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

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Revision 1513 - (show annotations)
Tue Apr 15 08:47:57 2008 UTC (11 years, 4 months ago) by gross
File MIME type: text/plain
File size: 13878 byte(s)
pragma ivdep removed. icc produced wrong code.
1 /* $Id:$ */
2
3 /*******************************************************
4 *
5 * Copyright 2007,2008 by University of Queensland
6 *
7 * http://esscc.uq.edu_m.au
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 /* Paso: Flux correction transport solver
17 *
18 * solves Mu_t=Ku+q
19 * u(0) >= u_min
20 *
21 * Warning: the program assums sum_{j} k_{ij}=0!!!
22 *
23 */
24 /**************************************************************/
25
26 /* Author: l.gross@uq.edu_m.au */
27
28 /**************************************************************/
29
30 #include "Paso.h"
31 #include "Solver.h"
32 #include "SolverFCT.h"
33 #include "escript/blocktimer.h"
34 #ifdef _OPENMP
35 #include <omp.h>
36 #endif
37 #ifdef PASO_MPI
38 #include <mpi.h>
39 #endif
40
41 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 /* extract the row sum of the advective part */
50 Paso_SystemMatrix_rowSum(fctp->mass_matrix,fctp->lumped_mass_matrix);
51
52 /* set low order transport operator */
53 Paso_FCTransportProblem_setLowOrderOperator(fctp);
54 /*
55 * calculate time step size:
56 */
57 dt_max=LARGE_POSITIVE_FLOAT;
58 if (fctp->theta < 1.) {
59 #pragma omp parallel private(dt_max_loc)
60 {
61 dt_max_loc=LARGE_POSITIVE_FLOAT;
62 #pragma omp for schedule(static) private(i,rtmp1,rtmp2)
63 for (i=0;i<n_rows;++i) {
64 rtmp1=fctp->main_diagonal_low_order_transport_matrix[i];
65 rtmp2=fctp->lumped_mass_matrix[i];
66 if ( (rtmp1<0 && rtmp2>0.) || (rtmp1>0 && rtmp2<0.) ) {
67 dt_max_loc=MIN(dt_max_loc,-rtmp2/rtmp1);
68 }
69 }
70 #pragma omp critical
71 {
72 dt_max=MIN(dt_max,dt_max_loc);
73 }
74 }
75 #ifdef PASO_MPI
76 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 Paso_setError(TYPE_ERROR,"Paso_SolverFCT_solve: dt must be positive.");
83 } else {
84 if (dt_max<LARGE_POSITIVE_FLOAT) printf("maximum time step size is %e (theta = %e).\n",dt_max,fctp->theta);
85 }
86 fctp->dt_max=dt_max;
87 fctp->valid_matrices=Paso_noError();
88 }
89 return fctp->dt_max;
90 }
91
92
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 /*
111 * allocate memory
112 *
113 */
114 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 if (Paso_noError()) {
140 Paso_SystemMatrix_allocBuffer(flux_matrix);
141 Paso_SystemMatrix_allocBuffer(fctp->iteration_matrix);
142 /*
143 * Preparation:
144 *
145 */
146
147 /* decide on substepping */
148 if (fctp->dt_max < LARGE_POSITIVE_FLOAT) {
149 n_substeps=ceil(dt/dt_max);
150 } else {
151 n_substeps=1;
152 }
153 dt2=dt/n_substeps;
154 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 sourceN[i]=-rtmp;
163 sourceP[i]=0;
164 } else {
165 sourceN[i]= 0;
166 sourceP[i]= rtmp;
167 }
168 }
169 /* for (i = 0; i < n_rows; ++i) printf("%d : %e \n",i,source[i],sourceP[i],sourceN[i]) */
170 /*
171 * let the show begin!!!!
172 *
173 */
174 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 #pragma omp parallel for private(i)
180 for (i = 0; i < n_rows; ++i) {
181 u[i]=fctp->u[i];
182 }
183 /*
184 * 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 *
186 * note that iteration_matrix stores the negative values of the
187 * low order transport matrix l therefore a=-dt2*(1-fctp->theta) is used.
188 *
189 */
190 Paso_SolverFCT_setMuPaLuPbQ(b_n,fctp->lumped_mass_matrix,u,
191 -dt2*(1-fctp->theta),fctp->iteration_matrix,dt2,sourceP);
192 /*
193 * uTilde_n[i]=b[i]/m[i]
194 *
195 * a[i,i]=m[i]/(dt2 theta) + \frac{1}{\theta} \frac{q^-[i]}-l[i,i]
196 *
197 */
198 if (fctp->theta > 0) {
199 Paso_solve_free(fctp->iteration_matrix);
200 omega=1./(dt2*fctp->theta);
201 rtmp2=dt2*omega;
202 #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 rtmp4=rtmp*omega-fctp->main_diagonal_low_order_transport_matrix[i];
211 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 }
215 } else {
216 #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 omega=1.;
227 /* 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 while ( (!converged) && (m<500) && Paso_noError()) {
242 printf("iteration step %d\n",m+1);
243 /*
244 * set the ant diffusion fluxes:
245 *
246 */
247 Paso_FCTransportProblem_setAntiDiffusionFlux(dt2,fctp,flux_matrix,u,fctp->u);
248 /*
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 Paso_FCTransportProblem_applyPreAntiDiffusionCorrection(flux_matrix,uTilde_n);
255 /*
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 * 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 *
263 * note that iteration_matrix stores the negative values of the
264 * low order transport matrix l therefore a=dt2*fctp->theta is used.
265 */
266
267 Paso_SolverFCT_setMuPaLuPbQ(z_m,fctp->lumped_mass_matrix,u,
268 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
272 /* add corrected fluxes into z_m */
273 Paso_FCTransportProblem_addCorrectedFluxes(z_m,flux_matrix,RN_m,RP_m);
274 /*
275 * now we solve the linear system to get the correction dt2:
276 *
277 */
278 if (fctp->theta > 0) {
279 /* set the right hand side of the linear system: */
280 options->tolerance=1.e-2;
281 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 rtmp1=z_m[i]/rtmp;
289 } 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 MPI_Allreduce(local_norm,norm, 2, MPI_DOUBLE, MPI_MAX, fctp->mpi_info->comm);
321 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 } /* 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 } /* end of time integration */
334 #pragma omp parallel for schedule(static) private(i)
335 for (i=0;i<n_rows;++i) u[i]=fctp->u[i]+fctp->u_min;
336 /* TODO: update u_min ? */
337
338 }
339 /*
340 * clean-up:
341 *
342 */
343 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 }

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