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

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Revision 4818 - (show annotations)
Mon Mar 31 00:16:20 2014 UTC (6 years, 1 month ago) by caltinay
File size: 30755 byte(s)
SystemMatrixPattern shptr

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

Properties

Name Value
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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