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

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Revision 3014 - (hide 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 gross 2987
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 gross 3005
119 gross 3014 /* set low order transport operator */
120     Paso_FCTSolver_setLowOrderOperator(fctp);
121 gross 2987
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 gross 3005 Paso_Options options;
160 gross 2987 Paso_FCTSolver *more=(Paso_FCTSolver *) (F->more);
161 gross 3005 Paso_Options_setDefaults(&options);
162     options.verbose=TRUE;
163 gross 2987
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 gross 3005 /* Paso_Solver(more->transportproblem->iteration_matrix,value,F->tmp,&options,pp); */
171    
172    
173 gross 2987 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 gross 3014 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 gross 2987 err_t errorCode=SOLVER_NO_ERROR;
184     Paso_FCTSolver *more=(Paso_FCTSolver *) (F->more);
185 gross 3014 const double omega=1./(dt*Paso_Transport_getTheta(more->transportproblem));
186 gross 2987 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 gross 3014 dim_t m=0, num_critical_rates=0 ;
192     bool_t converged=FALSE, max_m_reached=FALSE,diverged=FALSE;
193 gross 2987
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 gross 3005 if (more->transportproblem->useBackwardEuler && FALSE ) {
204 gross 2987 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 gross 3014 while ( (!converged) && (!diverged) && (! max_m_reached) && Paso_noError()) {
218 gross 2987 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 gross 3014 norm_du_old=norm_du;
222 gross 2987 norm_du=Paso_lsup(n,du, fctp->mpi_info);
223 gross 3014 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 gross 2987 max_m_reached=(m>max_m);
239 gross 3014 diverged = (num_critical_rates >= num_critical_rates_max);
240 gross 2987 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 gross 3014 } 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 gross 2987 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 gross 3014 const double omega=dt* Paso_Transport_getTheta(fctp);
271 gross 2987 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 gross 3005 Paso_FCTSolver_setMuPaLu(z_m, fctp->lumped_mass_matrix, u_m_coupler, omega, fctp->iteration_matrix);
299 gross 2987 /*{
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 gross 3005 Paso_FCTSolver_addCorrectedFluxes(z_m,flux_matrix,RN_m_coupler,RP_m_coupler);
311 gross 2987 return SOLVER_NO_ERROR;
312     }
313    
314 gross 3014 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 gross 2987 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 gross 3014 register double m;
346 gross 2987 /* 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 gross 3014 */
365     #pragma omp parallel for private(i,m)
366 gross 2987 for (i = 0; i < n; ++i) {
367     m=fctp->lumped_mass_matrix[i];
368 gross 3014 uTilde[i]=b[i]/m;
369     }
370 gross 2987 /* 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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