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/* $Id:$ */ |
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|
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/******************************************************* |
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* |
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* Copyright 2007,2008 by University of Queensland |
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* |
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* http://esscc.uq.edu_m.au |
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* Primary Business: Queensland, Australia |
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* Licensed under the Open Software License version 3.0 |
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* http://www.opensource.org/licenses/osl-3.0.php |
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* |
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*******************************************************/ |
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|
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/**************************************************************/ |
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|
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/* Paso: Flux correction transport solver |
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* |
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* solves Mu_t=Ku+q |
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* u(0) >= u_min |
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* |
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* Warning: the program assums sum_{j} k_{ij}=0!!! |
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* |
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*/ |
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/**************************************************************/ |
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|
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/* Author: l.gross@uq.edu_m.au */ |
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|
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/**************************************************************/ |
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|
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#include "Paso.h" |
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#include "Solver.h" |
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#include "SolverFCT.h" |
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#include "escript/blocktimer.h" |
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#ifdef _OPENMP |
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#include <omp.h> |
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#endif |
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#ifdef PASO_MPI |
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#include <mpi.h> |
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#endif |
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|
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double Paso_FCTransportProblem_getSafeTimeStepSize(Paso_FCTransportProblem* fctp) |
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{ |
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dim_t i, n_rows; |
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double dt_max, dt_max_loc; |
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register double rtmp1,rtmp2; |
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n_rows=Paso_SystemMatrix_getTotalNumRows(fctp->transport_matrix); |
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if (! fctp->valid_matrices) { |
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fctp->dt_max=LARGE_POSITIVE_FLOAT; |
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|
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|
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/* extract the row sum of the advective part */ |
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Paso_SystemMatrix_rowSum(fctp->mass_matrix,fctp->lumped_mass_matrix); |
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|
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/* set low order transport operator */ |
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Paso_FCTransportProblem_setLowOrderOperator(fctp); |
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/* |
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* calculate time step size: |
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*/ |
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dt_max=LARGE_POSITIVE_FLOAT; |
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if (fctp->theta < 1.) { |
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#pragma omp parallel private(dt_max_loc) |
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{ |
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dt_max_loc=LARGE_POSITIVE_FLOAT; |
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#pragma omp for schedule(static) private(i,rtmp1,rtmp2) |
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for (i=0;i<n_rows;++i) { |
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rtmp1=fctp->main_diagonal_low_order_transport_matrix[i]; |
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rtmp2=fctp->lumped_mass_matrix[i]; |
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if ( (rtmp1<0 && rtmp2>=0.) || (rtmp1>0 && rtmp2<=0.) ) { |
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dt_max_loc=MIN(dt_max_loc,-rtmp2/rtmp1); |
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} |
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} |
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#pragma omp critical |
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{ |
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dt_max=MIN(dt_max,dt_max_loc); |
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} |
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} |
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#ifdef PASO_MPI |
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dt_max_loc = dt_max; |
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MPI_Allreduce(&dt_max_loc, &dt_max, 1, MPI_DOUBLE, MPI_MIN, fctp->mpi_info->comm); |
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#endif |
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if (dt_max<LARGE_POSITIVE_FLOAT) dt_max*=1./(1.-fctp->theta); |
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} |
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if (dt_max <= 0.) { |
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Paso_setError(TYPE_ERROR,"Paso_SolverFCT_solve: dt must be positive."); |
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} else { |
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if (dt_max<LARGE_POSITIVE_FLOAT) printf("maximum time step size is %e (theta = %e).\n",dt_max,fctp->theta); |
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} |
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fctp->dt_max=dt_max; |
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fctp->valid_matrices=Paso_noError(); |
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} |
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return fctp->dt_max; |
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} |
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|
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|
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|
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|
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void Paso_SolverFCT_solve(Paso_FCTransportProblem* fctp, double* u, double dt, double* source, Paso_Options* options) { |
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|
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index_t i, j; |
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int n_substeps,n, m; |
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double dt_max, omega, dt2,t; |
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double local_norm[2],norm[2],local_norm_u,local_norm_du,norm_u,norm_du, tolerance; |
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register double rtmp1,rtmp2,rtmp3,rtmp4, rtmp; |
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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; |
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Paso_SystemMatrix *flux_matrix=NULL; |
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dim_t n_rows=Paso_SystemMatrix_getTotalNumRows(fctp->transport_matrix); |
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bool_t converged; |
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if (dt<=0.) { |
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Paso_setError(TYPE_ERROR,"Paso_SolverFCT_solve: dt must be positive."); |
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} |
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dt_max=Paso_FCTransportProblem_getSafeTimeStepSize(fctp); |
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/* |
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* allocate memory |
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* |
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*/ |
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Paso_SystemMatrix_allocBuffer(fctp->iteration_matrix); |
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b_n=TMPMEMALLOC(n_rows,double); |
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Paso_checkPtr(b_n); |
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sourceP=TMPMEMALLOC(n_rows,double); |
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Paso_checkPtr(sourceP); |
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sourceN=TMPMEMALLOC(n_rows,double); |
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Paso_checkPtr(sourceN); |
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uTilde_n=TMPMEMALLOC(n_rows,double); |
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Paso_checkPtr(uTilde_n); |
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QN_n=TMPMEMALLOC(n_rows,double); |
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Paso_checkPtr(QN_n); |
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QP_n=TMPMEMALLOC(n_rows,double); |
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Paso_checkPtr(QP_n); |
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RN_m=TMPMEMALLOC(n_rows,double); |
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Paso_checkPtr(RN_m); |
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RP_m=TMPMEMALLOC(n_rows,double); |
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Paso_checkPtr(RP_m); |
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z_m=TMPMEMALLOC(n_rows,double); |
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Paso_checkPtr(z_m); |
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du_m=TMPMEMALLOC(n_rows,double); |
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Paso_checkPtr(du_m); |
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flux_matrix=Paso_SystemMatrix_alloc(fctp->transport_matrix->type, |
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fctp->transport_matrix->pattern, |
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fctp->transport_matrix->row_block_size, |
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fctp->transport_matrix->col_block_size); |
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if (Paso_noError()) { |
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Paso_SystemMatrix_allocBuffer(flux_matrix); |
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Paso_SystemMatrix_allocBuffer(fctp->iteration_matrix); |
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/* |
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* Preparation: |
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* |
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*/ |
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|
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/* decide on substepping */ |
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if (fctp->dt_max < LARGE_POSITIVE_FLOAT) { |
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n_substeps=ceil(dt/dt_max); |
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} else { |
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n_substeps=1; |
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} |
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dt2=dt/n_substeps; |
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printf("%d time steps of size is %e (theta = %e, dt_max=%e).\n",n_substeps, dt2,fctp->theta, dt_max); |
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/* |
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* seperate source into positive and negative part: |
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*/ |
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#pragma omp parallel for private(i,rtmp) |
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for (i = 0; i < n_rows; ++i) { |
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rtmp=source[i]; |
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if (rtmp <0) { |
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sourceN[i]=-rtmp; |
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sourceP[i]=0; |
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} else { |
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sourceN[i]= 0; |
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sourceP[i]= rtmp; |
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} |
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} |
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/* for (i = 0; i < n_rows; ++i) printf("%d : %e \n",i,source[i],sourceP[i],sourceN[i]) */ |
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/* |
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* let the show begin!!!! |
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* |
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*/ |
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t=dt2; |
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n=0; |
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tolerance=options->tolerance; |
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while(n<n_substeps && Paso_noError()) { |
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printf("substep step %d at t=%e\n",n+1,t); |
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#pragma omp parallel for private(i) |
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for (i = 0; i < n_rows; ++i) { |
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u[i]=fctp->u[i]; |
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} |
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/* |
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* b^n[i]=m u^n[i] + dt2*(1-theta) sum_{j <> i} l_{ij}*(u^n[j]-u^n[i]) + dt2*sourceP[i] |
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* |
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* note that iteration_matrix stores the negative values of the |
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* low order transport matrix l therefore a=-dt2*(1-fctp->theta) is used. |
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* |
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*/ |
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Paso_SolverFCT_setMuPaLuPbQ(b_n,fctp->lumped_mass_matrix,u, |
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-dt2*(1-fctp->theta),fctp->iteration_matrix,dt2,sourceP); |
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/* |
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* uTilde_n[i]=b[i]/m[i] |
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* |
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* a[i,i]=m[i]/(dt2 theta) + \frac{1}{\theta} \frac{q^-[i]}-l[i,i] |
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* |
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*/ |
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if (fctp->theta > 0) { |
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Paso_solve_free(fctp->iteration_matrix); |
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omega=1./(dt2*fctp->theta); |
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rtmp2=dt2*omega; |
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#pragma omp parallel for private(i,rtmp,rtmp3,rtmp4) |
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for (i = 0; i < n_rows; ++i) { |
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rtmp=fctp->lumped_mass_matrix[i]; |
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if (ABS(rtmp)>0.) { |
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rtmp3=b_n[i]/rtmp; |
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} else { |
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rtmp3=u[i]; |
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} |
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rtmp4=rtmp*omega-fctp->main_diagonal_low_order_transport_matrix[i]; |
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if (ABS(rtmp3)>0) rtmp4+=sourceN[i]*rtmp2/rtmp3; |
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fctp->iteration_matrix->mainBlock->val[fctp->main_iptr[i]]=rtmp4; |
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uTilde_n[i]=rtmp3; |
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} |
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} else { |
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#pragma omp parallel for private(i,rtmp,rtmp3) |
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for (i = 0; i < n_rows; ++i) { |
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rtmp=fctp->lumped_mass_matrix[i]; |
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if (ABS(rtmp)>0.) { |
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rtmp3=b_n[i]/rtmp; |
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} else { |
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rtmp3=u[i]; |
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} |
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uTilde_n[i]=rtmp3; |
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} |
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omega=1.; |
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/* no update of iteration_matrix retquired! */ |
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} /* end (fctp->theta > 0) */ |
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/* |
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* calculate QP_n[i] max_{j} (\tilde{u}[j]- \tilde{u}[i] ) |
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* QN_n[i] min_{j} (\tilde{u}[j]- \tilde{u}[i] ) |
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* |
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*/ |
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Paso_SolverFCT_setQs(uTilde_n,QN_n,QP_n,fctp->iteration_matrix); |
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/* |
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* now we enter the mation on a time-step: |
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* |
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*/ |
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m=0; |
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converged=FALSE; |
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while ( (!converged) && (m<500) && Paso_noError()) { |
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printf("iteration step %d\n",m+1); |
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/* |
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* set the ant diffusion fluxes: |
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* |
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*/ |
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Paso_FCTransportProblem_setAntiDiffusionFlux(dt2,fctp,flux_matrix,u,fctp->u); |
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/* |
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* apply pre flux-correction: f_{ij}:=0 if f_{ij}*(\tilde{u}[i]- \tilde{u}[j])<=0 |
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* |
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* this is not entirely correct!!!!! |
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* |
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*/ |
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Paso_FCTransportProblem_applyPreAntiDiffusionCorrection(flux_matrix,uTilde_n); |
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/* |
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* set flux limms RN_m,RP_m |
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* |
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*/ |
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Paso_FCTransportProblem_setRs(flux_matrix,fctp->lumped_mass_matrix,QN_n,QP_n,RN_m,RP_m); |
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/* |
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* z_m[i]=b_n[i] - (m_i*u[i] - dt2*theta*sum_{j<>i} l_{ij} (u[j]-u[i]) + dt2 q^-[i]) |
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* |
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* note that iteration_matrix stores the negative values of the |
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* low order transport matrix l therefore a=dt2*fctp->theta is used. |
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*/ |
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|
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Paso_SolverFCT_setMuPaLuPbQ(z_m,fctp->lumped_mass_matrix,u, |
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dt2*fctp->theta,fctp->iteration_matrix,dt2,sourceN); |
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#pragma omp parallel for private(i) |
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for (i = 0; i < n_rows; ++i) z_m[i]=b_n[i]-z_m[i]; |
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/* add corrected fluxes into z_m */ |
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Paso_FCTransportProblem_addCorrectedFluxes(z_m,flux_matrix,RN_m,RP_m); |
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/* |
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* now we solve the linear system to get the correction dt2: |
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* |
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*/ |
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if (fctp->theta > 0) { |
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/* set the right hand side of the linear system: */ |
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options->tolerance=1.e-2; |
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Paso_solve(fctp->iteration_matrix,du_m,z_m,options); |
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/* TODO: check errors ! */ |
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} else { |
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#pragma omp parallel for private(i,rtmp,rtmp1) |
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for (i = 0; i < n_rows; ++i) { |
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rtmp=fctp->lumped_mass_matrix[i]; |
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if (ABS(rtmp)>0.) { |
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rtmp1=z_m[i]/rtmp; |
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} else { |
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rtmp1=0; |
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} |
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du_m[i]=rtmp1; |
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} |
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} |
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/* |
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* update u and calculate norm of du_m and the new u: |
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* |
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*/ |
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norm_u=0.; |
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norm_du=0.; |
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#pragma omp parallel private(local_norm_u,local_norm_du) |
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{ |
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local_norm_u=0.; |
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local_norm_du=0.; |
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#pragma omp for schedule(static) private(i) |
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for (i=0;i<n_rows;++i) { |
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u[i]+=omega*du_m[i]; |
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local_norm_u=MAX(local_norm_u,ABS(u[i])); |
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local_norm_du=MAX(local_norm_du,ABS(du_m[i])); |
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} |
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#pragma omp critical |
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{ |
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norm_u=MAX(norm_u,local_norm_u); |
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norm_du=MAX(norm_du,local_norm_du); |
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} |
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} |
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#ifdef PASO_MPI |
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local_norm[0]=norm_u; |
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local_norm[1]=norm_du; |
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MPI_Allreduce(local_norm,norm, 2, MPI_DOUBLE, MPI_MAX, fctp->mpi_info->comm); |
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norm_u=norm[0]; |
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norm_du=norm[1]; |
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#endif |
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norm_du*=omega; |
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converged=(norm_du <= tolerance * norm_u); |
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m++; |
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printf("iteration step %d: norm u and du_m : %e %e\n",m,norm_u,norm_du); |
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/* TODO: check if du_m has been redu_mced */ |
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} /* end of inner iteration */ |
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#pragma omp parallel for schedule(static) private(i) |
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for (i=0;i<n_rows;++i) fctp->u[i]=u[i]; |
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n++; |
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} /* end of time integration */ |
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#pragma omp parallel for schedule(static) private(i) |
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for (i=0;i<n_rows;++i) u[i]=fctp->u[i]+fctp->u_min; |
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/* TODO: update u_min ? */ |
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|
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} |
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/* |
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* clean-up: |
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* |
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*/ |
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TMPMEMFREE(b_n); |
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Paso_SystemMatrix_free(flux_matrix); |
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TMPMEMFREE(sourceP); |
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TMPMEMFREE(sourceN); |
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TMPMEMFREE(uTilde_n); |
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TMPMEMFREE(QN_n); |
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TMPMEMFREE(QP_n); |
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TMPMEMFREE(RN_m); |
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TMPMEMFREE(RP_m); |
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TMPMEMFREE(z_m); |
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TMPMEMFREE(du_m); |
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} |
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