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

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Revision 1417 - (hide annotations)
Mon Feb 25 04:45:48 2008 UTC (11 years, 4 months ago) by gross
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File size: 13880 byte(s)
some more work on the transport solver.
1 gross 1363 /* $Id:$ */
2    
3     /*******************************************************
4     *
5 gross 1407 * Copyright 2007,2008 by University of Queensland
6 gross 1363 *
7 gross 1407 * http://esscc.uq.edu_m.au
8 gross 1363 * 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     /* Paso: Flux correction transport solver
17     *
18 gross 1407 * solves Mu_t=Ku+q
19     * u(0) >= u_min
20 gross 1363 *
21 gross 1407 * Warning: the program assums sum_{j} k_{ij}=0!!!
22 gross 1363 *
23     */
24     /**************************************************************/
25    
26 gross 1407 /* Author: l.gross@uq.edu_m.au */
27 gross 1363
28     /**************************************************************/
29    
30     #include "Paso.h"
31     #include "Solver.h"
32     #include "SolverFCT.h"
33     #include "escript/blocktimer.h"
34 gross 1370 #ifdef _OPENMP
35     #include <omp.h>
36     #endif
37     #ifdef PASO_MPI
38     #include <mpi.h>
39     #endif
40 gross 1363
41 gross 1407 double Paso_FCTransportProblem_getSafeTimeStepSize(Paso_FCTransportProblem* fctp)
42     {
43     dim_t i, n_rows;
44     double dt_max, dt_max_loc;
45     register double rtmp1,rtmp2;
46     n_rows=Paso_SystemMatrix_getTotalNumRows(fctp->transport_matrix);
47     if (! fctp->valid_matrices) {
48     fctp->dt_max=LARGE_POSITIVE_FLOAT;
49 gross 1363 /* extract the row sum of the advective part */
50 gross 1407 Paso_SystemMatrix_rowSum(fctp->mass_matrix,fctp->lumped_mass_matrix);
51 gross 1363
52 gross 1407 /* set low order transport operator */
53     Paso_FCTransportProblem_setLowOrderOperator(fctp);
54     /*
55 gross 1370 * calculate time step size:
56 gross 1407 */
57     dt_max=LARGE_POSITIVE_FLOAT;
58 gross 1370 if (fctp->theta < 1.) {
59 gross 1407 #pragma omp parallel private(dt_max_loc)
60 gross 1370 {
61 gross 1407 dt_max_loc=LARGE_POSITIVE_FLOAT;
62     #pragma omp for schedule(static) private(i,rtmp1,rtmp2)
63 gross 1372 for (i=0;i<n_rows;++i) {
64 gross 1407 rtmp1=fctp->main_diagonal_low_order_transport_matrix[i];
65 gross 1370 rtmp2=fctp->lumped_mass_matrix[i];
66 gross 1407 if ( (rtmp1<0 && rtmp2>=0.) || (rtmp1>0 && rtmp2<=0.) ) {
67     dt_max_loc=MIN(dt_max_loc,-rtmp2/rtmp1);
68 gross 1370 }
69     }
70 gross 1372 #pragma omp critical
71 gross 1370 {
72 gross 1407 dt_max=MIN(dt_max,dt_max_loc);
73 gross 1370 }
74     }
75     #ifdef PASO_MPI
76 gross 1407 dt_max_loc = dt_max;
77     MPI_Allreduce(&dt_max_loc, &dt_max, 1, MPI_DOUBLE, MPI_MIN, fctp->mpi_info->comm);
78     #endif
79     if (dt_max<LARGE_POSITIVE_FLOAT) dt_max*=1./(1.-fctp->theta);
80     }
81     if (dt_max <= 0.) {
82 gross 1400 Paso_setError(TYPE_ERROR,"Paso_SolverFCT_solve: dt must be positive.");
83 gross 1407 } else {
84     if (dt_max<LARGE_POSITIVE_FLOAT) printf("maximum time step size is %e (theta = %e).\n",dt_max,fctp->theta);
85 gross 1370 }
86 gross 1407 fctp->dt_max=dt_max;
87 gross 1370 fctp->valid_matrices=Paso_noError();
88 gross 1363 }
89 gross 1407 return fctp->dt_max;
90     }
91 gross 1363
92 gross 1407
93    
94    
95     void Paso_SolverFCT_solve(Paso_FCTransportProblem* fctp, double* u, double dt, double* source, Paso_Options* options) {
96    
97     index_t i, j;
98     int n_substeps,n, m;
99     double dt_max, omega, dt2,t;
100     double local_norm[2],norm[2],local_norm_u,local_norm_du,norm_u,norm_du, tolerance;
101     register double rtmp1,rtmp2,rtmp3,rtmp4, rtmp;
102     double *b_n=NULL, *sourceP=NULL, *sourceN=NULL, *uTilde_n=NULL, *QN_n=NULL, *QP_n=NULL, *RN_m=NULL, *RP_m=NULL, *z_m=NULL, *du_m=NULL;
103     Paso_SystemMatrix *flux_matrix=NULL;
104     dim_t n_rows=Paso_SystemMatrix_getTotalNumRows(fctp->transport_matrix);
105     bool_t converged;
106     if (dt<=0.) {
107     Paso_setError(TYPE_ERROR,"Paso_SolverFCT_solve: dt must be positive.");
108     }
109     dt_max=Paso_FCTransportProblem_getSafeTimeStepSize(fctp);
110 gross 1400 /*
111 gross 1407 * allocate memory
112 gross 1400 *
113     */
114 gross 1407 Paso_SystemMatrix_allocBuffer(fctp->iteration_matrix);
115     b_n=TMPMEMALLOC(n_rows,double);
116     Paso_checkPtr(b_n);
117     sourceP=TMPMEMALLOC(n_rows,double);
118     Paso_checkPtr(sourceP);
119     sourceN=TMPMEMALLOC(n_rows,double);
120     Paso_checkPtr(sourceN);
121     uTilde_n=TMPMEMALLOC(n_rows,double);
122     Paso_checkPtr(uTilde_n);
123     QN_n=TMPMEMALLOC(n_rows,double);
124     Paso_checkPtr(QN_n);
125     QP_n=TMPMEMALLOC(n_rows,double);
126     Paso_checkPtr(QP_n);
127     RN_m=TMPMEMALLOC(n_rows,double);
128     Paso_checkPtr(RN_m);
129     RP_m=TMPMEMALLOC(n_rows,double);
130     Paso_checkPtr(RP_m);
131     z_m=TMPMEMALLOC(n_rows,double);
132     Paso_checkPtr(z_m);
133     du_m=TMPMEMALLOC(n_rows,double);
134     Paso_checkPtr(du_m);
135     flux_matrix=Paso_SystemMatrix_alloc(fctp->transport_matrix->type,
136     fctp->transport_matrix->pattern,
137     fctp->transport_matrix->row_block_size,
138     fctp->transport_matrix->col_block_size);
139 gross 1400 if (Paso_noError()) {
140 gross 1407 Paso_SystemMatrix_allocBuffer(flux_matrix);
141     Paso_SystemMatrix_allocBuffer(fctp->iteration_matrix);
142 gross 1400 /*
143     * Preparation:
144     *
145     */
146    
147     /* decide on substepping */
148 gross 1407 if (fctp->dt_max < LARGE_POSITIVE_FLOAT) {
149     n_substeps=ceil(dt/dt_max);
150 gross 1400 } else {
151 gross 1407 n_substeps=1;
152 gross 1400 }
153     dt2=dt/n_substeps;
154 gross 1407 printf("%d time steps of size is %e (theta = %e, dt_max=%e).\n",n_substeps, dt2,fctp->theta, dt_max);
155     /*
156     * seperate source into positive and negative part:
157     */
158     #pragma omp parallel for private(i,rtmp)
159     for (i = 0; i < n_rows; ++i) {
160     rtmp=source[i];
161     if (rtmp <0) {
162 gross 1410 sourceN[i]=-rtmp;
163     sourceP[i]=0;
164 gross 1407 } else {
165 gross 1410 sourceN[i]= 0;
166     sourceP[i]= rtmp;
167 gross 1400 }
168 gross 1407 }
169 gross 1410 /* for (i = 0; i < n_rows; ++i) printf("%d : %e \n",i,source[i],sourceP[i],sourceN[i]) */
170 gross 1407 /*
171 gross 1410 * let the show begin!!!!
172 gross 1407 *
173     */
174 gross 1400 t=dt2;
175     n=0;
176     tolerance=options->tolerance;
177     while(n<n_substeps && Paso_noError()) {
178     printf("substep step %d at t=%e\n",n+1,t);
179 gross 1410 #pragma omp parallel for private(i)
180     for (i = 0; i < n_rows; ++i) {
181     u[i]=fctp->u[i];
182     }
183 gross 1407 /*
184 gross 1410 * b^n[i]=m u^n[i] + dt2*(1-theta) sum_{j <> i} l_{ij}*(u^n[j]-u^n[i]) + dt2*sourceP[i]
185 gross 1407 *
186     * note that iteration_matrix stores the negative values of the
187 gross 1410 * low order transport matrix l therefore a=-dt2*(1-fctp->theta) is used.
188 gross 1407 *
189     */
190     Paso_SolverFCT_setMuPaLuPbQ(b_n,fctp->lumped_mass_matrix,u,
191 gross 1410 -dt2*(1-fctp->theta),fctp->iteration_matrix,dt2,sourceP);
192 gross 1407 /*
193     * uTilde_n[i]=b[i]/m[i]
194     *
195 gross 1410 * a[i,i]=m[i]/(dt2 theta) + \frac{1}{\theta} \frac{q^-[i]}-l[i,i]
196 gross 1407 *
197     */
198     if (fctp->theta > 0) {
199     Paso_solve_free(fctp->iteration_matrix);
200 gross 1410 omega=1./(dt2*fctp->theta);
201     rtmp2=dt2*omega;
202 gross 1407 #pragma omp parallel for private(i,rtmp,rtmp3,rtmp4)
203     for (i = 0; i < n_rows; ++i) {
204     rtmp=fctp->lumped_mass_matrix[i];
205     if (ABS(rtmp)>0.) {
206     rtmp3=b_n[i]/rtmp;
207     } else {
208     rtmp3=u[i];
209     }
210 gross 1410 rtmp4=rtmp*omega-fctp->main_diagonal_low_order_transport_matrix[i];
211 gross 1407 if (ABS(rtmp3)>0) rtmp4+=sourceN[i]*rtmp2/rtmp3;
212     fctp->iteration_matrix->mainBlock->val[fctp->main_iptr[i]]=rtmp4;
213     uTilde_n[i]=rtmp3;
214 gross 1400 }
215     } else {
216 gross 1407 #pragma omp parallel for private(i,rtmp,rtmp3)
217     for (i = 0; i < n_rows; ++i) {
218     rtmp=fctp->lumped_mass_matrix[i];
219     if (ABS(rtmp)>0.) {
220     rtmp3=b_n[i]/rtmp;
221     } else {
222     rtmp3=u[i];
223     }
224     uTilde_n[i]=rtmp3;
225     }
226 gross 1410 omega=1.;
227 gross 1407 /* no update of iteration_matrix retquired! */
228     } /* end (fctp->theta > 0) */
229     /*
230     * calculate QP_n[i] max_{j} (\tilde{u}[j]- \tilde{u}[i] )
231     * QN_n[i] min_{j} (\tilde{u}[j]- \tilde{u}[i] )
232     *
233     */
234     Paso_SolverFCT_setQs(uTilde_n,QN_n,QP_n,fctp->iteration_matrix);
235     /*
236     * now we enter the mation on a time-step:
237     *
238     */
239     m=0;
240     converged=FALSE;
241 gross 1410 while ( (!converged) && (m<500) && Paso_noError()) {
242 gross 1407 printf("iteration step %d\n",m+1);
243     /*
244     * set the ant diffusion fluxes:
245     *
246     */
247 gross 1410 Paso_FCTransportProblem_setAntiDiffusionFlux(dt2,fctp,flux_matrix,u,fctp->u);
248 gross 1407 /*
249     * apply pre flux-correction: f_{ij}:=0 if f_{ij}*(\tilde{u}[i]- \tilde{u}[j])<=0
250     *
251     * this is not entirely correct!!!!!
252     *
253     */
254 gross 1410 Paso_FCTransportProblem_applyPreAntiDiffusionCorrection(flux_matrix,uTilde_n);
255 gross 1407 /*
256     * set flux limms RN_m,RP_m
257     *
258     */
259     Paso_FCTransportProblem_setRs(flux_matrix,fctp->lumped_mass_matrix,QN_n,QP_n,RN_m,RP_m);
260     /*
261 gross 1410 * z_m[i]=b_n[i] - (m_i*u[i] - dt2*theta*sum_{j<>i} l_{ij} (u[j]-u[i]) + dt2 q^-[i])
262 gross 1407 *
263     * note that iteration_matrix stores the negative values of the
264 gross 1410 * low order transport matrix l therefore a=dt2*fctp->theta is used.
265 gross 1407 */
266 gross 1410
267 gross 1407 Paso_SolverFCT_setMuPaLuPbQ(z_m,fctp->lumped_mass_matrix,u,
268 gross 1410 dt2*fctp->theta,fctp->iteration_matrix,dt2,sourceN);
269     #pragma omp parallel for private(i)
270     for (i = 0; i < n_rows; ++i) z_m[i]=b_n[i]-z_m[i];
271 gross 1407
272     /* add corrected fluxes into z_m */
273 gross 1410 Paso_FCTransportProblem_addCorrectedFluxes(z_m,flux_matrix,RN_m,RP_m);
274 gross 1407 /*
275 gross 1410 * now we solve the linear system to get the correction dt2:
276 gross 1407 *
277     */
278     if (fctp->theta > 0) {
279     /* set the right hand side of the linear system: */
280 gross 1410 options->tolerance=1.e-2;
281 gross 1407 Paso_solve(fctp->iteration_matrix,du_m,z_m,options);
282     /* TODO: check errors ! */
283     } else {
284     #pragma omp parallel for private(i,rtmp,rtmp1)
285     for (i = 0; i < n_rows; ++i) {
286     rtmp=fctp->lumped_mass_matrix[i];
287     if (ABS(rtmp)>0.) {
288 gross 1410 rtmp1=z_m[i]/rtmp;
289 gross 1407 } else {
290     rtmp1=0;
291     }
292     du_m[i]=rtmp1;
293     }
294     }
295     /*
296     * update u and calculate norm of du_m and the new u:
297     *
298     */
299     norm_u=0.;
300     norm_du=0.;
301     #pragma omp parallel private(local_norm_u,local_norm_du)
302     {
303     local_norm_u=0.;
304     local_norm_du=0.;
305     #pragma omp for schedule(static) private(i)
306     for (i=0;i<n_rows;++i) {
307     u[i]+=omega*du_m[i];
308     local_norm_u=MAX(local_norm_u,ABS(u[i]));
309     local_norm_du=MAX(local_norm_du,ABS(du_m[i]));
310     }
311     #pragma omp critical
312     {
313     norm_u=MAX(norm_u,local_norm_u);
314     norm_du=MAX(norm_du,local_norm_du);
315     }
316     }
317     #ifdef PASO_MPI
318     local_norm[0]=norm_u;
319     local_norm[1]=norm_du;
320 ksteube 1415 MPI_Allreduce(local_norm,norm, 2, MPI_DOUBLE, MPI_MAX, fctp->mpi_info->comm);
321 gross 1407 norm_u=norm[0];
322     norm_du=norm[1];
323     #endif
324     norm_du*=omega;
325     converged=(norm_du <= tolerance * norm_u);
326     m++;
327     printf("iteration step %d: norm u and du_m : %e %e\n",m,norm_u,norm_du);
328     /* TODO: check if du_m has been redu_mced */
329 gross 1410 } /* end of inner iteration */
330     #pragma omp parallel for schedule(static) private(i)
331     for (i=0;i<n_rows;++i) fctp->u[i]=u[i];
332     n++;
333 gross 1407 } /* end of time integration */
334     #pragma omp parallel for schedule(static) private(i)
335 gross 1410 for (i=0;i<n_rows;++i) u[i]=fctp->u[i]+fctp->u_min;
336     /* TODO: update u_min ? */
337 gross 1407
338 gross 1370 }
339 gross 1407 /*
340     * clean-up:
341 gross 1400 *
342     */
343 gross 1407 TMPMEMFREE(b_n);
344     Paso_SystemMatrix_free(flux_matrix);
345     TMPMEMFREE(sourceP);
346     TMPMEMFREE(sourceN);
347     TMPMEMFREE(uTilde_n);
348     TMPMEMFREE(QN_n);
349     TMPMEMFREE(QP_n);
350     TMPMEMFREE(RN_m);
351     TMPMEMFREE(RP_m);
352     TMPMEMFREE(z_m);
353     TMPMEMFREE(du_m);
354 gross 1375 }

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