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

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Revision 3793 - (show annotations)
Wed Feb 1 07:39:43 2012 UTC (7 years, 9 months ago) by gross
File MIME type: text/plain
File size: 30071 byte(s)
new implementation of FCT solver with some modifications to the python interface
1
2 /*******************************************************
3 *
4 * Copyright (c) 2003-2010 by University of Queensland
5 * Earth Systems Science Computational Center (ESSCC)
6 * http://www.uq.edu.au/esscc
7 *
8 * Primary Business: Queensland, Australia
9 * Licensed under the Open Software License version 3.0
10 * http://www.opensource.org/licenses/osl-3.0.php
11 *
12 *******************************************************/
13
14
15 /**************************************************************/
16
17 /* Paso: Transport solver with flux 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 index_t fail=0;
102 n=Paso_SystemMatrix_getTotalNumRows(fctp->transport_matrix);
103 /* set low order transport operator */
104 Paso_FCT_setLowOrderOperator(fctp);
105
106 if (Esys_noError()) {
107 /*
108 * calculate time step size:
109 */
110 dt_max=LARGE_POSITIVE_FLOAT;
111 fail=0;
112 #pragma omp parallel private(i)
113 {
114 double dt_max_loc=LARGE_POSITIVE_FLOAT;
115 index_t fail_loc=0;
116 #pragma omp for schedule(static)
117 for (i=0;i<n;++i) {
118 const register double l_ii=fctp->main_diagonal_low_order_transport_matrix[i];
119 const register double m_i=fctp->lumped_mass_matrix[i];
120 if ( (m_i > 0) ) {
121 if (l_ii<0) dt_max_loc=MIN(dt_max_loc,m_i/(-l_ii));
122 } else {
123 fail_loc=-1;
124 }
125 }
126 #pragma omp critical
127 {
128 dt_max=MIN(dt_max,dt_max_loc);
129 fail=MIN(fail, fail_loc);
130 }
131 }
132 #ifdef ESYS_MPI
133 {
134 double rtmp_loc[2], rtmp[2];
135 rtmp_loc[0]=dt_max;
136 rtmp_loc[1]= (double) fail;
137 MPI_Allreduce(rtmp_loc, rtmp, 2, MPI_DOUBLE, MPI_MIN, fctp->mpi_info->comm);
138 dt_max=rtmp[0];
139 fail = rtmp[1] < 0 ? -1 : 0;
140 }
141 #endif
142 if (fail < 0 ) {
143 Esys_setError(VALUE_ERROR, "Paso_FCTSolver_getSafeTimeStepSize: negative mass matrix entries detected.");
144 return -1;
145 } else {
146 if (dt_max<LARGE_POSITIVE_FLOAT) dt_max*=2.;
147 }
148 }
149 return dt_max;
150 }
151
152 /* modifies the main diagonal of the iteration matrix to introduce new dt */
153 void Paso_FCT_Solver_initialize(const double dt, Paso_FCT_Solver *fct_solver, Paso_Options* options, Paso_Performance* pp)
154 {
155 Paso_TransportProblem* fctp = fct_solver->transportproblem;
156 const index_t* main_iptr=Paso_TransportProblem_borrowMainDiagonalPointer(fctp);
157 const dim_t n=Paso_SystemMatrix_getTotalNumRows(fctp->transport_matrix);
158 const double theta = Paso_FCT_Solver_getTheta(fct_solver);
159 const double omega=1./(dt* theta);
160 dim_t i;
161 Paso_Options options2;
162
163
164
165 Paso_solve_free(fctp->iteration_matrix);
166 /*
167 * fctp->iteration_matrix[i,i]=m[i]/(dt theta) -l[i,i]
168 *
169 */
170 fct_solver->omega=omega;
171 fct_solver->dt = dt;
172 #pragma omp parallel for private(i)
173 for (i = 0; i < n; ++i) {
174 const register double m=fctp->lumped_mass_matrix[i];
175 const register double l_ii = fctp->main_diagonal_low_order_transport_matrix[i];
176 fctp->iteration_matrix->mainBlock->val[main_iptr[i]] = m * omega - l_ii;
177 }
178
179 /* allocate preconditioner/solver */
180 Paso_Options_setDefaults(&options2);
181 options2.verbose = options->verbose;
182 if (fct_solver->method == PASO_LINEAR_CRANK_NICOLSON ) {
183 options2.preconditioner = PASO_GS;
184 } else {
185 options2.preconditioner = PASO_JACOBI;
186 /* options2.preconditioner = PASO_GS; */
187 }
188 options2.use_local_preconditioner = FALSE;
189 options2.sweeps=1;
190
191 Performance_startMonitor(pp,PERFORMANCE_PRECONDITIONER_INIT);
192 Paso_SystemMatrix_setPreconditioner(fctp->iteration_matrix, &options2);
193 Performance_stopMonitor(pp,PERFORMANCE_PRECONDITIONER_INIT);
194 }
195
196 /* entry point for update proceedures */
197 err_t Paso_FCT_Solver_update(Paso_FCT_Solver *fct_solver, double* u, double *u_old, Paso_Options* options, Paso_Performance *pp)
198 {
199 const index_t method=fct_solver->method;
200 err_t err_out = SOLVER_NO_ERROR;
201
202
203 if (method == PASO_LINEAR_CRANK_NICOLSON) {
204 err_out=Paso_FCT_Solver_update_LCN(fct_solver, u, u_old, options, pp);
205
206 } else if (method == PASO_CRANK_NICOLSON) {
207 err_out=Paso_FCT_Solver_updateNL(fct_solver, u, u_old, options, pp);
208
209 } else if (method == PASO_BACKWARD_EULER) {
210 err_out=Paso_FCT_Solver_updateNL(fct_solver, u, u_old, options, pp);
211 } else {
212 err_out = SOLVER_INPUT_ERROR;
213 }
214 return err_out;
215
216 }
217
218 /* linear crank-nicolson update */
219 err_t Paso_FCT_Solver_update_LCN(Paso_FCT_Solver *fct_solver, double * u, double *u_old, Paso_Options* options, Paso_Performance *pp)
220 {
221 double const dt = fct_solver->dt;
222 dim_t sweep_max;
223 double *b = fct_solver->b;
224 double const RTOL = options->tolerance;
225 const dim_t n=Paso_TransportProblem_getTotalNumRows(fct_solver->transportproblem);
226 Paso_SystemMatrix * iteration_matrix = fct_solver->transportproblem->iteration_matrix;
227 err_t errorCode = SOLVER_NO_ERROR;
228
229
230 Paso_Coupler_startCollect(fct_solver->u_old_coupler,u_old);
231 Paso_Coupler_finishCollect(fct_solver->u_old_coupler);
232
233 /* b[i]=m*u_tilde[i] = m u_old[i] + dt/2 sum_{j <> i} l_{ij}*(u_old[j]-u_old[i])
234 * note that iteration_matrix stores the negative values of the
235 * low order transport matrix l. Therefore a=-dt*0.5 is used. */
236
237 Paso_FCT_Solver_setMuPaLu(b, fct_solver->transportproblem->lumped_mass_matrix,
238 fct_solver->u_old_coupler, -dt*0.5, iteration_matrix);
239
240 /* solve for u_tilde : u_tilda = m^{-1} * b */
241 Paso_FCT_FluxLimiter_setU_tilda(fct_solver->flux_limiter, b);
242 /* u_tilda_connector is completed */
243
244 /* calculate anti-diffusive fluxes for u_tilda */
245 Paso_FCT_setAntiDiffusionFlux_linearCN(fct_solver->flux_limiter->antidiffusive_fluxes,
246 fct_solver->transportproblem, dt,
247 fct_solver->flux_limiter->u_tilde_coupler,
248 fct_solver->u_old_coupler);
249
250 /* b_i += sum_{j} limitation factor_{ij} * antidiffusive_flux_{ij} */
251 Paso_FCT_FluxLimiter_addLimitedFluxes_Start(fct_solver->flux_limiter);
252 Paso_FCT_FluxLimiter_addLimitedFluxes_Complete(fct_solver->flux_limiter, b);
253
254
255 /* solve (m-dt/2*L) u = b */
256 /* initial guess is u<- -u + 2*u_tilde */
257 Paso_Update(n, -1., u, 2., fct_solver->flux_limiter->u_tilde);
258 sweep_max = MAX((int) (- 2 * log(RTOL)/log(2.)-0.5),1);
259
260 errorCode = Paso_Preconditioner_Smoother_solve_byTolerance( iteration_matrix, ((Paso_Preconditioner*) (iteration_matrix->solver_p))->gs,
261 u, b, RTOL, &sweep_max, TRUE);
262 if (errorCode == PRECONDITIONER_NO_ERROR) {
263 if (options->verbose) printf("Paso_FCT_Solver_update_LCN: convergence after %d Gauss-Seidel steps.\n",sweep_max);
264 errorCode=SOLVER_NO_ERROR;
265 } else {
266 if (options->verbose) printf("Paso_FCT_Solver_update_LCN: Gauss-Seidel failed within %d stesp (rel. tolerance %e).\n",sweep_max,RTOL);
267 errorCode= SOLVER_MAXITER_REACHED;
268 }
269 return errorCode;
270
271 }
272
273 err_t Paso_FCT_Solver_updateNL(Paso_FCT_Solver *fct_solver, double* u, double *u_old, Paso_Options* options, Paso_Performance *pp)
274 {
275 double *b = fct_solver->b;
276 double *z = fct_solver->z;
277 double *du = fct_solver->du;
278 double const dt = fct_solver->dt;
279 Paso_TransportProblem* fctp = fct_solver->transportproblem;
280 Paso_FCT_FluxLimiter* flux_limiter = fct_solver->flux_limiter;
281 dim_t i;
282 const dim_t num_critical_rates_max=3; /* number of rates >=critical_rate accepted before divergence is triggered */
283 const double critical_rate=0.95; /* expected value of convergence rate */
284
285 double norm_u_tilde, ATOL, norm_du=LARGE_POSITIVE_FLOAT, norm_du_old, rate;
286 err_t errorCode=SOLVER_NO_ERROR;
287 const dim_t n=Paso_SystemMatrix_getTotalNumRows(fctp->transport_matrix);
288 const double atol=options->absolute_tolerance;
289 const double rtol=options->tolerance;
290 const dim_t max_m=options->iter_max;
291 dim_t m=0, num_critical_rates=0 ;
292 /* ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////// */
293
294 bool_t converged=FALSE, max_m_reached=FALSE,diverged=FALSE;
295 options->num_iter=0;
296
297 Paso_Coupler_startCollect(fct_solver->u_old_coupler,u_old);
298 Paso_Coupler_finishCollect(fct_solver->u_old_coupler);
299 /* prepare u_tilda and flux limiter */
300 if ( fct_solver->method == PASO_BACKWARD_EULER ) {
301 /* b[i]=m_i* u_old[i] */
302 #pragma omp for private(i) schedule(static)
303 for (i = 0; i < n; ++i) {
304 b[i]=u_old[i]* fctp->lumped_mass_matrix[i];
305 }
306 } else {
307 /* 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
308 * 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
315 /**********************************************************************************************************************/
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 * z_m[i]=b[i] - (m_i*u[i] - omega*sum_{j<>i} l_{ij} (u[j]-u[i]) ) omega = dt/2 or dt .
340 *
341 * note that iteration_matrix stores the negative values of the
342 * low order transport matrix l. Therefore a=dt*theta is used.
343 */
344 if (fct_solver-> method == PASO_BACKWARD_EULER) {
345 Paso_FCT_Solver_setMuPaLu(z, fctp->lumped_mass_matrix, fct_solver->u_coupler, dt, fctp->iteration_matrix);
346 } else {
347 Paso_FCT_Solver_setMuPaLu(z, fctp->lumped_mass_matrix, fct_solver->u_coupler, dt/2, fctp->iteration_matrix);
348 }
349
350
351 Paso_Update(n,-1.,z,1.,b); /* z=b-z */
352
353
354 /* z_i += sum_{j} limitation factor_{ij} * antidiffusive_flux_{ij} */
355 Paso_FCT_FluxLimiter_addLimitedFluxes_Complete(flux_limiter, z);
356
357 /* we solve (m/omega - L ) * du = z */
358 if (fct_solver->method == PASO_BACKWARD_EULER) {
359 dim_t cntIter = options->iter_max;
360 double tol= Paso_l2(n, z, fctp->mpi_info) ;
361
362 if ( m ==0) {
363 tol *=0.5;
364 } else {
365 tol *= MIN(MAX(rate*rate, 1e-2), 0.5);
366 }
367 /* use BiCGSTab with jacobi preconditioner ( m - omega * L ) */
368 Paso_zeroes(n,du);
369 errorCode = Paso_Solver_BiCGStab(fctp->iteration_matrix, z, du, &cntIter, &tol, pp);
370
371 /* errorCode = Paso_Solver_GMRES(fctp->iteration_matrix, z, du, &cntIter, &tol, 10, 2000, pp); */
372 if (options->verbose) printf("Paso_FCT_Solver_updateNL: BiCGStab is completed after %d steps (residual =%e).\n",cntIter, tol);
373 options->num_iter+=cntIter;
374 if ( errorCode != SOLVER_NO_ERROR) break;
375 } else {
376 /* just use the main diagonal of (m/omega - L ) */
377
378 Paso_Preconditioner_Smoother_solve(fctp->iteration_matrix, ((Paso_Preconditioner*) (fctp->iteration_matrix->solver_p))->jacobi,
379 du, z, 1, FALSE);
380 options->num_iter++;
381 }
382
383
384 Paso_Update(n,1.,u,fct_solver->omega,du);
385 norm_du_old=norm_du;
386 norm_du=Paso_lsup(n,du, fctp->mpi_info);
387 if (m ==0) {
388 if (options->verbose) printf("Paso_FCT_Solver_updateNL: step %d: increment= %e\n",m+1, norm_du * fct_solver->omega);
389 } else {
390 if (norm_du_old > 0.) {
391 rate=norm_du/norm_du_old;
392 } else if (norm_du <= 0.) {
393 rate=0.;
394 } else {
395 rate=LARGE_POSITIVE_FLOAT;
396 }
397 if (options->verbose) printf("Paso_FCT_Solver_updateNL: step %d: increment= %e (rate = %e)\n",m+1, norm_du * fct_solver->omega, rate);
398 num_critical_rates+=( rate<critical_rate ? 0 : 1);
399 max_m_reached=(m>max_m);
400 diverged = (num_critical_rates >= num_critical_rates_max);
401 converged=(norm_du * fct_solver->omega <= ATOL) ;
402 }
403 m++;
404 } /* end of while loop */
405 if (errorCode == SOLVER_NO_ERROR) {
406 if (converged) {
407 if (options->verbose) printf("Paso_FCT_Solver_updateNL: iteration is completed.\n");
408 errorCode=SOLVER_NO_ERROR;
409 } else if (diverged) {
410 if (options->verbose) printf("Paso_FCT_Solver_updateNL: divergence.\n");
411 errorCode=SOLVER_DIVERGENCE;
412 } else if (max_m_reached) {
413 if (options->verbose) printf("Paso_FCT_Solver_updateNL: maximum number of iteration steps reached.\n");
414 errorCode=SOLVER_MAXITER_REACHED;
415 }
416
417 }
418 return errorCode;
419 }
420
421
422 /*
423 * AntiDiffusionFlux:
424 *
425 * 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])
426 *
427 * m=fc->mass matrix
428 * d=artifical diffusion matrix = L - K = - fc->iteration matrix - fc->transport matrix (away from main diagonal)
429 *
430 * for CN : theta =0.5
431 * for BE : theta = 1.
432 */
433
434 void Paso_FCT_setAntiDiffusionFlux_CN(Paso_SystemMatrix *flux_matrix,
435 const Paso_TransportProblem* fct,
436 const double dt,
437 const Paso_Coupler* u_coupler,
438 const Paso_Coupler* u_old_coupler)
439 {
440 dim_t i;
441 index_t iptr_ij;
442
443 const double *u = Paso_Coupler_borrowLocalData(u_coupler);
444 const double *u_old= Paso_Coupler_borrowLocalData(u_old_coupler);
445 const double *remote_u=Paso_Coupler_borrowRemoteData(u_coupler);
446 const double *remote_u_old=Paso_Coupler_borrowRemoteData(u_old_coupler);
447 const double dt_half= dt/2;
448 const Paso_SystemMatrixPattern *pattern=fct->iteration_matrix->pattern;
449 const dim_t n=Paso_SystemMatrix_getTotalNumRows(fct->iteration_matrix);
450
451 #pragma omp parallel for schedule(static) private(i, iptr_ij)
452 for (i = 0; i < n; ++i) {
453 const register double u_i = u[i];
454 const register double u_old_i = u_old[i];
455
456 #pragma ivdep
457 for (iptr_ij=(pattern->mainPattern->ptr[i]);iptr_ij<pattern->mainPattern->ptr[i+1]; ++iptr_ij) {
458 const register index_t j = pattern->mainPattern->index[iptr_ij];
459 const register double m_ij = fct->mass_matrix->mainBlock->val[iptr_ij];
460 const register double d_ij = fct->transport_matrix->mainBlock->val[iptr_ij]+fct->iteration_matrix->mainBlock->val[iptr_ij]; /* this is in fact -d_ij */
461 const register double u_old_j = u_old[j];
462 const register double u_j = u[j];
463
464 /* (m_{ij} - dt (1-theta) d_{ij}) (u_old[j]-u_old[i]) - (m_{ij} + dt theta d_{ij}) (u[j]-u[i]) */
465 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);
466
467 }
468 #pragma ivdep
469 for (iptr_ij=(pattern->col_couplePattern->ptr[i]);iptr_ij<pattern->col_couplePattern->ptr[i+1]; ++iptr_ij) {
470 const register index_t j = pattern->col_couplePattern->index[iptr_ij];
471 const register double m_ij = fct->mass_matrix->col_coupleBlock->val[iptr_ij];
472 const register 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 */
473 const register double u_old_j = remote_u_old[j];
474 const register double u_j = remote_u[j];
475 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);
476 }
477 }
478 }
479
480 void Paso_FCT_setAntiDiffusionFlux_BE(Paso_SystemMatrix *flux_matrix,
481 const Paso_TransportProblem* fct,
482 const double dt,
483 const Paso_Coupler* u_coupler,
484 const Paso_Coupler* u_old_coupler)
485 {
486 dim_t i;
487 index_t iptr_ij;
488
489 const double *u=Paso_Coupler_borrowLocalData(u_coupler);
490 const double *u_old= Paso_Coupler_borrowLocalData(u_old_coupler);
491 const double *remote_u=Paso_Coupler_borrowRemoteData(u_coupler);
492 const double *remote_u_old=Paso_Coupler_borrowRemoteData(u_old_coupler);
493 const Paso_SystemMatrixPattern *pattern=fct->iteration_matrix->pattern;
494 const dim_t n=Paso_SystemMatrix_getTotalNumRows(fct->iteration_matrix);
495
496 #pragma omp parallel for schedule(static) private(i, iptr_ij)
497 for (i = 0; i < n; ++i) {
498 const register double u_i = u[i];
499 const register double u_old_i = u_old[i];
500 #pragma ivdep
501 for (iptr_ij=pattern->mainPattern->ptr[i]; iptr_ij<pattern->mainPattern->ptr[i+1]; ++iptr_ij) {
502
503 const register index_t j = pattern->mainPattern->index[iptr_ij];
504 const register double m_ij = fct->mass_matrix->mainBlock->val[iptr_ij];
505 const register double d_ij = fct->transport_matrix->mainBlock->val[iptr_ij]+fct->iteration_matrix->mainBlock->val[iptr_ij]; /* this is in fact -d_ij */
506 const register double u_old_j = u_old[j];
507 const register double u_j = u[j];
508
509 flux_matrix->mainBlock->val[iptr_ij]=m_ij*(u_old_j-u_old_i)- (m_ij-dt*d_ij)*(u_j-u_i);
510 }
511 #pragma ivdep
512 for (iptr_ij=pattern->col_couplePattern->ptr[i]; iptr_ij<pattern->col_couplePattern->ptr[i+1]; ++iptr_ij) {
513 const register index_t j = pattern->col_couplePattern->index[iptr_ij];
514 const register double m_ij = fct->mass_matrix->col_coupleBlock->val[iptr_ij]; /* this is in fact -d_ij */
515 const register double d_ij = fct->transport_matrix->col_coupleBlock->val[iptr_ij]+fct->iteration_matrix->col_coupleBlock->val[iptr_ij];
516 const register double u_old_j = remote_u_old[j];
517 const register double u_j = remote_u[j];
518
519 flux_matrix->col_coupleBlock->val[iptr_ij]=m_ij*(u_old_j-u_old_i)- (m_ij-dt*d_ij)*(u_j-u_i);
520 }
521 }
522 }
523
524 /* special version of the ant-diffusive fluxes for the linear Crank-Nicolson scheme
525 * in fact this is evaluated for u = 2*u_tilde - u_old which is the predictor
526 * of the solution of the the stabilized problem at time dt using the forward Euler scheme
527 *
528 * f_{ij} = (m_{ij} - dt/2 d_{ij}) (u_old[j]-u_old[i]) - (m_{ij} + dt/2 d_{ij}) (u[j]-u[i])
529 * = (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]) )
530 * = 2* m_{ij} * ( (u_old[j]-u_tilde[j] - (u_old[i]) - u_tilde[i]) ) - dt d_{ij} * (u_tilde[j]-u_tilde[i])
531 *
532 */
533
534 void Paso_FCT_setAntiDiffusionFlux_linearCN(Paso_SystemMatrix *flux_matrix,
535 const Paso_TransportProblem* fct,
536 const double dt,
537 const Paso_Coupler* u_tilde_coupler,
538 const Paso_Coupler* u_old_coupler)
539 {
540 dim_t i;
541 index_t iptr_ij;
542
543 const double *u_tilde=Paso_Coupler_borrowLocalData(u_tilde_coupler);
544 const double *u_old= Paso_Coupler_borrowLocalData(u_old_coupler);
545 const double *remote_u_tilde=Paso_Coupler_borrowRemoteData(u_tilde_coupler);
546 const double *remote_u_old=Paso_Coupler_borrowRemoteData(u_old_coupler);
547 const Paso_SystemMatrixPattern *pattern=fct->iteration_matrix->pattern;
548 const dim_t n=Paso_SystemMatrix_getTotalNumRows(fct->iteration_matrix);
549
550 #pragma omp parallel for schedule(static) private(i, iptr_ij)
551 for (i = 0; i < n; ++i) {
552 const register double u_tilde_i = u_tilde[i];
553 const register double u_old_i = u_old[i];
554 const register double du_i = u_old_i - u_tilde_i;
555 #pragma ivdep
556 for (iptr_ij=(pattern->mainPattern->ptr[i]);iptr_ij<pattern->mainPattern->ptr[i+1]; ++iptr_ij) {
557
558 const register index_t j = pattern->mainPattern->index[iptr_ij];
559 const register double m_ij = fct->mass_matrix->mainBlock->val[iptr_ij];
560 const register double d_ij = fct->transport_matrix->mainBlock->val[iptr_ij]+fct->iteration_matrix->mainBlock->val[iptr_ij]; /* this is in fact -d_ij */
561 const register double u_tilde_j = u_tilde[j];
562 const register double u_old_j = u_old[j];
563 const register double du_j = u_old_j - u_tilde_j;
564
565 flux_matrix->mainBlock->val[iptr_ij]=2 * m_ij * ( du_i - du_j ) + dt * d_ij * ( u_tilde_j - u_tilde_i);
566
567 }
568 #pragma ivdep
569 for (iptr_ij=(pattern->col_couplePattern->ptr[i]);iptr_ij<pattern->col_couplePattern->ptr[i+1]; ++iptr_ij) {
570
571 const register index_t j = pattern->col_couplePattern->index[iptr_ij];
572 const register double m_ij = fct->mass_matrix->col_coupleBlock->val[iptr_ij];
573 const register 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 */
574 const register double u_tilde_j = remote_u_tilde[j];
575 const register double u_old_j = remote_u_old[j];
576 const register double du_j = u_old_j - u_tilde_j;
577
578 flux_matrix->col_coupleBlock->val[iptr_ij]= 2 * m_ij * ( du_i - du_j ) + dt * d_ij * ( u_tilde_j - u_tilde_i);
579
580 }
581 }
582
583 }
584
585 /**************************************************************/
586
587 /* Creates the low order transport matrix and stores its negative values
588 * into the iteration_matrix except for the main diagonal which is stored
589 * separately.
590 * If fc->iteration_matrix==NULL, fc->iteration_matrix is allocated
591 *
592 * a=transport_matrix
593 * b= low_order_transport_matrix = - iteration_matrix
594 * c=main diagonal low_order_transport_matrix
595 * initialize c[i] mit a[i,i]
596 *
597 * d_ij=max(0,-a[i,j],-a[j,i])
598 * b[i,j]=-(a[i,j]+d_ij)
599 * c[i]-=d_ij
600 */
601
602 void Paso_FCT_setLowOrderOperator(Paso_TransportProblem * fc) {
603
604 dim_t i;
605 index_t iptr_ij, iptr_ji;
606 const index_t* main_iptr=Paso_TransportProblem_borrowMainDiagonalPointer(fc);
607
608 if (fc->iteration_matrix==NULL) {
609 fc->iteration_matrix=Paso_SystemMatrix_alloc(fc->transport_matrix->type,
610 fc->transport_matrix->pattern,
611 fc->transport_matrix->row_block_size,
612 fc->transport_matrix->col_block_size, TRUE);
613 }
614
615 if (Esys_noError()) {
616 const Paso_SystemMatrixPattern *pattern=fc->iteration_matrix->pattern;
617 const dim_t n=Paso_SystemMatrix_getTotalNumRows(fc->iteration_matrix);
618 #pragma omp parallel for private(i, iptr_ij, iptr_ji) schedule(static)
619 for (i = 0; i < n; ++i) {
620 double sum=fc->transport_matrix->mainBlock->val[main_iptr[i]];
621
622 /* printf("sum[%d] = %e -> ", i, sum); */
623 /* look at a[i,j] */
624 for (iptr_ij=pattern->mainPattern->ptr[i];iptr_ij<pattern->mainPattern->ptr[i+1]; ++iptr_ij) {
625 const register index_t j = pattern->mainPattern->index[iptr_ij];
626 const register double rtmp1 = fc->transport_matrix->mainBlock->val[iptr_ij];
627 if (j!=i) {
628 /* find entry a[j,i] */
629 #pragma ivdep
630 for (iptr_ji=pattern->mainPattern->ptr[j]; iptr_ji<pattern->mainPattern->ptr[j+1]; ++iptr_ji) {
631
632 if ( pattern->mainPattern->index[iptr_ji] == i) {
633 const register double rtmp2=fc->transport_matrix->mainBlock->val[iptr_ji];
634 /*
635 printf("a[%d,%d]=%e\n",i,j,rtmp1);
636 printf("a[%d,%d]=%e\n",j,i,rtmp2);
637 */
638
639 const register double d_ij=-MIN3(0.,rtmp1,rtmp2);
640 fc->iteration_matrix->mainBlock->val[iptr_ij]=-(rtmp1+d_ij);
641 /* printf("l[%d,%d]=%e\n",i,j,fc->iteration_matrix->mainBlock->val[iptr_ij]); */
642 sum-=d_ij;
643 break;
644 }
645 }
646 }
647 }
648 for (iptr_ij=pattern->col_couplePattern->ptr[i];iptr_ij<pattern->col_couplePattern->ptr[i+1]; ++iptr_ij) {
649 const register index_t j = pattern->col_couplePattern->index[iptr_ij];
650 const register double rtmp1 = fc->transport_matrix->col_coupleBlock->val[iptr_ij];
651 /* find entry a[j,i] */
652 #pragma ivdep
653 for (iptr_ji=pattern->row_couplePattern->ptr[j]; iptr_ji<pattern->row_couplePattern->ptr[j+1]; ++iptr_ji) {
654 if (pattern->row_couplePattern->index[iptr_ji]==i) {
655 const register double rtmp2=fc->transport_matrix->row_coupleBlock->val[iptr_ji];
656 const register double d_ij=-MIN3(0.,rtmp1,rtmp2);
657 fc->iteration_matrix->col_coupleBlock->val[iptr_ij]=-(rtmp1+d_ij);
658 fc->iteration_matrix->row_coupleBlock->val[iptr_ji]=-(rtmp2+d_ij);
659 sum-=d_ij;
660 break;
661 }
662 }
663 }
664 /* set main diagonal entry */
665 fc->main_diagonal_low_order_transport_matrix[i]=sum;
666 /* printf("%e \n", sum); */
667 }
668
669 }
670 }
671
672 /*
673 * out_i=m_i u_i + a * \sum_{j <> i} l_{ij} (u_j-u_i)
674 *
675 */
676 void Paso_FCT_Solver_setMuPaLu(double* out,
677 const double* M,
678 const Paso_Coupler* u_coupler,
679 const double a,
680 const Paso_SystemMatrix *L)
681 {
682 dim_t i;
683 const Paso_SystemMatrixPattern *pattern = L->pattern;
684 const double *u=Paso_Coupler_borrowLocalData(u_coupler);
685 const double *remote_u=Paso_Coupler_borrowRemoteData(u_coupler);
686 register index_t iptr_ij;
687 const dim_t n=Paso_SystemMatrix_getTotalNumRows(L);
688
689 #pragma omp parallel for private(i) schedule(static)
690 for (i = 0; i < n; ++i) {
691 out[i]=M[i]*u[i];
692 }
693 if (ABS(a)>0) {
694 #pragma omp parallel for schedule(static) private(i, iptr_ij)
695 for (i = 0; i < n; ++i) {
696 register double sum=0;
697 const register double u_i=u[i];
698 #pragma ivdep
699 for (iptr_ij=(pattern->mainPattern->ptr[i]);iptr_ij<pattern->mainPattern->ptr[i+1]; ++iptr_ij) {
700 const index_t j=pattern->mainPattern->index[iptr_ij];
701 const register double l_ij=L->mainBlock->val[iptr_ij];
702 sum+=l_ij*(u[j]-u_i);
703
704 }
705 #pragma ivdep
706 for (iptr_ij=(pattern->col_couplePattern->ptr[i]);iptr_ij<pattern->col_couplePattern->ptr[i+1]; ++iptr_ij) {
707 const index_t j=pattern->col_couplePattern->index[iptr_ij];
708 const register double l_ij=L->col_coupleBlock->val[iptr_ij];
709 sum+=l_ij*(remote_u[j]-u_i);
710 }
711 out[i]+=a*sum;
712 }
713 }
714 }
715
716 /* *************************************************************************************************************************** */
717
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