/[escript]/trunk/paso/src/FCT_Solver.cpp
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Contents of /trunk/paso/src/FCT_Solver.cpp

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Revision 4657 - (show annotations)
Thu Feb 6 06:12:20 2014 UTC (6 years, 3 months ago) by jfenwick
File size: 30887 byte(s)
I changed some files.
Updated copyright notices, added GeoComp.



1
2 /*****************************************************************************
3 *
4 * Copyright (c) 2003-2014 by University of Queensland
5 * http://www.uq.edu.au
6 *
7 * Primary Business: Queensland, Australia
8 * Licensed under the Open Software License version 3.0
9 * http://www.opensource.org/licenses/osl-3.0.php
10 *
11 * Development until 2012 by Earth Systems Science Computational Center (ESSCC)
12 * Development 2012-2013 by School of Earth Sciences
13 * Development from 2014 by Centre for Geoscience Computing (GeoComp)
14 *
15 *****************************************************************************/
16
17
18 /************************************************************************************/
19
20 /* Paso: Transport solver with flux correction (L is row sum zero)
21 *
22 * - Mv_t=Lv v(0)=u
23 *
24 * to return v(dt)
25 *
26 */
27 /************************************************************************************/
28
29 /* Author: l.gross@uq.edu.au */
30
31 /************************************************************************************/
32
33 #include "FCT_Solver.h"
34 #include "Preconditioner.h"
35 #include "PasoUtil.h"
36
37
38 Paso_FCT_Solver* Paso_FCT_Solver_alloc(Paso_TransportProblem *fctp, Paso_Options* options)
39 {
40 Paso_FCT_Solver* out=NULL;
41 const dim_t blockSize=Paso_TransportProblem_getBlockSize(fctp);
42 const dim_t n = Paso_TransportProblem_getTotalNumRows(fctp);
43
44 out=new Paso_FCT_Solver;
45 if (! Esys_checkPtr(out)) {
46 out->transportproblem = Paso_TransportProblem_getReference(fctp);
47 out->mpi_info = Esys_MPIInfo_getReference(fctp->mpi_info);
48 out->flux_limiter = Paso_FCT_FluxLimiter_alloc(fctp);
49 out->b = new double[n];
50 if ( (options->ode_solver == PASO_CRANK_NICOLSON) || (options->ode_solver == PASO_BACKWARD_EULER) ) {
51 out->du = new double[n];
52 out->z = new double[n];
53 } else {
54 out->du = NULL;
55 out->z=NULL;
56 }
57 out->u_coupler = Paso_Coupler_alloc(Paso_TransportProblem_borrowConnector(fctp), blockSize);
58 out->u_old_coupler = Paso_Coupler_alloc(Paso_TransportProblem_borrowConnector(fctp), blockSize);
59 out->omega=0;
60
61 if ( options->ode_solver == PASO_LINEAR_CRANK_NICOLSON ) {
62 out->method = PASO_LINEAR_CRANK_NICOLSON;
63 } else if ( options->ode_solver == PASO_CRANK_NICOLSON ) {
64 out->method = PASO_CRANK_NICOLSON;
65 } else if ( options->ode_solver == PASO_BACKWARD_EULER ) {
66 out->method = PASO_BACKWARD_EULER;
67 } else {
68 Esys_setError(VALUE_ERROR, "Paso_FCT_Solver_alloc: unknown integration scheme.");
69 out->method = UNKNOWN;
70 }
71
72 }
73
74 if (Esys_noError()) {
75 return out;
76 } else {
77 Paso_FCT_Solver_free(out);
78 return NULL;
79 }
80
81 }
82
83 void Paso_FCT_Solver_free(Paso_FCT_Solver *in)
84 {
85 if (in != NULL) {
86 Paso_TransportProblem_free(in->transportproblem);
87 Paso_FCT_FluxLimiter_free(in->flux_limiter);
88 Esys_MPIInfo_free(in->mpi_info);
89 Paso_Coupler_free(in->u_old_coupler);
90 Paso_Coupler_free(in->u_coupler);
91
92 delete[] in->b;
93 delete[] in->z;
94 delete[] in->du;
95 delete in;
96
97 }
98 }
99
100 double Paso_FCT_Solver_getSafeTimeStepSize(Paso_TransportProblem* fctp)
101 {
102 dim_t i, n;
103 double dt_max_loc=LARGE_POSITIVE_FLOAT;
104 double dt_max=LARGE_POSITIVE_FLOAT;
105 n=Paso_SystemMatrix_getTotalNumRows(fctp->transport_matrix);
106 /* set low order transport operator */
107 Paso_FCT_setLowOrderOperator(fctp);
108
109 if (Esys_noError()) {
110 /*
111 * calculate time step size:
112 */
113 dt_max=LARGE_POSITIVE_FLOAT;
114 #pragma omp parallel private(i, dt_max_loc)
115 {
116 dt_max_loc=LARGE_POSITIVE_FLOAT;
117 #pragma omp for schedule(static)
118 for (i=0;i<n;++i) {
119 const double l_ii=fctp->main_diagonal_low_order_transport_matrix[i];
120 const double m_i=fctp->lumped_mass_matrix[i];
121 if ( m_i > 0 ) {
122 if (l_ii<0) dt_max_loc=MIN(dt_max_loc,m_i/(-l_ii));
123 }
124 }
125 #pragma omp critical
126 {
127 dt_max=MIN(dt_max,dt_max_loc);
128 }
129 }
130 #ifdef ESYS_MPI
131 {
132 dt_max_loc=dt_max;
133 MPI_Allreduce(&dt_max_loc, &dt_max, 1, MPI_DOUBLE, MPI_MIN, fctp->mpi_info->comm);
134 }
135 #endif
136 if (dt_max<LARGE_POSITIVE_FLOAT) dt_max*=2.;
137 }
138 return dt_max;
139 }
140
141 /* modifies the main diagonal of the iteration matrix to introduce new dt */
142 void Paso_FCT_Solver_initialize(const double dt, Paso_FCT_Solver *fct_solver, Paso_Options* options, Paso_Performance* pp)
143 {
144 Paso_TransportProblem* fctp = fct_solver->transportproblem;
145 const index_t* main_iptr=Paso_TransportProblem_borrowMainDiagonalPointer(fctp);
146 const dim_t n=Paso_SystemMatrix_getTotalNumRows(fctp->transport_matrix);
147 const double theta = Paso_FCT_Solver_getTheta(fct_solver);
148 const double omega=1./(dt* theta);
149 dim_t i;
150 Paso_Options options2;
151
152
153
154 Paso_solve_free(fctp->iteration_matrix);
155 /*
156 * fctp->iteration_matrix[i,i]=m[i]/(dt theta) -l[i,i]
157 *
158 */
159 fct_solver->omega=omega;
160 fct_solver->dt = dt;
161 #pragma omp parallel for private(i)
162 for (i = 0; i < n; ++i) {
163 const double m_i=fctp->lumped_mass_matrix[i];
164 const double l_ii = fctp->main_diagonal_low_order_transport_matrix[i];
165 if ( m_i > 0 ) {
166 fctp->iteration_matrix->mainBlock->val[main_iptr[i]] = m_i * omega - l_ii;
167 } else {
168 fctp->iteration_matrix->mainBlock->val[main_iptr[i]] = ABS(m_i * omega - l_ii)/(EPSILON*EPSILON);
169 }
170 }
171
172 /* allocate preconditioner/solver */
173 Paso_Options_setDefaults(&options2);
174 options2.verbose = options->verbose;
175 if (fct_solver->method == PASO_LINEAR_CRANK_NICOLSON ) {
176 options2.preconditioner = PASO_GS;
177 } else {
178 options2.preconditioner = PASO_JACOBI;
179 /* options2.preconditioner = PASO_GS; */
180 }
181 options2.use_local_preconditioner = FALSE;
182 options2.sweeps=-1;
183
184 Performance_startMonitor(pp,PERFORMANCE_PRECONDITIONER_INIT);
185 Paso_SystemMatrix_setPreconditioner(fctp->iteration_matrix, &options2);
186 Performance_stopMonitor(pp,PERFORMANCE_PRECONDITIONER_INIT);
187 }
188
189 /* entry point for update procedures */
190 err_t Paso_FCT_Solver_update(Paso_FCT_Solver *fct_solver, double* u, double *u_old, Paso_Options* options, Paso_Performance *pp)
191 {
192 const index_t method=fct_solver->method;
193 err_t err_out = SOLVER_NO_ERROR;
194
195
196 if (method == PASO_LINEAR_CRANK_NICOLSON) {
197 err_out=Paso_FCT_Solver_update_LCN(fct_solver, u, u_old, options, pp);
198
199 } else if (method == PASO_CRANK_NICOLSON) {
200 err_out=Paso_FCT_Solver_updateNL(fct_solver, u, u_old, options, pp);
201
202 } else if (method == PASO_BACKWARD_EULER) {
203 err_out=Paso_FCT_Solver_updateNL(fct_solver, u, u_old, options, pp);
204 } else {
205 err_out = SOLVER_INPUT_ERROR;
206 }
207 return err_out;
208
209 }
210
211 /* linear crank-nicolson update */
212 err_t Paso_FCT_Solver_update_LCN(Paso_FCT_Solver *fct_solver, double * u, double *u_old, Paso_Options* options, Paso_Performance *pp)
213 {
214 double const dt = fct_solver->dt;
215 dim_t sweep_max, i;
216 double *b = fct_solver->b;
217 double const RTOL = options->tolerance;
218 const dim_t n=Paso_TransportProblem_getTotalNumRows(fct_solver->transportproblem);
219 Paso_SystemMatrix * iteration_matrix = fct_solver->transportproblem->iteration_matrix;
220 const index_t* main_iptr=Paso_TransportProblem_borrowMainDiagonalPointer(fct_solver->transportproblem);
221 err_t errorCode = SOLVER_NO_ERROR;
222 double norm_u_tilde;
223
224 Paso_Coupler_startCollect(fct_solver->u_old_coupler,u_old);
225 Paso_Coupler_finishCollect(fct_solver->u_old_coupler);
226
227 /* b[i]=m*u_tilde[i] = m u_old[i] + dt/2 sum_{j <> i} l_{ij}*(u_old[j]-u_old[i])
228 = u_tilde[i] = u_old[i] where constraint m<0.
229 * note that iteration_matrix stores the negative values of the
230 * low order transport matrix l. Therefore a=-dt*0.5 is used. */
231
232 Paso_FCT_Solver_setMuPaLu(b, fct_solver->transportproblem->lumped_mass_matrix,
233 fct_solver->u_old_coupler, -dt*0.5, iteration_matrix);
234 /* solve for u_tilde : u_tilda = m^{-1} * b */
235 Paso_FCT_FluxLimiter_setU_tilda(fct_solver->flux_limiter, b);
236 /* u_tilda_connector is completed */
237
238 /* calculate anti-diffusive fluxes for u_tilda */
239 Paso_FCT_setAntiDiffusionFlux_linearCN(fct_solver->flux_limiter->antidiffusive_fluxes,
240 fct_solver->transportproblem, dt,
241 fct_solver->flux_limiter->u_tilde_coupler,
242 fct_solver->u_old_coupler);
243
244
245 /* b_i += sum_{j} limitation factor_{ij} * antidiffusive_flux_{ij} */
246 Paso_FCT_FluxLimiter_addLimitedFluxes_Start(fct_solver->flux_limiter);
247 Paso_FCT_FluxLimiter_addLimitedFluxes_Complete(fct_solver->flux_limiter, b);
248
249 Paso_Scale(n, b,fct_solver->omega );
250 /* solve (m-dt/2*L) u = b in the form (omega*m-L) u = b * omega with omega*dt/2=1 */
251 #pragma omp for private(i) schedule(static)
252 for (i = 0; i < n; ++i) {
253 if (! (fct_solver->transportproblem->lumped_mass_matrix[i] > 0 ) ) {
254 b[i] = fct_solver->flux_limiter->u_tilde[i]
255 * fct_solver->transportproblem->iteration_matrix->mainBlock->val[main_iptr[i]];
256 }
257 }
258 /* initial guess is u<- -u + 2*u_tilde */
259 Paso_Update(n, -1., u, 2., fct_solver->flux_limiter->u_tilde);
260
261 sweep_max = MAX((int) (- 2 * log(RTOL)/log(2.)-0.5),1);
262 norm_u_tilde=Paso_lsup(n, fct_solver->flux_limiter->u_tilde, fct_solver->flux_limiter->mpi_info);
263 if (options->verbose) {
264 printf("Paso_FCT_Solver_update_LCN: u_tilda lsup = %e (rtol = %e, max. sweeps = %d)\n",norm_u_tilde,RTOL * norm_u_tilde ,sweep_max);
265 }
266 errorCode = Paso_Preconditioner_Smoother_solve_byTolerance( iteration_matrix, ((Paso_Preconditioner*) (iteration_matrix->solver_p))->gs,
267 u, b, RTOL, &sweep_max, TRUE);
268 if (errorCode == PRECONDITIONER_NO_ERROR) {
269 if (options->verbose) printf("Paso_FCT_Solver_update_LCN: convergence after %d Gauss-Seidel steps.\n",sweep_max);
270 errorCode=SOLVER_NO_ERROR;
271 } else {
272 if (options->verbose) printf("Paso_FCT_Solver_update_LCN: Gauss-Seidel failed within %d stesp (rel. tolerance %e).\n",sweep_max,RTOL);
273 errorCode= SOLVER_MAXITER_REACHED;
274 }
275 return errorCode;
276
277 }
278
279 err_t Paso_FCT_Solver_updateNL(Paso_FCT_Solver *fct_solver, double* u, double *u_old, Paso_Options* options, Paso_Performance *pp)
280 {
281 const dim_t num_critical_rates_max=3; /* number of rates >=critical_rate accepted before divergence is triggered */
282 const double critical_rate=0.95; /* expected value of convergence rate */
283
284 double *b = fct_solver->b;
285 double *z = fct_solver->z;
286 double *du = fct_solver->du;
287 double const dt = fct_solver->dt;
288 Paso_TransportProblem* fctp = fct_solver->transportproblem;
289 Paso_FCT_FluxLimiter* flux_limiter = fct_solver->flux_limiter;
290 dim_t i;
291 double norm_u_tilde, ATOL, norm_du=LARGE_POSITIVE_FLOAT, norm_du_old, rate=1.;
292 err_t errorCode=SOLVER_NO_ERROR;
293 const dim_t n=Paso_SystemMatrix_getTotalNumRows(fctp->transport_matrix);
294 const double atol=options->absolute_tolerance;
295 const double rtol=options->tolerance;
296 const dim_t max_m=options->iter_max;
297 dim_t m=0, num_critical_rates=0 ;
298 /* ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////// */
299
300 bool converged=FALSE, max_m_reached=FALSE,diverged=FALSE;
301 options->num_iter=0;
302
303 Paso_Coupler_startCollect(fct_solver->u_old_coupler,u_old);
304 Paso_Coupler_finishCollect(fct_solver->u_old_coupler);
305 /* prepare u_tilda and flux limiter */
306 if ( fct_solver->method == PASO_BACKWARD_EULER ) {
307 /* b[i]=m_i* u_old[i] */
308 #pragma omp for private(i) schedule(static)
309 for (i = 0; i < n; ++i) {
310 if (fctp->lumped_mass_matrix[i] > 0 ) {
311 b[i]=u_old[i]* fctp->lumped_mass_matrix[i];
312 } else {
313 b[i]=u_old[i];
314 }
315 }
316 } else {
317 /* 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
318 * = u_old[i] otherwise
319 * note that iteration_matrix stores the negative values of the
320 * low order transport matrix l. Therefore a=-dt*0.5 is used. */
321 Paso_FCT_Solver_setMuPaLu(b,fctp->lumped_mass_matrix,fct_solver->u_old_coupler,-dt*0.5,fctp->iteration_matrix);
322 }
323 Paso_FCT_FluxLimiter_setU_tilda(flux_limiter, b); /* u_tilda = m^{-1} b */
324 /* u_tilda_connector is completed */
325 /********************************************************************************************************************************************/
326 /* calculate stopping criterion */
327 norm_u_tilde=Paso_lsup(n, flux_limiter->u_tilde, flux_limiter->mpi_info);
328 ATOL= rtol * norm_u_tilde + atol ;
329 if (options->verbose) printf("Paso_FCT_Solver_updateNL: iteration starts u_tilda lsup = %e (abs. tol = %e)\n",norm_u_tilde,ATOL);
330 /* ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////// */
331
332 /* u_old is an initial guess for u*/
333 Paso_Copy(n,u,u_old);
334
335 while ( (!converged) && (!diverged) && (! max_m_reached) && Esys_noError()) {
336 Paso_Coupler_startCollect(fct_solver->u_coupler,u);
337 Paso_Coupler_finishCollect(fct_solver->u_coupler);
338
339 /* set antidiffusive_flux_{ij} for u */
340 if (fct_solver->method == PASO_BACKWARD_EULER) {
341 Paso_FCT_setAntiDiffusionFlux_BE(fct_solver->flux_limiter->antidiffusive_fluxes, fctp, dt, fct_solver->u_coupler, fct_solver->u_old_coupler);
342 } else {
343 Paso_FCT_setAntiDiffusionFlux_CN(fct_solver->flux_limiter->antidiffusive_fluxes, fctp, dt, fct_solver->u_coupler, fct_solver->u_old_coupler);
344 }
345 /* start the calculation of the limitation factors_{fct_solver->ij} */
346 Paso_FCT_FluxLimiter_addLimitedFluxes_Start(flux_limiter); /* uses u_tilde */
347
348 /*
349 * z_m[i]=b[i] - (m_i*u[i] - omega*sum_{j<>i} l_{ij} (u[j]-u[i]) ) where m_i>0
350 * ==b[i] - u[i] = u_tilda[i]-u[i] =0 otherwise
351 *
352 * omega = dt/2 or dt .
353 *
354 * note that iteration_matrix stores the negative values of the
355 * low order transport matrix l. Therefore a=dt*theta is used.
356 */
357 if (fct_solver-> method == PASO_BACKWARD_EULER) {
358 Paso_FCT_Solver_setMuPaLu(z, fctp->lumped_mass_matrix, fct_solver->u_coupler, dt, fctp->iteration_matrix);
359 } else {
360 Paso_FCT_Solver_setMuPaLu(z, fctp->lumped_mass_matrix, fct_solver->u_coupler, dt/2, fctp->iteration_matrix);
361 }
362
363
364 Paso_Update(n,-1.,z,1.,b); /* z=b-z */
365
366 /* z_i += sum_{j} limitation factor_{ij} * antidiffusive_flux_{ij} */
367 Paso_FCT_FluxLimiter_addLimitedFluxes_Complete(flux_limiter, z);
368
369 /* we solve (m/omega - L ) * du = z */
370 if (fct_solver->method == PASO_BACKWARD_EULER) {
371 dim_t cntIter = options->iter_max;
372 double tol= Paso_l2(n, z, fctp->mpi_info) ;
373
374 if ( m ==0) {
375 tol *=0.5;
376 } else {
377 tol *= MIN(MAX(rate*rate, 1e-2), 0.5);
378 }
379 /* use BiCGSTab with jacobi preconditioner ( m - omega * L ) */
380 Paso_zeroes(n,du);
381 errorCode = Paso_Solver_BiCGStab(fctp->iteration_matrix, z, du, &cntIter, &tol, pp);
382
383 /* errorCode = Paso_Solver_GMRES(fctp->iteration_matrix, z, du, &cntIter, &tol, 10, 2000, pp); */
384 if (options->verbose) printf("Paso_FCT_Solver_updateNL: BiCGStab is completed after %d steps (residual =%e).\n",cntIter, tol);
385 options->num_iter+=cntIter;
386 if ( errorCode != SOLVER_NO_ERROR) break;
387 } else {
388 /* just use the main diagonal of (m/omega - L ) */
389
390 Paso_Preconditioner_Smoother_solve(fctp->iteration_matrix, ((Paso_Preconditioner*) (fctp->iteration_matrix->solver_p))->jacobi,
391 du, z, 1, FALSE);
392
393 options->num_iter++;
394 }
395
396
397 Paso_Update(n,1.,u,fct_solver->omega,du);
398 norm_du_old=norm_du;
399 norm_du=Paso_lsup(n,du, fctp->mpi_info);
400 if (m ==0) {
401 if (options->verbose) printf("Paso_FCT_Solver_updateNL: step %d: increment= %e\n",m+1, norm_du * fct_solver->omega);
402 } else {
403 if (norm_du_old > 0.) {
404 rate=norm_du/norm_du_old;
405 } else if (norm_du <= 0.) {
406 rate=0.;
407 } else {
408 rate=LARGE_POSITIVE_FLOAT;
409 }
410 if (options->verbose) printf("Paso_FCT_Solver_updateNL: step %d: increment= %e (rate = %e)\n",m+1, norm_du * fct_solver->omega, rate);
411 num_critical_rates+=( rate<critical_rate ? 0 : 1);
412 max_m_reached=(m>max_m);
413 diverged = (num_critical_rates >= num_critical_rates_max);
414 converged=(norm_du * fct_solver->omega <= ATOL) ;
415 }
416 m++;
417 } /* end of while loop */
418 if (errorCode == SOLVER_NO_ERROR) {
419 if (converged) {
420 if (options->verbose) printf("Paso_FCT_Solver_updateNL: iteration is completed.\n");
421 errorCode=SOLVER_NO_ERROR;
422 } else if (diverged) {
423 if (options->verbose) printf("Paso_FCT_Solver_updateNL: divergence.\n");
424 errorCode=SOLVER_DIVERGENCE;
425 } else if (max_m_reached) {
426 if (options->verbose) printf("Paso_FCT_Solver_updateNL: maximum number of iteration steps reached.\n");
427 errorCode=SOLVER_MAXITER_REACHED;
428 }
429
430 }
431 return errorCode;
432 }
433
434
435 /*
436 * AntiDiffusionFlux:
437 *
438 * 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])
439 *
440 * m=fc->mass matrix
441 * d=artificial diffusion matrix = L - K = - fc->iteration matrix - fc->transport matrix (away from main diagonal)
442 *
443 * for CN : theta =0.5
444 * for BE : theta = 1.
445 */
446
447 void Paso_FCT_setAntiDiffusionFlux_CN(Paso_SystemMatrix *flux_matrix,
448 const Paso_TransportProblem* fct,
449 const double dt,
450 const Paso_Coupler* u_coupler,
451 const Paso_Coupler* u_old_coupler)
452 {
453 dim_t i;
454 index_t iptr_ij;
455
456 const double *u = Paso_Coupler_borrowLocalData(u_coupler);
457 const double *u_old= Paso_Coupler_borrowLocalData(u_old_coupler);
458 const double *remote_u=Paso_Coupler_borrowRemoteData(u_coupler);
459 const double *remote_u_old=Paso_Coupler_borrowRemoteData(u_old_coupler);
460 const double dt_half= dt/2;
461 const Paso_SystemMatrixPattern *pattern=fct->iteration_matrix->pattern;
462 const dim_t n=Paso_SystemMatrix_getTotalNumRows(fct->iteration_matrix);
463
464 #pragma omp parallel for schedule(static) private(i, iptr_ij)
465 for (i = 0; i < n; ++i) {
466 const double u_i = u[i];
467 const double u_old_i = u_old[i];
468
469 #pragma ivdep
470 for (iptr_ij=(pattern->mainPattern->ptr[i]);iptr_ij<pattern->mainPattern->ptr[i+1]; ++iptr_ij) {
471 const index_t j = pattern->mainPattern->index[iptr_ij];
472 const double m_ij = fct->mass_matrix->mainBlock->val[iptr_ij];
473 const double d_ij = fct->transport_matrix->mainBlock->val[iptr_ij]+fct->iteration_matrix->mainBlock->val[iptr_ij]; /* this is in fact -d_ij */
474 const double u_old_j = u_old[j];
475 const double u_j = u[j];
476
477 /* (m_{ij} - dt (1-theta) d_{ij}) (u_old[j]-u_old[i]) - (m_{ij} + dt theta d_{ij}) (u[j]-u[i]) */
478 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);
479
480 }
481 #pragma ivdep
482 for (iptr_ij=(pattern->col_couplePattern->ptr[i]);iptr_ij<pattern->col_couplePattern->ptr[i+1]; ++iptr_ij) {
483 const index_t j = pattern->col_couplePattern->index[iptr_ij];
484 const double m_ij = fct->mass_matrix->col_coupleBlock->val[iptr_ij];
485 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 */
486 const double u_old_j = remote_u_old[j];
487 const double u_j = remote_u[j];
488 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);
489 }
490 }
491 }
492
493 void Paso_FCT_setAntiDiffusionFlux_BE(Paso_SystemMatrix *flux_matrix,
494 const Paso_TransportProblem* fct,
495 const double dt,
496 const Paso_Coupler* u_coupler,
497 const Paso_Coupler* u_old_coupler)
498 {
499 dim_t i;
500 index_t iptr_ij;
501
502 const double *u=Paso_Coupler_borrowLocalData(u_coupler);
503 const double *u_old= Paso_Coupler_borrowLocalData(u_old_coupler);
504 const double *remote_u=Paso_Coupler_borrowRemoteData(u_coupler);
505 const double *remote_u_old=Paso_Coupler_borrowRemoteData(u_old_coupler);
506 const Paso_SystemMatrixPattern *pattern=fct->iteration_matrix->pattern;
507 const dim_t n=Paso_SystemMatrix_getTotalNumRows(fct->iteration_matrix);
508
509 #pragma omp parallel for schedule(static) private(i, iptr_ij)
510 for (i = 0; i < n; ++i) {
511 const double u_i = u[i];
512 const double u_old_i = u_old[i];
513 #pragma ivdep
514 for (iptr_ij=pattern->mainPattern->ptr[i]; iptr_ij<pattern->mainPattern->ptr[i+1]; ++iptr_ij) {
515
516 const index_t j = pattern->mainPattern->index[iptr_ij];
517 const double m_ij = fct->mass_matrix->mainBlock->val[iptr_ij];
518 const double d_ij = fct->transport_matrix->mainBlock->val[iptr_ij]+fct->iteration_matrix->mainBlock->val[iptr_ij]; /* this is in fact -d_ij */
519 const double u_old_j = u_old[j];
520 const double u_j = u[j];
521
522 flux_matrix->mainBlock->val[iptr_ij]=m_ij*(u_old_j-u_old_i)- (m_ij-dt*d_ij)*(u_j-u_i);
523 }
524 #pragma ivdep
525 for (iptr_ij=pattern->col_couplePattern->ptr[i]; iptr_ij<pattern->col_couplePattern->ptr[i+1]; ++iptr_ij) {
526 const index_t j = pattern->col_couplePattern->index[iptr_ij];
527 const double m_ij = fct->mass_matrix->col_coupleBlock->val[iptr_ij]; /* this is in fact -d_ij */
528 const double d_ij = fct->transport_matrix->col_coupleBlock->val[iptr_ij]+fct->iteration_matrix->col_coupleBlock->val[iptr_ij];
529 const double u_old_j = remote_u_old[j];
530 const double u_j = remote_u[j];
531
532 flux_matrix->col_coupleBlock->val[iptr_ij]=m_ij*(u_old_j-u_old_i)- (m_ij-dt*d_ij)*(u_j-u_i);
533 }
534 }
535 }
536
537 /* special version of the ant-diffusive fluxes for the linear Crank-Nicolson scheme
538 * in fact this is evaluated for u = 2*u_tilde - u_old which is the predictor
539 * of the solution of the the stabilised problem at time dt using the forward Euler scheme
540 *
541 * f_{ij} = (m_{ij} - dt/2 d_{ij}) (u_old[j]-u_old[i]) - (m_{ij} + dt/2 d_{ij}) (u[j]-u[i])
542 * = (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]) )
543 * = 2* m_{ij} * ( (u_old[j]-u_tilde[j] - (u_old[i]) - u_tilde[i]) ) - dt d_{ij} * (u_tilde[j]-u_tilde[i])
544 *
545 */
546
547 void Paso_FCT_setAntiDiffusionFlux_linearCN(Paso_SystemMatrix *flux_matrix,
548 const Paso_TransportProblem* fct,
549 const double dt,
550 const Paso_Coupler* u_tilde_coupler,
551 const Paso_Coupler* u_old_coupler)
552 {
553 dim_t i;
554 index_t iptr_ij;
555
556 const double *u_tilde=Paso_Coupler_borrowLocalData(u_tilde_coupler);
557 const double *u_old= Paso_Coupler_borrowLocalData(u_old_coupler);
558 const double *remote_u_tilde=Paso_Coupler_borrowRemoteData(u_tilde_coupler);
559 const double *remote_u_old=Paso_Coupler_borrowRemoteData(u_old_coupler);
560 const Paso_SystemMatrixPattern *pattern=fct->iteration_matrix->pattern;
561 const dim_t n=Paso_SystemMatrix_getTotalNumRows(fct->iteration_matrix);
562
563 #pragma omp parallel for schedule(static) private(i, iptr_ij)
564 for (i = 0; i < n; ++i) {
565 const double u_tilde_i = u_tilde[i];
566 const double u_old_i = u_old[i];
567 const double du_i = u_tilde_i - u_old_i;
568 #pragma ivdep
569 for (iptr_ij=(pattern->mainPattern->ptr[i]);iptr_ij<pattern->mainPattern->ptr[i+1]; ++iptr_ij) {
570
571 const index_t j = pattern->mainPattern->index[iptr_ij];
572 const double m_ij = fct->mass_matrix->mainBlock->val[iptr_ij];
573 const double d_ij = fct->transport_matrix->mainBlock->val[iptr_ij]+fct->iteration_matrix->mainBlock->val[iptr_ij]; /* this is in fact -d_ij */
574 const double u_tilde_j = u_tilde[j];
575 const double u_old_j = u_old[j];
576 const double du_j = u_tilde_j - u_old_j;
577
578 flux_matrix->mainBlock->val[iptr_ij]= 2 * m_ij * ( du_i - du_j ) - dt * d_ij * ( u_tilde_i - u_tilde_j);
579 }
580 #pragma ivdep
581 for (iptr_ij=(pattern->col_couplePattern->ptr[i]);iptr_ij<pattern->col_couplePattern->ptr[i+1]; ++iptr_ij) {
582
583 const index_t j = pattern->col_couplePattern->index[iptr_ij];
584 const double m_ij = fct->mass_matrix->col_coupleBlock->val[iptr_ij];
585 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 */
586 const double u_tilde_j = remote_u_tilde[j];
587 const double u_old_j = remote_u_old[j];
588 const double du_j = u_tilde_j - u_old_j;
589
590 flux_matrix->col_coupleBlock->val[iptr_ij]= 2 * m_ij * ( du_i - du_j ) - dt * d_ij * ( u_tilde_i - u_tilde_j);
591
592 }
593 }
594
595 }
596
597 /************************************************************************************/
598
599 /* Creates the low order transport matrix and stores its negative values
600 * into the iteration_matrix except for the main diagonal which is stored
601 * separately.
602 * If fc->iteration_matrix==NULL, fc->iteration_matrix is allocated
603 *
604 * a=transport_matrix
605 * b= low_order_transport_matrix = - iteration_matrix
606 * c=main diagonal low_order_transport_matrix
607 * initialise c[i] mit a[i,i]
608 *
609 * d_ij=max(0,-a[i,j],-a[j,i])
610 * b[i,j]=-(a[i,j]+d_ij)
611 * c[i]-=d_ij
612 */
613
614 void Paso_FCT_setLowOrderOperator(Paso_TransportProblem * fc) {
615
616 dim_t i;
617 index_t iptr_ij, iptr_ji;
618 const index_t* main_iptr=Paso_TransportProblem_borrowMainDiagonalPointer(fc);
619
620 if (fc->iteration_matrix==NULL) {
621 fc->iteration_matrix=Paso_SystemMatrix_alloc(fc->transport_matrix->type,
622 fc->transport_matrix->pattern,
623 fc->transport_matrix->row_block_size,
624 fc->transport_matrix->col_block_size, TRUE);
625 }
626
627 if (Esys_noError()) {
628 const Paso_SystemMatrixPattern *pattern=fc->iteration_matrix->pattern;
629 const dim_t n=Paso_SystemMatrix_getTotalNumRows(fc->iteration_matrix);
630 #pragma omp parallel for private(i, iptr_ij, iptr_ji) schedule(static)
631 for (i = 0; i < n; ++i) {
632 double sum=fc->transport_matrix->mainBlock->val[main_iptr[i]];
633
634 /* printf("sum[%d] = %e -> ", i, sum); */
635 /* look at a[i,j] */
636 for (iptr_ij=pattern->mainPattern->ptr[i];iptr_ij<pattern->mainPattern->ptr[i+1]; ++iptr_ij) {
637 const index_t j = pattern->mainPattern->index[iptr_ij];
638 const double rtmp1 = fc->transport_matrix->mainBlock->val[iptr_ij];
639 if (j!=i) {
640 /* find entry a[j,i] */
641 #pragma ivdep
642 for (iptr_ji=pattern->mainPattern->ptr[j]; iptr_ji<pattern->mainPattern->ptr[j+1]; ++iptr_ji) {
643
644 if ( pattern->mainPattern->index[iptr_ji] == i) {
645 const double rtmp2=fc->transport_matrix->mainBlock->val[iptr_ji];
646 /*
647 printf("a[%d,%d]=%e\n",i,j,rtmp1);
648 printf("a[%d,%d]=%e\n",j,i,rtmp2);
649 */
650
651 const double d_ij=-MIN3(0.,rtmp1,rtmp2);
652 fc->iteration_matrix->mainBlock->val[iptr_ij]=-(rtmp1+d_ij);
653 /* printf("l[%d,%d]=%e\n",i,j,fc->iteration_matrix->mainBlock->val[iptr_ij]); */
654 sum-=d_ij;
655 break;
656 }
657 }
658 }
659 }
660 for (iptr_ij=pattern->col_couplePattern->ptr[i];iptr_ij<pattern->col_couplePattern->ptr[i+1]; ++iptr_ij) {
661 const index_t j = pattern->col_couplePattern->index[iptr_ij];
662 const double rtmp1 = fc->transport_matrix->col_coupleBlock->val[iptr_ij];
663 /* find entry a[j,i] */
664 #pragma ivdep
665 for (iptr_ji=pattern->row_couplePattern->ptr[j]; iptr_ji<pattern->row_couplePattern->ptr[j+1]; ++iptr_ji) {
666 if (pattern->row_couplePattern->index[iptr_ji]==i) {
667 const double rtmp2=fc->transport_matrix->row_coupleBlock->val[iptr_ji];
668 const double d_ij=-MIN3(0.,rtmp1,rtmp2);
669 fc->iteration_matrix->col_coupleBlock->val[iptr_ij]=-(rtmp1+d_ij);
670 fc->iteration_matrix->row_coupleBlock->val[iptr_ji]=-(rtmp2+d_ij);
671 sum-=d_ij;
672 break;
673 }
674 }
675 }
676 /* set main diagonal entry */
677 fc->main_diagonal_low_order_transport_matrix[i]=sum;
678 /* printf("%e \n", sum); */
679 }
680
681 }
682 }
683
684 /*
685 * out_i=m_i u_i + a * \sum_{j <> i} l_{ij} (u_j-u_i) where m_i>0
686 * = u_i where m_i<=0
687 *
688 */
689 void Paso_FCT_Solver_setMuPaLu(double* out,
690 const double* M,
691 const Paso_Coupler* u_coupler,
692 const double a,
693 const Paso_SystemMatrix *L)
694 {
695 dim_t i;
696 const Paso_SystemMatrixPattern *pattern = L->pattern;
697 const double *u=Paso_Coupler_borrowLocalData(u_coupler);
698 const double *remote_u=Paso_Coupler_borrowRemoteData(u_coupler);
699 index_t iptr_ij;
700 const dim_t n=Paso_SystemMatrix_getTotalNumRows(L);
701
702 #pragma omp parallel for private(i) schedule(static)
703 for (i = 0; i < n; ++i) {
704 if ( M[i] > 0.) {
705 out[i]=M[i]*u[i];
706 } else {
707 out[i]=u[i];
708 }
709 }
710 if (ABS(a)>0) {
711 #pragma omp parallel for schedule(static) private(i, iptr_ij)
712 for (i = 0; i < n; ++i) {
713 if ( M[i] > 0.) {
714 double sum=0;
715 const double u_i=u[i];
716 #pragma ivdep
717 for (iptr_ij=(pattern->mainPattern->ptr[i]);iptr_ij<pattern->mainPattern->ptr[i+1]; ++iptr_ij) {
718 const index_t j=pattern->mainPattern->index[iptr_ij];
719 const double l_ij=L->mainBlock->val[iptr_ij];
720 sum+=l_ij*(u[j]-u_i);
721
722 }
723 #pragma ivdep
724 for (iptr_ij=(pattern->col_couplePattern->ptr[i]);iptr_ij<pattern->col_couplePattern->ptr[i+1]; ++iptr_ij) {
725 const index_t j=pattern->col_couplePattern->index[iptr_ij];
726 const double l_ij=L->col_coupleBlock->val[iptr_ij];
727 sum+=l_ij*(remote_u[j]-u_i);
728 }
729 out[i]+=a*sum;
730 }
731 }
732 }
733 }
734
735 /* ************************************************************************************************************************************************* */
736
737
738
739
740
741
742

Properties

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svn:mergeinfo /branches/amg_from_3530/paso/src/FCT_Solver.cpp:3531-3826 /branches/lapack2681/paso/src/FCT_Solver.cpp:2682-2741 /branches/pasowrap/paso/src/FCT_Solver.cpp:3661-3674 /branches/py3_attempt2/paso/src/FCT_Solver.cpp:3871-3891 /branches/restext/paso/src/FCT_Solver.cpp:2610-2624 /branches/ripleygmg_from_3668/paso/src/FCT_Solver.cpp:3669-3791 /branches/stage3.0/paso/src/FCT_Solver.cpp:2569-2590 /branches/symbolic_from_3470/paso/src/FCT_Solver.cpp:3471-3974 /branches/symbolic_from_3470/ripley/test/python/paso/src/FCT_Solver.cpp:3517-3974 /release/3.0/paso/src/FCT_Solver.cpp:2591-2601 /trunk/paso/src/FCT_Solver.cpp:4257-4344 /trunk/ripley/test/python/paso/src/FCT_Solver.cpp:3480-3515

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