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

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Revision 1410 - (hide annotations)
Thu Feb 7 04:24:00 2008 UTC (12 years ago) by gross
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a new version of the algebric upwinding a. flux limiter
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
50    
51     /* extract the row sum of the advective part */
52 gross 1407 Paso_SystemMatrix_rowSum(fctp->mass_matrix,fctp->lumped_mass_matrix);
53 gross 1363
54 gross 1407 /* set low order transport operator */
55     Paso_FCTransportProblem_setLowOrderOperator(fctp);
56     /*
57 gross 1370 * calculate time step size:
58 gross 1407 */
59     dt_max=LARGE_POSITIVE_FLOAT;
60 gross 1370 if (fctp->theta < 1.) {
61 gross 1407 #pragma omp parallel private(dt_max_loc)
62 gross 1370 {
63 gross 1407 dt_max_loc=LARGE_POSITIVE_FLOAT;
64     #pragma omp for schedule(static) private(i,rtmp1,rtmp2)
65 gross 1372 for (i=0;i<n_rows;++i) {
66 gross 1407 rtmp1=fctp->main_diagonal_low_order_transport_matrix[i];
67 gross 1370 rtmp2=fctp->lumped_mass_matrix[i];
68 gross 1407 if ( (rtmp1<0 && rtmp2>=0.) || (rtmp1>0 && rtmp2<=0.) ) {
69     dt_max_loc=MIN(dt_max_loc,-rtmp2/rtmp1);
70 gross 1370 }
71     }
72 gross 1372 #pragma omp critical
73 gross 1370 {
74 gross 1407 dt_max=MIN(dt_max,dt_max_loc);
75 gross 1370 }
76     }
77     #ifdef PASO_MPI
78 gross 1407 dt_max_loc = dt_max;
79     MPI_Allreduce(&dt_max_loc, &dt_max, 1, MPI_DOUBLE, MPI_MIN, fctp->mpi_info->comm);
80     #endif
81     if (dt_max<LARGE_POSITIVE_FLOAT) dt_max*=1./(1.-fctp->theta);
82     }
83     if (dt_max <= 0.) {
84 gross 1400 Paso_setError(TYPE_ERROR,"Paso_SolverFCT_solve: dt must be positive.");
85 gross 1407 } else {
86     if (dt_max<LARGE_POSITIVE_FLOAT) printf("maximum time step size is %e (theta = %e).\n",dt_max,fctp->theta);
87 gross 1370 }
88 gross 1407 fctp->dt_max=dt_max;
89 gross 1370 fctp->valid_matrices=Paso_noError();
90 gross 1363 }
91 gross 1407 return fctp->dt_max;
92     }
93 gross 1363
94 gross 1407
95    
96    
97     void Paso_SolverFCT_solve(Paso_FCTransportProblem* fctp, double* u, double dt, double* source, Paso_Options* options) {
98    
99     index_t i, j;
100     int n_substeps,n, m;
101     double dt_max, omega, dt2,t;
102     double local_norm[2],norm[2],local_norm_u,local_norm_du,norm_u,norm_du, tolerance;
103     register double rtmp1,rtmp2,rtmp3,rtmp4, rtmp;
104     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;
105     Paso_SystemMatrix *flux_matrix=NULL;
106     dim_t n_rows=Paso_SystemMatrix_getTotalNumRows(fctp->transport_matrix);
107     bool_t converged;
108     if (dt<=0.) {
109     Paso_setError(TYPE_ERROR,"Paso_SolverFCT_solve: dt must be positive.");
110     }
111     dt_max=Paso_FCTransportProblem_getSafeTimeStepSize(fctp);
112 gross 1400 /*
113 gross 1407 * allocate memory
114 gross 1400 *
115     */
116 gross 1407 Paso_SystemMatrix_allocBuffer(fctp->iteration_matrix);
117     b_n=TMPMEMALLOC(n_rows,double);
118     Paso_checkPtr(b_n);
119     sourceP=TMPMEMALLOC(n_rows,double);
120     Paso_checkPtr(sourceP);
121     sourceN=TMPMEMALLOC(n_rows,double);
122     Paso_checkPtr(sourceN);
123     uTilde_n=TMPMEMALLOC(n_rows,double);
124     Paso_checkPtr(uTilde_n);
125     QN_n=TMPMEMALLOC(n_rows,double);
126     Paso_checkPtr(QN_n);
127     QP_n=TMPMEMALLOC(n_rows,double);
128     Paso_checkPtr(QP_n);
129     RN_m=TMPMEMALLOC(n_rows,double);
130     Paso_checkPtr(RN_m);
131     RP_m=TMPMEMALLOC(n_rows,double);
132     Paso_checkPtr(RP_m);
133     z_m=TMPMEMALLOC(n_rows,double);
134     Paso_checkPtr(z_m);
135     du_m=TMPMEMALLOC(n_rows,double);
136     Paso_checkPtr(du_m);
137     flux_matrix=Paso_SystemMatrix_alloc(fctp->transport_matrix->type,
138     fctp->transport_matrix->pattern,
139     fctp->transport_matrix->row_block_size,
140     fctp->transport_matrix->col_block_size);
141 gross 1400 if (Paso_noError()) {
142 gross 1407 Paso_SystemMatrix_allocBuffer(flux_matrix);
143     Paso_SystemMatrix_allocBuffer(fctp->iteration_matrix);
144 gross 1400 /*
145     * Preparation:
146     *
147     */
148    
149     /* decide on substepping */
150 gross 1407 if (fctp->dt_max < LARGE_POSITIVE_FLOAT) {
151     n_substeps=ceil(dt/dt_max);
152 gross 1400 } else {
153 gross 1407 n_substeps=1;
154 gross 1400 }
155     dt2=dt/n_substeps;
156 gross 1407 printf("%d time steps of size is %e (theta = %e, dt_max=%e).\n",n_substeps, dt2,fctp->theta, dt_max);
157     /*
158     * seperate source into positive and negative part:
159     */
160     #pragma omp parallel for private(i,rtmp)
161     for (i = 0; i < n_rows; ++i) {
162     rtmp=source[i];
163     if (rtmp <0) {
164 gross 1410 sourceN[i]=-rtmp;
165     sourceP[i]=0;
166 gross 1407 } else {
167 gross 1410 sourceN[i]= 0;
168     sourceP[i]= rtmp;
169 gross 1400 }
170 gross 1407 }
171 gross 1410 /* for (i = 0; i < n_rows; ++i) printf("%d : %e \n",i,source[i],sourceP[i],sourceN[i]) */
172 gross 1407 /*
173 gross 1410 * let the show begin!!!!
174 gross 1407 *
175     */
176 gross 1400 t=dt2;
177     n=0;
178     tolerance=options->tolerance;
179     while(n<n_substeps && Paso_noError()) {
180     printf("substep step %d at t=%e\n",n+1,t);
181 gross 1410 #pragma omp parallel for private(i)
182     for (i = 0; i < n_rows; ++i) {
183     u[i]=fctp->u[i];
184     }
185 gross 1407 /*
186 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]
187 gross 1407 *
188     * note that iteration_matrix stores the negative values of the
189 gross 1410 * low order transport matrix l therefore a=-dt2*(1-fctp->theta) is used.
190 gross 1407 *
191     */
192     Paso_SolverFCT_setMuPaLuPbQ(b_n,fctp->lumped_mass_matrix,u,
193 gross 1410 -dt2*(1-fctp->theta),fctp->iteration_matrix,dt2,sourceP);
194 gross 1407 /*
195     * uTilde_n[i]=b[i]/m[i]
196     *
197 gross 1410 * a[i,i]=m[i]/(dt2 theta) + \frac{1}{\theta} \frac{q^-[i]}-l[i,i]
198 gross 1407 *
199     */
200     if (fctp->theta > 0) {
201     Paso_solve_free(fctp->iteration_matrix);
202 gross 1410 omega=1./(dt2*fctp->theta);
203     rtmp2=dt2*omega;
204 gross 1407 #pragma omp parallel for private(i,rtmp,rtmp3,rtmp4)
205     for (i = 0; i < n_rows; ++i) {
206     rtmp=fctp->lumped_mass_matrix[i];
207     if (ABS(rtmp)>0.) {
208     rtmp3=b_n[i]/rtmp;
209     } else {
210     rtmp3=u[i];
211     }
212 gross 1410 rtmp4=rtmp*omega-fctp->main_diagonal_low_order_transport_matrix[i];
213 gross 1407 if (ABS(rtmp3)>0) rtmp4+=sourceN[i]*rtmp2/rtmp3;
214     fctp->iteration_matrix->mainBlock->val[fctp->main_iptr[i]]=rtmp4;
215     uTilde_n[i]=rtmp3;
216 gross 1400 }
217     } else {
218 gross 1407 #pragma omp parallel for private(i,rtmp,rtmp3)
219     for (i = 0; i < n_rows; ++i) {
220     rtmp=fctp->lumped_mass_matrix[i];
221     if (ABS(rtmp)>0.) {
222     rtmp3=b_n[i]/rtmp;
223     } else {
224     rtmp3=u[i];
225     }
226     uTilde_n[i]=rtmp3;
227     }
228 gross 1410 omega=1.;
229 gross 1407 /* no update of iteration_matrix retquired! */
230     } /* end (fctp->theta > 0) */
231     /*
232     * calculate QP_n[i] max_{j} (\tilde{u}[j]- \tilde{u}[i] )
233     * QN_n[i] min_{j} (\tilde{u}[j]- \tilde{u}[i] )
234     *
235     */
236     Paso_SolverFCT_setQs(uTilde_n,QN_n,QP_n,fctp->iteration_matrix);
237     /*
238     * now we enter the mation on a time-step:
239     *
240     */
241     m=0;
242     converged=FALSE;
243 gross 1410 while ( (!converged) && (m<500) && Paso_noError()) {
244 gross 1407 printf("iteration step %d\n",m+1);
245     /*
246     * set the ant diffusion fluxes:
247     *
248     */
249 gross 1410 Paso_FCTransportProblem_setAntiDiffusionFlux(dt2,fctp,flux_matrix,u,fctp->u);
250 gross 1407 /*
251     * apply pre flux-correction: f_{ij}:=0 if f_{ij}*(\tilde{u}[i]- \tilde{u}[j])<=0
252     *
253     * this is not entirely correct!!!!!
254     *
255     */
256 gross 1410 Paso_FCTransportProblem_applyPreAntiDiffusionCorrection(flux_matrix,uTilde_n);
257 gross 1407 /*
258     * set flux limms RN_m,RP_m
259     *
260     */
261     Paso_FCTransportProblem_setRs(flux_matrix,fctp->lumped_mass_matrix,QN_n,QP_n,RN_m,RP_m);
262     /*
263 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])
264 gross 1407 *
265     * note that iteration_matrix stores the negative values of the
266 gross 1410 * low order transport matrix l therefore a=dt2*fctp->theta is used.
267 gross 1407 */
268 gross 1410
269 gross 1407 Paso_SolverFCT_setMuPaLuPbQ(z_m,fctp->lumped_mass_matrix,u,
270 gross 1410 dt2*fctp->theta,fctp->iteration_matrix,dt2,sourceN);
271     #pragma omp parallel for private(i)
272     for (i = 0; i < n_rows; ++i) z_m[i]=b_n[i]-z_m[i];
273 gross 1407
274     /* add corrected fluxes into z_m */
275 gross 1410 Paso_FCTransportProblem_addCorrectedFluxes(z_m,flux_matrix,RN_m,RP_m);
276 gross 1407 /*
277 gross 1410 * now we solve the linear system to get the correction dt2:
278 gross 1407 *
279     */
280     if (fctp->theta > 0) {
281     /* set the right hand side of the linear system: */
282 gross 1410 options->tolerance=1.e-2;
283 gross 1407 Paso_solve(fctp->iteration_matrix,du_m,z_m,options);
284     /* TODO: check errors ! */
285     } else {
286     #pragma omp parallel for private(i,rtmp,rtmp1)
287     for (i = 0; i < n_rows; ++i) {
288     rtmp=fctp->lumped_mass_matrix[i];
289     if (ABS(rtmp)>0.) {
290 gross 1410 rtmp1=z_m[i]/rtmp;
291 gross 1407 } else {
292     rtmp1=0;
293     }
294     du_m[i]=rtmp1;
295     }
296     }
297     /*
298     * update u and calculate norm of du_m and the new u:
299     *
300     */
301     norm_u=0.;
302     norm_du=0.;
303     #pragma omp parallel private(local_norm_u,local_norm_du)
304     {
305     local_norm_u=0.;
306     local_norm_du=0.;
307     #pragma omp for schedule(static) private(i)
308     for (i=0;i<n_rows;++i) {
309     u[i]+=omega*du_m[i];
310     local_norm_u=MAX(local_norm_u,ABS(u[i]));
311     local_norm_du=MAX(local_norm_du,ABS(du_m[i]));
312     }
313     #pragma omp critical
314     {
315     norm_u=MAX(norm_u,local_norm_u);
316     norm_du=MAX(norm_du,local_norm_du);
317     }
318     }
319     #ifdef PASO_MPI
320     local_norm[0]=norm_u;
321     local_norm[1]=norm_du;
322     MPI_Allredu_mce(local_norm,norm, 2, MPI_DOUBLE, MPI_MAX, fctp->mpi_info->comm);
323     norm_u=norm[0];
324     norm_du=norm[1];
325     #endif
326     norm_du*=omega;
327     converged=(norm_du <= tolerance * norm_u);
328     m++;
329     printf("iteration step %d: norm u and du_m : %e %e\n",m,norm_u,norm_du);
330     /* TODO: check if du_m has been redu_mced */
331 gross 1410 } /* end of inner iteration */
332     #pragma omp parallel for schedule(static) private(i)
333     for (i=0;i<n_rows;++i) fctp->u[i]=u[i];
334     n++;
335 gross 1407 } /* end of time integration */
336     #pragma omp parallel for schedule(static) private(i)
337 gross 1410 for (i=0;i<n_rows;++i) u[i]=fctp->u[i]+fctp->u_min;
338     /* TODO: update u_min ? */
339 gross 1407
340 gross 1370 }
341 gross 1407 /*
342     * clean-up:
343 gross 1400 *
344     */
345 gross 1407 TMPMEMFREE(b_n);
346     Paso_SystemMatrix_free(flux_matrix);
347     TMPMEMFREE(sourceP);
348     TMPMEMFREE(sourceN);
349     TMPMEMFREE(uTilde_n);
350     TMPMEMFREE(QN_n);
351     TMPMEMFREE(QP_n);
352     TMPMEMFREE(RN_m);
353     TMPMEMFREE(RP_m);
354     TMPMEMFREE(z_m);
355     TMPMEMFREE(du_m);
356 gross 1375 }

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