theta);
321 register double m, rtmp4;
322
323 /*
324 * fctp->iteration_matrix[i,i]=m[i]/(dt theta) -l[i,i]
325 *
326 */
327 Paso_solve_free(fctp->iteration_matrix);
328 #pragma omp parallel for private(i,m,rtmp4)
329 for (i = 0; i < n; ++i) {
330 m=fctp->lumped_mass_matrix[i];
331 rtmp4=m*omega-(fctp->main_diagonal_low_order_transport_matrix[i]);
332 fctp->iteration_matrix->mainBlock->val[main_iptr[i]]=rtmp4;
333 }
334 Performance_startMonitor(pp,PERFORMANCE_PRECONDITIONER_INIT);
335 Paso_Solver_setPreconditioner(fctp->iteration_matrix,options);
336 Performance_stopMonitor(pp,PERFORMANCE_PRECONDITIONER_INIT);
337 }
338
339 void Paso_FCTSolver_setUp(Paso_TransportProblem* fctp, const double dt, const double *u, double* b, double* uTilde,
340 Paso_Coupler* uTilde_coupler, double *QN, Paso_Coupler* QN_coupler, double *QP, Paso_Coupler* QP_coupler,
341 Paso_Options* options, Paso_Performance* pp)
342 {
343 dim_t i;
344 const dim_t n=Paso_SystemMatrix_getTotalNumRows(fctp->transport_matrix);
345 register double m;
346 /* distribute u */
347 Paso_Coupler_startCollect(fctp->u_coupler,u);
348 Paso_Coupler_finishCollect(fctp->u_coupler);
349 /*
350 * b^n[i]=m u^n[i] + dt*(1-theta) sum_{j <> i} l_{ij}*(u^n[j]-u^n[i])
351 *
352 * note that iteration_matrix stores the negative values of the
353 * low order transport matrix l therefore a=-dt*(1-fctp->theta) is used.
354 *
355 */
356 if (fctp->useBackwardEuler) {
357 Paso_FCTSolver_setMuPaLu(b,fctp->lumped_mass_matrix,fctp->u_coupler,0.,fctp->iteration_matrix);
358 } else {
359 Paso_FCTSolver_setMuPaLu(b,fctp->lumped_mass_matrix,fctp->u_coupler,-dt*0.5,fctp->iteration_matrix);
360 }
361 /*
362 * uTilde[i]=b[i]/m[i]
363 *
364 */
365 #pragma omp parallel for private(i,m)
366 for (i = 0; i < n; ++i) {
367 m=fctp->lumped_mass_matrix[i];
368 uTilde[i]=b[i]/m;
369 }
370 /* distribute uTilde: */
371 Paso_Coupler_startCollect(uTilde_coupler,uTilde);
372 Paso_Coupler_finishCollect(uTilde_coupler);
373 /*
374 * calculate QP[i] max_{j} (\tilde{u}[j]- \tilde{u}[i] )
375 * QN[i] min_{j} (\tilde{u}[j]- \tilde{u}[i] )
376 *
377 */
378 Paso_FCTSolver_setQs(uTilde_coupler,QN,QP,fctp->iteration_matrix);
379 Paso_Coupler_startCollect(QN_coupler,QN);
380 Paso_Coupler_startCollect(QP_coupler,QP);
381 Paso_Coupler_finishCollect(QN_coupler);
382 Paso_Coupler_finishCollect(QP_coupler);
383 }

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