/[escript]/trunk/paso/src/FCT_Solver.c
ViewVC logotype

Annotation of /trunk/paso/src/FCT_Solver.c

Parent Directory Parent Directory | Revision Log Revision Log


Revision 3822 - (hide annotations)
Mon Feb 13 06:22:06 2012 UTC (7 years, 7 months ago) by gross
File MIME type: text/plain
File size: 30294 byte(s)
Transport solver supports now constraints (except the linear CN)
1 gross 3793
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 correction (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 "FCT_Solver.h"
31     #include "Preconditioner.h"
32     #include "PasoUtil.h"
33    
34    
35     Paso_FCT_Solver* Paso_FCT_Solver_alloc(Paso_TransportProblem *fctp, Paso_Options* options)
36     {
37     Paso_FCT_Solver* out=NULL;
38     const dim_t blockSize=Paso_TransportProblem_getBlockSize(fctp);
39     const dim_t n = Paso_TransportProblem_getTotalNumRows(fctp);
40    
41     out=MEMALLOC(1,Paso_FCT_Solver);
42     if (! Esys_checkPtr(out)) {
43     out->transportproblem = Paso_TransportProblem_getReference(fctp);
44     out->mpi_info = Esys_MPIInfo_getReference(fctp->mpi_info);
45     out->flux_limiter = Paso_FCT_FluxLimiter_alloc(fctp);
46     out->b = MEMALLOC(n, double);
47     if ( (options->ode_solver == PASO_CRANK_NICOLSON) || (options->ode_solver == PASO_BACKWARD_EULER) ) {
48     out->du = MEMALLOC(n, double);
49     out->z = MEMALLOC(n, double);
50     } else {
51     out->du = NULL;
52     out->z=NULL;
53     }
54     out->u_coupler = Paso_Coupler_alloc(Paso_TransportProblem_borrowConnector(fctp), blockSize);
55     out->u_old_coupler = Paso_Coupler_alloc(Paso_TransportProblem_borrowConnector(fctp), blockSize);
56     out->omega=0;
57    
58     if ( options->ode_solver == PASO_LINEAR_CRANK_NICOLSON ) {
59     out->method = PASO_LINEAR_CRANK_NICOLSON;
60     } else if ( options->ode_solver == PASO_CRANK_NICOLSON ) {
61     out->method = PASO_CRANK_NICOLSON;
62     } else if ( options->ode_solver == PASO_BACKWARD_EULER ) {
63     out->method = PASO_BACKWARD_EULER;
64     } else {
65     Esys_setError(VALUE_ERROR, "Paso_FCT_Solver_alloc: unknown integration scheme.");
66     out->method = UNKNOWN;
67     }
68    
69     }
70    
71     if (Esys_noError()) {
72     return out;
73     } else {
74     Paso_FCT_Solver_free(out);
75     return NULL;
76     }
77    
78     }
79    
80     void Paso_FCT_Solver_free(Paso_FCT_Solver *in)
81     {
82     if (in != NULL) {
83     Paso_TransportProblem_free(in->transportproblem);
84     Paso_FCT_FluxLimiter_free(in->flux_limiter);
85     Esys_MPIInfo_free(in->mpi_info);
86     Paso_Coupler_free(in->u_old_coupler);
87     Paso_Coupler_free(in->u_coupler);
88    
89     MEMFREE(in->b);
90     MEMFREE(in->z);
91     MEMFREE(in->du);
92     MEMFREE(in);
93    
94     }
95     }
96    
97     double Paso_FCT_Solver_getSafeTimeStepSize(Paso_TransportProblem* fctp)
98     {
99     dim_t i, n;
100     double dt_max=LARGE_POSITIVE_FLOAT;
101     n=Paso_SystemMatrix_getTotalNumRows(fctp->transport_matrix);
102     /* set low order transport operator */
103     Paso_FCT_setLowOrderOperator(fctp);
104    
105     if (Esys_noError()) {
106     /*
107     * calculate time step size:
108     */
109     dt_max=LARGE_POSITIVE_FLOAT;
110     #pragma omp parallel private(i)
111     {
112     double dt_max_loc=LARGE_POSITIVE_FLOAT;
113     #pragma omp for schedule(static)
114     for (i=0;i<n;++i) {
115 caltinay 3795 const double l_ii=fctp->main_diagonal_low_order_transport_matrix[i];
116     const double m_i=fctp->lumped_mass_matrix[i];
117 gross 3822 if ( m_i > 0 ) {
118 gross 3793 if (l_ii<0) dt_max_loc=MIN(dt_max_loc,m_i/(-l_ii));
119 gross 3822 }
120     }
121 gross 3793 #pragma omp critical
122     {
123     dt_max=MIN(dt_max,dt_max_loc);
124     }
125     }
126     #ifdef ESYS_MPI
127     {
128 gross 3822 dt_max_loc=dt_max;
129     MPI_Allreduce(&dt_max_loc, &dt_max, 1, MPI_DOUBLE, MPI_MIN, fctp->mpi_info->comm);
130 gross 3793 }
131     #endif
132 gross 3822 if (dt_max<LARGE_POSITIVE_FLOAT) dt_max*=2.;
133 gross 3793 }
134     return dt_max;
135     }
136    
137     /* modifies the main diagonal of the iteration matrix to introduce new dt */
138     void Paso_FCT_Solver_initialize(const double dt, Paso_FCT_Solver *fct_solver, Paso_Options* options, Paso_Performance* pp)
139     {
140     Paso_TransportProblem* fctp = fct_solver->transportproblem;
141     const index_t* main_iptr=Paso_TransportProblem_borrowMainDiagonalPointer(fctp);
142     const dim_t n=Paso_SystemMatrix_getTotalNumRows(fctp->transport_matrix);
143     const double theta = Paso_FCT_Solver_getTheta(fct_solver);
144     const double omega=1./(dt* theta);
145     dim_t i;
146     Paso_Options options2;
147    
148    
149    
150     Paso_solve_free(fctp->iteration_matrix);
151     /*
152     * fctp->iteration_matrix[i,i]=m[i]/(dt theta) -l[i,i]
153     *
154     */
155     fct_solver->omega=omega;
156     fct_solver->dt = dt;
157     #pragma omp parallel for private(i)
158     for (i = 0; i < n; ++i) {
159 gross 3822 const double m_i=fctp->lumped_mass_matrix[i];
160 caltinay 3795 const double l_ii = fctp->main_diagonal_low_order_transport_matrix[i];
161 gross 3822 if ( m_i > 0 ) {
162     fctp->iteration_matrix->mainBlock->val[main_iptr[i]] = m_i * omega - l_ii;
163     } else {
164     fctp->iteration_matrix->mainBlock->val[main_iptr[i]] = ABS(m_i * omega - l_ii)/(EPSILON*EPSILON);
165     }
166 gross 3793 }
167    
168     /* allocate preconditioner/solver */
169     Paso_Options_setDefaults(&options2);
170     options2.verbose = options->verbose;
171     if (fct_solver->method == PASO_LINEAR_CRANK_NICOLSON ) {
172     options2.preconditioner = PASO_GS;
173     } else {
174     options2.preconditioner = PASO_JACOBI;
175     /* options2.preconditioner = PASO_GS; */
176     }
177     options2.use_local_preconditioner = FALSE;
178 gross 3807 options2.sweeps=-1;
179 gross 3793
180     Performance_startMonitor(pp,PERFORMANCE_PRECONDITIONER_INIT);
181     Paso_SystemMatrix_setPreconditioner(fctp->iteration_matrix, &options2);
182     Performance_stopMonitor(pp,PERFORMANCE_PRECONDITIONER_INIT);
183     }
184    
185     /* entry point for update proceedures */
186     err_t Paso_FCT_Solver_update(Paso_FCT_Solver *fct_solver, double* u, double *u_old, Paso_Options* options, Paso_Performance *pp)
187     {
188     const index_t method=fct_solver->method;
189     err_t err_out = SOLVER_NO_ERROR;
190    
191    
192     if (method == PASO_LINEAR_CRANK_NICOLSON) {
193     err_out=Paso_FCT_Solver_update_LCN(fct_solver, u, u_old, options, pp);
194    
195     } else if (method == PASO_CRANK_NICOLSON) {
196     err_out=Paso_FCT_Solver_updateNL(fct_solver, u, u_old, options, pp);
197    
198     } else if (method == PASO_BACKWARD_EULER) {
199     err_out=Paso_FCT_Solver_updateNL(fct_solver, u, u_old, options, pp);
200     } else {
201     err_out = SOLVER_INPUT_ERROR;
202     }
203     return err_out;
204    
205     }
206    
207     /* linear crank-nicolson update */
208     err_t Paso_FCT_Solver_update_LCN(Paso_FCT_Solver *fct_solver, double * u, double *u_old, Paso_Options* options, Paso_Performance *pp)
209     {
210     double const dt = fct_solver->dt;
211     dim_t sweep_max;
212     double *b = fct_solver->b;
213     double const RTOL = options->tolerance;
214     const dim_t n=Paso_TransportProblem_getTotalNumRows(fct_solver->transportproblem);
215     Paso_SystemMatrix * iteration_matrix = fct_solver->transportproblem->iteration_matrix;
216     err_t errorCode = SOLVER_NO_ERROR;
217    
218     Paso_Coupler_startCollect(fct_solver->u_old_coupler,u_old);
219     Paso_Coupler_finishCollect(fct_solver->u_old_coupler);
220    
221 gross 3822 /* b[i]=m*u_tilde[i] = m u_old[i] + dt/2 sum_{j <> i} l_{ij}*(u_old[j]-u_old[i])
222     = u_tilde[i] = u_old[i] where constraint m<0.
223 gross 3793 * note that iteration_matrix stores the negative values of the
224     * low order transport matrix l. Therefore a=-dt*0.5 is used. */
225    
226     Paso_FCT_Solver_setMuPaLu(b, fct_solver->transportproblem->lumped_mass_matrix,
227 gross 3807 fct_solver->u_old_coupler, -dt*0.5, iteration_matrix);
228 gross 3793 /* solve for u_tilde : u_tilda = m^{-1} * b */
229     Paso_FCT_FluxLimiter_setU_tilda(fct_solver->flux_limiter, b);
230     /* u_tilda_connector is completed */
231 gross 3807
232 gross 3793 /* calculate anti-diffusive fluxes for u_tilda */
233     Paso_FCT_setAntiDiffusionFlux_linearCN(fct_solver->flux_limiter->antidiffusive_fluxes,
234     fct_solver->transportproblem, dt,
235     fct_solver->flux_limiter->u_tilde_coupler,
236     fct_solver->u_old_coupler);
237 gross 3807
238    
239 gross 3793 /* b_i += sum_{j} limitation factor_{ij} * antidiffusive_flux_{ij} */
240     Paso_FCT_FluxLimiter_addLimitedFluxes_Start(fct_solver->flux_limiter);
241     Paso_FCT_FluxLimiter_addLimitedFluxes_Complete(fct_solver->flux_limiter, b);
242    
243    
244 gross 3807 /* solve (m-dt/2*L) u = b in the form (omega*m-L) u = b * omega with omega*dt/2=1 */
245    
246 gross 3793 /* initial guess is u<- -u + 2*u_tilde */
247     Paso_Update(n, -1., u, 2., fct_solver->flux_limiter->u_tilde);
248 gross 3807 Paso_Scale(n, b,fct_solver->omega );
249 gross 3793 sweep_max = MAX((int) (- 2 * log(RTOL)/log(2.)-0.5),1);
250 gross 3807
251     if (options->verbose) {
252     const double norm_u_tilde=Paso_lsup(n, fct_solver->flux_limiter->u_tilde, fct_solver->flux_limiter->mpi_info);
253     printf("Paso_FCT_Solver_update_LCN: u_tilda lsup = %e (rtol = %e, max. sweeps = %d)\n",norm_u_tilde,RTOL,sweep_max);
254     }
255 gross 3793 errorCode = Paso_Preconditioner_Smoother_solve_byTolerance( iteration_matrix, ((Paso_Preconditioner*) (iteration_matrix->solver_p))->gs,
256     u, b, RTOL, &sweep_max, TRUE);
257     if (errorCode == PRECONDITIONER_NO_ERROR) {
258     if (options->verbose) printf("Paso_FCT_Solver_update_LCN: convergence after %d Gauss-Seidel steps.\n",sweep_max);
259     errorCode=SOLVER_NO_ERROR;
260     } else {
261     if (options->verbose) printf("Paso_FCT_Solver_update_LCN: Gauss-Seidel failed within %d stesp (rel. tolerance %e).\n",sweep_max,RTOL);
262     errorCode= SOLVER_MAXITER_REACHED;
263     }
264     return errorCode;
265    
266     }
267    
268     err_t Paso_FCT_Solver_updateNL(Paso_FCT_Solver *fct_solver, double* u, double *u_old, Paso_Options* options, Paso_Performance *pp)
269     {
270 gross 3794 const dim_t num_critical_rates_max=3; /* number of rates >=critical_rate accepted before divergence is triggered */
271     const double critical_rate=0.95; /* expected value of convergence rate */
272    
273 gross 3793 double *b = fct_solver->b;
274     double *z = fct_solver->z;
275     double *du = fct_solver->du;
276     double const dt = fct_solver->dt;
277     Paso_TransportProblem* fctp = fct_solver->transportproblem;
278     Paso_FCT_FluxLimiter* flux_limiter = fct_solver->flux_limiter;
279     dim_t i;
280 gross 3794 double norm_u_tilde, ATOL, norm_du=LARGE_POSITIVE_FLOAT, norm_du_old, rate=1.;
281 gross 3793 err_t errorCode=SOLVER_NO_ERROR;
282     const dim_t n=Paso_SystemMatrix_getTotalNumRows(fctp->transport_matrix);
283     const double atol=options->absolute_tolerance;
284     const double rtol=options->tolerance;
285     const dim_t max_m=options->iter_max;
286     dim_t m=0, num_critical_rates=0 ;
287     /* ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////// */
288    
289     bool_t converged=FALSE, max_m_reached=FALSE,diverged=FALSE;
290     options->num_iter=0;
291    
292     Paso_Coupler_startCollect(fct_solver->u_old_coupler,u_old);
293     Paso_Coupler_finishCollect(fct_solver->u_old_coupler);
294     /* prepare u_tilda and flux limiter */
295     if ( fct_solver->method == PASO_BACKWARD_EULER ) {
296     /* b[i]=m_i* u_old[i] */
297     #pragma omp for private(i) schedule(static)
298     for (i = 0; i < n; ++i) {
299 gross 3822 if (fctp->lumped_mass_matrix[i] > 0 ) {
300     b[i]=u_old[i]* fctp->lumped_mass_matrix[i];
301     } else {
302     b[i]=u_old[i];
303     }
304 gross 3793 }
305     } else {
306 gross 3822 /* b[i]=m_i* u_old[i] + dt/2 sum_{j <> i} l_{ij}*(u_old[j]-u_old[i]) = m_i * u_tilde_i where m_i>0
307     * = u_old[i] otherwise
308 gross 3793 * note that iteration_matrix stores the negative values of the
309     * low order transport matrix l. Therefore a=-dt*0.5 is used. */
310     Paso_FCT_Solver_setMuPaLu(b,fctp->lumped_mass_matrix,fct_solver->u_old_coupler,-dt*0.5,fctp->iteration_matrix);
311     }
312     Paso_FCT_FluxLimiter_setU_tilda(flux_limiter, b); /* u_tilda = m^{-1} b */
313     /* u_tilda_connector is completed */
314 gross 3822 for (i = 0; i < n; ++i) printf("%d : %e %e\n",i, fctp->lumped_mass_matrix[i], flux_limiter->u_tilde[i]);
315 gross 3793 /**********************************************************************************************************************/
316     /* calculate stopping criterium */
317     norm_u_tilde=Paso_lsup(n, flux_limiter->u_tilde, flux_limiter->mpi_info);
318     ATOL= rtol * norm_u_tilde + atol ;
319     if (options->verbose) printf("Paso_FCT_Solver_updateNL: iteration starts u_tilda lsup = %e (abs. tol = %e)\n",norm_u_tilde,ATOL);
320     /* ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////// */
321    
322     /* u_old is an initial guess for u*/
323     Paso_Copy(n,u,u_old);
324    
325     while ( (!converged) && (!diverged) && (! max_m_reached) && Esys_noError()) {
326     Paso_Coupler_startCollect(fct_solver->u_coupler,u);
327     Paso_Coupler_finishCollect(fct_solver->u_coupler);
328    
329     /* set antidiffusive_flux_{ij} for u */
330     if (fct_solver->method == PASO_BACKWARD_EULER) {
331     Paso_FCT_setAntiDiffusionFlux_BE(fct_solver->flux_limiter->antidiffusive_fluxes, fctp, dt, fct_solver->u_coupler, fct_solver->u_old_coupler);
332     } else {
333     Paso_FCT_setAntiDiffusionFlux_CN(fct_solver->flux_limiter->antidiffusive_fluxes, fctp, dt, fct_solver->u_coupler, fct_solver->u_old_coupler);
334     }
335     /* start the calculation of the limitation factors_{fct_solver->ij} */
336     Paso_FCT_FluxLimiter_addLimitedFluxes_Start(flux_limiter); /* uses u_tilde */
337    
338     /*
339 gross 3822 * z_m[i]=b[i] - (m_i*u[i] - omega*sum_{j<>i} l_{ij} (u[j]-u[i]) ) where m_i>0
340     * ==b[i] - u[i] = u_tilda[i]-u[i] =0 otherwise
341     *
342     * omega = dt/2 or dt .
343 gross 3793 *
344     * note that iteration_matrix stores the negative values of the
345     * low order transport matrix l. Therefore a=dt*theta is used.
346     */
347     if (fct_solver-> method == PASO_BACKWARD_EULER) {
348     Paso_FCT_Solver_setMuPaLu(z, fctp->lumped_mass_matrix, fct_solver->u_coupler, dt, fctp->iteration_matrix);
349     } else {
350     Paso_FCT_Solver_setMuPaLu(z, fctp->lumped_mass_matrix, fct_solver->u_coupler, dt/2, fctp->iteration_matrix);
351     }
352    
353    
354     Paso_Update(n,-1.,z,1.,b); /* z=b-z */
355 gross 3822 for (i = 0; i < n; ++i) printf("%d : %e\n",i,z[i]);
356 gross 3793
357     /* z_i += sum_{j} limitation factor_{ij} * antidiffusive_flux_{ij} */
358     Paso_FCT_FluxLimiter_addLimitedFluxes_Complete(flux_limiter, z);
359    
360     /* we solve (m/omega - L ) * du = z */
361     if (fct_solver->method == PASO_BACKWARD_EULER) {
362     dim_t cntIter = options->iter_max;
363     double tol= Paso_l2(n, z, fctp->mpi_info) ;
364    
365     if ( m ==0) {
366     tol *=0.5;
367     } else {
368     tol *= MIN(MAX(rate*rate, 1e-2), 0.5);
369     }
370     /* use BiCGSTab with jacobi preconditioner ( m - omega * L ) */
371     Paso_zeroes(n,du);
372     errorCode = Paso_Solver_BiCGStab(fctp->iteration_matrix, z, du, &cntIter, &tol, pp);
373    
374     /* errorCode = Paso_Solver_GMRES(fctp->iteration_matrix, z, du, &cntIter, &tol, 10, 2000, pp); */
375     if (options->verbose) printf("Paso_FCT_Solver_updateNL: BiCGStab is completed after %d steps (residual =%e).\n",cntIter, tol);
376     options->num_iter+=cntIter;
377     if ( errorCode != SOLVER_NO_ERROR) break;
378     } else {
379     /* just use the main diagonal of (m/omega - L ) */
380    
381     Paso_Preconditioner_Smoother_solve(fctp->iteration_matrix, ((Paso_Preconditioner*) (fctp->iteration_matrix->solver_p))->jacobi,
382     du, z, 1, FALSE);
383     options->num_iter++;
384     }
385 gross 3822 for (i = 0; i < n; ++i) printf("%d : %e\n",i,du[i]);
386 gross 3793
387     Paso_Update(n,1.,u,fct_solver->omega,du);
388     norm_du_old=norm_du;
389     norm_du=Paso_lsup(n,du, fctp->mpi_info);
390     if (m ==0) {
391     if (options->verbose) printf("Paso_FCT_Solver_updateNL: step %d: increment= %e\n",m+1, norm_du * fct_solver->omega);
392     } else {
393     if (norm_du_old > 0.) {
394     rate=norm_du/norm_du_old;
395     } else if (norm_du <= 0.) {
396     rate=0.;
397     } else {
398     rate=LARGE_POSITIVE_FLOAT;
399     }
400     if (options->verbose) printf("Paso_FCT_Solver_updateNL: step %d: increment= %e (rate = %e)\n",m+1, norm_du * fct_solver->omega, rate);
401     num_critical_rates+=( rate<critical_rate ? 0 : 1);
402     max_m_reached=(m>max_m);
403     diverged = (num_critical_rates >= num_critical_rates_max);
404     converged=(norm_du * fct_solver->omega <= ATOL) ;
405     }
406     m++;
407     } /* end of while loop */
408     if (errorCode == SOLVER_NO_ERROR) {
409     if (converged) {
410     if (options->verbose) printf("Paso_FCT_Solver_updateNL: iteration is completed.\n");
411     errorCode=SOLVER_NO_ERROR;
412     } else if (diverged) {
413     if (options->verbose) printf("Paso_FCT_Solver_updateNL: divergence.\n");
414     errorCode=SOLVER_DIVERGENCE;
415     } else if (max_m_reached) {
416     if (options->verbose) printf("Paso_FCT_Solver_updateNL: maximum number of iteration steps reached.\n");
417     errorCode=SOLVER_MAXITER_REACHED;
418     }
419    
420     }
421     return errorCode;
422     }
423    
424    
425     /*
426     * AntiDiffusionFlux:
427     *
428     * f_{ij} = (m_{ij} - dt (1-theta) d_{ij}) (u_old[j]-u_old[i]) - (m_{ij} + dt theta d_{ij}) (u[j]-u[i])
429     *
430     * m=fc->mass matrix
431     * d=artifical diffusion matrix = L - K = - fc->iteration matrix - fc->transport matrix (away from main diagonal)
432     *
433     * for CN : theta =0.5
434     * for BE : theta = 1.
435     */
436    
437     void Paso_FCT_setAntiDiffusionFlux_CN(Paso_SystemMatrix *flux_matrix,
438     const Paso_TransportProblem* fct,
439     const double dt,
440     const Paso_Coupler* u_coupler,
441     const Paso_Coupler* u_old_coupler)
442     {
443     dim_t i;
444     index_t iptr_ij;
445    
446     const double *u = Paso_Coupler_borrowLocalData(u_coupler);
447     const double *u_old= Paso_Coupler_borrowLocalData(u_old_coupler);
448     const double *remote_u=Paso_Coupler_borrowRemoteData(u_coupler);
449     const double *remote_u_old=Paso_Coupler_borrowRemoteData(u_old_coupler);
450     const double dt_half= dt/2;
451     const Paso_SystemMatrixPattern *pattern=fct->iteration_matrix->pattern;
452     const dim_t n=Paso_SystemMatrix_getTotalNumRows(fct->iteration_matrix);
453    
454     #pragma omp parallel for schedule(static) private(i, iptr_ij)
455     for (i = 0; i < n; ++i) {
456 caltinay 3795 const double u_i = u[i];
457     const double u_old_i = u_old[i];
458 gross 3793
459     #pragma ivdep
460     for (iptr_ij=(pattern->mainPattern->ptr[i]);iptr_ij<pattern->mainPattern->ptr[i+1]; ++iptr_ij) {
461 caltinay 3795 const index_t j = pattern->mainPattern->index[iptr_ij];
462     const double m_ij = fct->mass_matrix->mainBlock->val[iptr_ij];
463     const double d_ij = fct->transport_matrix->mainBlock->val[iptr_ij]+fct->iteration_matrix->mainBlock->val[iptr_ij]; /* this is in fact -d_ij */
464     const double u_old_j = u_old[j];
465     const double u_j = u[j];
466 gross 3793
467     /* (m_{ij} - dt (1-theta) d_{ij}) (u_old[j]-u_old[i]) - (m_{ij} + dt theta d_{ij}) (u[j]-u[i]) */
468     flux_matrix->mainBlock->val[iptr_ij]=(m_ij+dt_half*d_ij)*(u_old_j-u_old_i) - (m_ij-dt_half*d_ij)*(u_j-u_i);
469    
470     }
471     #pragma ivdep
472     for (iptr_ij=(pattern->col_couplePattern->ptr[i]);iptr_ij<pattern->col_couplePattern->ptr[i+1]; ++iptr_ij) {
473 caltinay 3795 const index_t j = pattern->col_couplePattern->index[iptr_ij];
474     const double m_ij = fct->mass_matrix->col_coupleBlock->val[iptr_ij];
475     const double d_ij = fct->transport_matrix->col_coupleBlock->val[iptr_ij]+fct->iteration_matrix->col_coupleBlock->val[iptr_ij]; /* this is in fact -d_ij */
476     const double u_old_j = remote_u_old[j];
477     const double u_j = remote_u[j];
478 gross 3793 flux_matrix->col_coupleBlock->val[iptr_ij]=(m_ij+dt_half*d_ij)*(u_old_j-u_old_i)- (m_ij-dt_half*d_ij)*(u_j-u_i);
479     }
480     }
481     }
482    
483     void Paso_FCT_setAntiDiffusionFlux_BE(Paso_SystemMatrix *flux_matrix,
484     const Paso_TransportProblem* fct,
485     const double dt,
486     const Paso_Coupler* u_coupler,
487     const Paso_Coupler* u_old_coupler)
488     {
489     dim_t i;
490     index_t iptr_ij;
491    
492     const double *u=Paso_Coupler_borrowLocalData(u_coupler);
493     const double *u_old= Paso_Coupler_borrowLocalData(u_old_coupler);
494     const double *remote_u=Paso_Coupler_borrowRemoteData(u_coupler);
495     const double *remote_u_old=Paso_Coupler_borrowRemoteData(u_old_coupler);
496     const Paso_SystemMatrixPattern *pattern=fct->iteration_matrix->pattern;
497     const dim_t n=Paso_SystemMatrix_getTotalNumRows(fct->iteration_matrix);
498    
499     #pragma omp parallel for schedule(static) private(i, iptr_ij)
500     for (i = 0; i < n; ++i) {
501 caltinay 3795 const double u_i = u[i];
502     const double u_old_i = u_old[i];
503 gross 3793 #pragma ivdep
504     for (iptr_ij=pattern->mainPattern->ptr[i]; iptr_ij<pattern->mainPattern->ptr[i+1]; ++iptr_ij) {
505    
506 caltinay 3795 const index_t j = pattern->mainPattern->index[iptr_ij];
507     const double m_ij = fct->mass_matrix->mainBlock->val[iptr_ij];
508     const double d_ij = fct->transport_matrix->mainBlock->val[iptr_ij]+fct->iteration_matrix->mainBlock->val[iptr_ij]; /* this is in fact -d_ij */
509     const double u_old_j = u_old[j];
510     const double u_j = u[j];
511 gross 3793
512     flux_matrix->mainBlock->val[iptr_ij]=m_ij*(u_old_j-u_old_i)- (m_ij-dt*d_ij)*(u_j-u_i);
513     }
514     #pragma ivdep
515     for (iptr_ij=pattern->col_couplePattern->ptr[i]; iptr_ij<pattern->col_couplePattern->ptr[i+1]; ++iptr_ij) {
516 caltinay 3795 const index_t j = pattern->col_couplePattern->index[iptr_ij];
517     const double m_ij = fct->mass_matrix->col_coupleBlock->val[iptr_ij]; /* this is in fact -d_ij */
518     const double d_ij = fct->transport_matrix->col_coupleBlock->val[iptr_ij]+fct->iteration_matrix->col_coupleBlock->val[iptr_ij];
519     const double u_old_j = remote_u_old[j];
520     const double u_j = remote_u[j];
521 gross 3793
522     flux_matrix->col_coupleBlock->val[iptr_ij]=m_ij*(u_old_j-u_old_i)- (m_ij-dt*d_ij)*(u_j-u_i);
523     }
524     }
525     }
526    
527     /* special version of the ant-diffusive fluxes for the linear Crank-Nicolson scheme
528     * in fact this is evaluated for u = 2*u_tilde - u_old which is the predictor
529     * of the solution of the the stabilized problem at time dt using the forward Euler scheme
530     *
531     * f_{ij} = (m_{ij} - dt/2 d_{ij}) (u_old[j]-u_old[i]) - (m_{ij} + dt/2 d_{ij}) (u[j]-u[i])
532     * = (m_{ij} - dt/2 d_{ij}) * (u_old[j]-u_old[i]) - (m_{ij} + dt/2 d_{ij}) * ( 2*(u_tilde[j]-u_tilde[i]) - (u_old[j] -u_old [i]) )
533     * = 2* m_{ij} * ( (u_old[j]-u_tilde[j] - (u_old[i]) - u_tilde[i]) ) - dt d_{ij} * (u_tilde[j]-u_tilde[i])
534     *
535     */
536    
537     void Paso_FCT_setAntiDiffusionFlux_linearCN(Paso_SystemMatrix *flux_matrix,
538     const Paso_TransportProblem* fct,
539     const double dt,
540     const Paso_Coupler* u_tilde_coupler,
541     const Paso_Coupler* u_old_coupler)
542     {
543     dim_t i;
544     index_t iptr_ij;
545    
546     const double *u_tilde=Paso_Coupler_borrowLocalData(u_tilde_coupler);
547     const double *u_old= Paso_Coupler_borrowLocalData(u_old_coupler);
548     const double *remote_u_tilde=Paso_Coupler_borrowRemoteData(u_tilde_coupler);
549     const double *remote_u_old=Paso_Coupler_borrowRemoteData(u_old_coupler);
550     const Paso_SystemMatrixPattern *pattern=fct->iteration_matrix->pattern;
551     const dim_t n=Paso_SystemMatrix_getTotalNumRows(fct->iteration_matrix);
552    
553     #pragma omp parallel for schedule(static) private(i, iptr_ij)
554     for (i = 0; i < n; ++i) {
555 caltinay 3795 const double u_tilde_i = u_tilde[i];
556     const double u_old_i = u_old[i];
557 gross 3807 const double du_i = u_tilde_i - u_old_i;
558 gross 3793 #pragma ivdep
559     for (iptr_ij=(pattern->mainPattern->ptr[i]);iptr_ij<pattern->mainPattern->ptr[i+1]; ++iptr_ij) {
560    
561 caltinay 3795 const index_t j = pattern->mainPattern->index[iptr_ij];
562     const double m_ij = fct->mass_matrix->mainBlock->val[iptr_ij];
563     const double d_ij = fct->transport_matrix->mainBlock->val[iptr_ij]+fct->iteration_matrix->mainBlock->val[iptr_ij]; /* this is in fact -d_ij */
564     const double u_tilde_j = u_tilde[j];
565     const double u_old_j = u_old[j];
566 gross 3807 const double du_j = u_tilde_j - u_old_j;
567 gross 3793
568 gross 3807 flux_matrix->mainBlock->val[iptr_ij]= 2 * m_ij * ( du_i - du_j ) - dt * d_ij * ( u_tilde_i - u_tilde_j);
569 gross 3793 }
570     #pragma ivdep
571     for (iptr_ij=(pattern->col_couplePattern->ptr[i]);iptr_ij<pattern->col_couplePattern->ptr[i+1]; ++iptr_ij) {
572    
573 caltinay 3795 const index_t j = pattern->col_couplePattern->index[iptr_ij];
574     const double m_ij = fct->mass_matrix->col_coupleBlock->val[iptr_ij];
575     const double d_ij = fct->transport_matrix->col_coupleBlock->val[iptr_ij]+fct->iteration_matrix->col_coupleBlock->val[iptr_ij];/* this is in fact -d_ij */
576     const double u_tilde_j = remote_u_tilde[j];
577     const double u_old_j = remote_u_old[j];
578 gross 3807 const double du_j = u_tilde_j - u_old_j;
579 gross 3793
580 gross 3807 flux_matrix->col_coupleBlock->val[iptr_ij]= 2 * m_ij * ( du_i - du_j ) - dt * d_ij * ( u_tilde_i - u_tilde_j);
581 gross 3793
582     }
583     }
584    
585     }
586    
587     /**************************************************************/
588    
589     /* Creates the low order transport matrix and stores its negative values
590     * into the iteration_matrix except for the main diagonal which is stored
591     * separately.
592     * If fc->iteration_matrix==NULL, fc->iteration_matrix is allocated
593     *
594     * a=transport_matrix
595     * b= low_order_transport_matrix = - iteration_matrix
596     * c=main diagonal low_order_transport_matrix
597     * initialize c[i] mit a[i,i]
598     *
599     * d_ij=max(0,-a[i,j],-a[j,i])
600     * b[i,j]=-(a[i,j]+d_ij)
601     * c[i]-=d_ij
602     */
603    
604     void Paso_FCT_setLowOrderOperator(Paso_TransportProblem * fc) {
605    
606     dim_t i;
607     index_t iptr_ij, iptr_ji;
608     const index_t* main_iptr=Paso_TransportProblem_borrowMainDiagonalPointer(fc);
609    
610     if (fc->iteration_matrix==NULL) {
611     fc->iteration_matrix=Paso_SystemMatrix_alloc(fc->transport_matrix->type,
612     fc->transport_matrix->pattern,
613     fc->transport_matrix->row_block_size,
614     fc->transport_matrix->col_block_size, TRUE);
615     }
616    
617     if (Esys_noError()) {
618     const Paso_SystemMatrixPattern *pattern=fc->iteration_matrix->pattern;
619     const dim_t n=Paso_SystemMatrix_getTotalNumRows(fc->iteration_matrix);
620     #pragma omp parallel for private(i, iptr_ij, iptr_ji) schedule(static)
621     for (i = 0; i < n; ++i) {
622     double sum=fc->transport_matrix->mainBlock->val[main_iptr[i]];
623    
624     /* printf("sum[%d] = %e -> ", i, sum); */
625     /* look at a[i,j] */
626     for (iptr_ij=pattern->mainPattern->ptr[i];iptr_ij<pattern->mainPattern->ptr[i+1]; ++iptr_ij) {
627 caltinay 3795 const index_t j = pattern->mainPattern->index[iptr_ij];
628     const double rtmp1 = fc->transport_matrix->mainBlock->val[iptr_ij];
629 gross 3793 if (j!=i) {
630     /* find entry a[j,i] */
631     #pragma ivdep
632     for (iptr_ji=pattern->mainPattern->ptr[j]; iptr_ji<pattern->mainPattern->ptr[j+1]; ++iptr_ji) {
633    
634     if ( pattern->mainPattern->index[iptr_ji] == i) {
635 caltinay 3795 const double rtmp2=fc->transport_matrix->mainBlock->val[iptr_ji];
636 gross 3793 /*
637     printf("a[%d,%d]=%e\n",i,j,rtmp1);
638     printf("a[%d,%d]=%e\n",j,i,rtmp2);
639     */
640    
641 caltinay 3795 const double d_ij=-MIN3(0.,rtmp1,rtmp2);
642 gross 3793 fc->iteration_matrix->mainBlock->val[iptr_ij]=-(rtmp1+d_ij);
643     /* printf("l[%d,%d]=%e\n",i,j,fc->iteration_matrix->mainBlock->val[iptr_ij]); */
644     sum-=d_ij;
645     break;
646     }
647     }
648     }
649     }
650     for (iptr_ij=pattern->col_couplePattern->ptr[i];iptr_ij<pattern->col_couplePattern->ptr[i+1]; ++iptr_ij) {
651 caltinay 3795 const index_t j = pattern->col_couplePattern->index[iptr_ij];
652     const double rtmp1 = fc->transport_matrix->col_coupleBlock->val[iptr_ij];
653 gross 3793 /* find entry a[j,i] */
654     #pragma ivdep
655     for (iptr_ji=pattern->row_couplePattern->ptr[j]; iptr_ji<pattern->row_couplePattern->ptr[j+1]; ++iptr_ji) {
656     if (pattern->row_couplePattern->index[iptr_ji]==i) {
657 caltinay 3795 const double rtmp2=fc->transport_matrix->row_coupleBlock->val[iptr_ji];
658     const double d_ij=-MIN3(0.,rtmp1,rtmp2);
659 gross 3793 fc->iteration_matrix->col_coupleBlock->val[iptr_ij]=-(rtmp1+d_ij);
660     fc->iteration_matrix->row_coupleBlock->val[iptr_ji]=-(rtmp2+d_ij);
661     sum-=d_ij;
662     break;
663     }
664     }
665     }
666     /* set main diagonal entry */
667     fc->main_diagonal_low_order_transport_matrix[i]=sum;
668     /* printf("%e \n", sum); */
669     }
670    
671     }
672     }
673    
674     /*
675 gross 3822 * out_i=m_i u_i + a * \sum_{j <> i} l_{ij} (u_j-u_i) where m_i>0
676     * = u_i where m_i<=0
677 gross 3793 *
678     */
679     void Paso_FCT_Solver_setMuPaLu(double* out,
680     const double* M,
681     const Paso_Coupler* u_coupler,
682     const double a,
683     const Paso_SystemMatrix *L)
684     {
685     dim_t i;
686     const Paso_SystemMatrixPattern *pattern = L->pattern;
687     const double *u=Paso_Coupler_borrowLocalData(u_coupler);
688     const double *remote_u=Paso_Coupler_borrowRemoteData(u_coupler);
689 caltinay 3795 index_t iptr_ij;
690 gross 3793 const dim_t n=Paso_SystemMatrix_getTotalNumRows(L);
691    
692     #pragma omp parallel for private(i) schedule(static)
693     for (i = 0; i < n; ++i) {
694 gross 3822 if ( M[i] > 0.) {
695     out[i]=M[i]*u[i];
696     } else {
697     out[i]=u[i];
698     }
699 gross 3793 }
700     if (ABS(a)>0) {
701     #pragma omp parallel for schedule(static) private(i, iptr_ij)
702     for (i = 0; i < n; ++i) {
703 caltinay 3795 double sum=0;
704     const double u_i=u[i];
705 gross 3793 #pragma ivdep
706     for (iptr_ij=(pattern->mainPattern->ptr[i]);iptr_ij<pattern->mainPattern->ptr[i+1]; ++iptr_ij) {
707     const index_t j=pattern->mainPattern->index[iptr_ij];
708 caltinay 3795 const double l_ij=L->mainBlock->val[iptr_ij];
709 gross 3793 sum+=l_ij*(u[j]-u_i);
710    
711     }
712     #pragma ivdep
713     for (iptr_ij=(pattern->col_couplePattern->ptr[i]);iptr_ij<pattern->col_couplePattern->ptr[i+1]; ++iptr_ij) {
714     const index_t j=pattern->col_couplePattern->index[iptr_ij];
715 caltinay 3795 const double l_ij=L->col_coupleBlock->val[iptr_ij];
716 gross 3793 sum+=l_ij*(remote_u[j]-u_i);
717     }
718     out[i]+=a*sum;
719     }
720     }
721     }
722    
723     /* *************************************************************************************************************************** */
724    
725    
726    
727    
728    
729    
730    

  ViewVC Help
Powered by ViewVC 1.1.26