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/******************************************************* |
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* |
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* Copyright (c) 2003-2008 by University of Queensland |
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* Earth Systems Science Computational Center (ESSCC) |
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* http://www.uq.edu.au/esscc |
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* |
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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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|
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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) >=0 |
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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.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 "PasoUtil.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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/* |
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* inserts the source term into the problem |
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*/ |
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void Paso_FCT_setSource(const dim_t n,const double *source, double* sourceN, double* sourceP) |
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{ |
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dim_t i; |
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register double rtmp; |
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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; ++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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} |
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|
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err_t Paso_FCT_setUpRightHandSide(Paso_FCTransportProblem* fctp, const double dt, const double *u_m, Paso_Coupler* u_m_coupler, double * z_m, |
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Paso_SystemMatrix* flux_matrix, Paso_Coupler* uTilde_coupler, const double *b, |
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Paso_Coupler* QN_coupler, Paso_Coupler* QP_coupler, |
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double *RN_m, Paso_Coupler* RN_m_coupler, double* RP_m, Paso_Coupler* RP_m_coupler, const double *sourceN, |
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Paso_Performance* pp) |
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{ |
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const dim_t n=Paso_SystemMatrix_getTotalNumRows(fctp->transport_matrix); |
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/* distribute u */ |
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Paso_Coupler_startCollect(u_m_coupler,u_m); |
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Paso_Coupler_finishCollect(u_m_coupler); |
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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(dt,fctp,flux_matrix,u_m_coupler); |
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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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*/ |
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Paso_FCTransportProblem_applyPreAntiDiffusionCorrection(flux_matrix,uTilde_coupler); |
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/* |
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* set flux limiters 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_coupler,QP_coupler,RN_m,RP_m); |
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Paso_Coupler_startCollect(RN_m_coupler,RN_m); |
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Paso_Coupler_startCollect(RP_m_coupler,RP_m); |
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/* |
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* z_m[i]=b[i] - (m_i*u_m[i] - dt*theta*sum_{j<>i} l_{ij} (u_m[j]-u_m[i]) + dt 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=dt*fctp->theta is used. |
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*/ |
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Paso_SolverFCT_setMuPaLuPbQ(z_m,fctp->lumped_mass_matrix, u_m_coupler,dt*fctp->theta,fctp->iteration_matrix,dt,sourceN); |
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/* z_m=b-z_m */ |
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Paso_Update(n,-1.,z_m,1.,b); |
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|
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Paso_Coupler_finishCollect(RN_m_coupler); |
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Paso_Coupler_finishCollect(RP_m_coupler); |
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/* add corrected fluxes into z_m */ |
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Paso_FCTransportProblem_addCorrectedFluxes(z_m,flux_matrix,RN_m_coupler,RP_m_coupler); |
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return NO_ERROR; |
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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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const dim_t FAILURES_MAX=5; |
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dim_t m, i_substeps, Failed, i; |
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double *z_m=NULL, *b_n=NULL, *sourceP=NULL, *sourceN=NULL, *uTilde_n=NULL, *QN_n=NULL, *QP_n=NULL, *RN_m=NULL, *RP_m=NULL, *du_m=NULL; |
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Paso_Coupler *QN_n_coupler=NULL, *QP_n_coupler=NULL, *RN_m_coupler=NULL, *RP_m_coupler=NULL, *uTilde_n_coupler=NULL, *u_m_coupler=NULL; |
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Paso_SystemMatrix *flux_matrix_m=NULL; |
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double dt_max, dt2,t, norm_u_m, omega, norm_du_m; |
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register double mass, rtmp; |
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const dim_t n=Paso_SystemMatrix_getTotalNumRows(fctp->transport_matrix); |
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dim_t blockSize=Paso_FCTransportProblem_getBlockSize(fctp); |
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const double atol=options->absolute_tolerance; |
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const double rtol=options->tolerance; |
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const dim_t max_m=options->iter_max; |
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Paso_Performance pp; |
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bool_t converged=FALSE, max_m_reached=FALSE; |
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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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z_m=TMPMEMALLOC(n,double); |
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Paso_checkPtr(z_m); |
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du_m=TMPMEMALLOC(n,double); |
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Paso_checkPtr(du_m); |
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b_n=TMPMEMALLOC(n,double); |
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Paso_checkPtr(b_n); |
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sourceP=TMPMEMALLOC(n,double); |
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Paso_checkPtr(sourceP); |
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sourceN=TMPMEMALLOC(n,double); |
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Paso_checkPtr(sourceN); |
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uTilde_n=TMPMEMALLOC(n,double); |
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Paso_checkPtr(uTilde_n); |
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QN_n=TMPMEMALLOC(n,double); |
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Paso_checkPtr(QN_n); |
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QP_n=TMPMEMALLOC(n,double); |
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Paso_checkPtr(QP_n); |
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RN_m=TMPMEMALLOC(n,double); |
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Paso_checkPtr(RN_m); |
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RP_m=TMPMEMALLOC(n,double); |
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Paso_checkPtr(RP_m); |
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QN_n_coupler=Paso_Coupler_alloc(Paso_FCTransportProblem_borrowConnector(fctp),blockSize); |
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QP_n_coupler=Paso_Coupler_alloc(Paso_FCTransportProblem_borrowConnector(fctp),blockSize); |
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RN_m_coupler=Paso_Coupler_alloc(Paso_FCTransportProblem_borrowConnector(fctp),blockSize); |
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RP_m_coupler=Paso_Coupler_alloc(Paso_FCTransportProblem_borrowConnector(fctp),blockSize); |
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uTilde_n_coupler=Paso_Coupler_alloc(Paso_FCTransportProblem_borrowConnector(fctp),blockSize); |
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u_m_coupler=Paso_Coupler_alloc(Paso_FCTransportProblem_borrowConnector(fctp),blockSize); |
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flux_matrix_m=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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|
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if (Paso_noError()) { |
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/* |
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* Preparation: |
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* |
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*/ |
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Paso_FCT_setSource(n, source, sourceN, sourceP); |
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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=0; |
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i_substeps=0; |
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Paso_Copy(n,u,fctp->u); |
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norm_u_m=Paso_lsup(n,u, fctp->mpi_info); |
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/* while(i_substeps<n_substeps && Paso_noError()) { */ |
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if (fctp->dt_max < LARGE_POSITIVE_FLOAT) { |
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dt2=MIN(dt_max,dt); |
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} else { |
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dt2=dt; |
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} |
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while(t<dt && Paso_noError()) { |
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printf("substep step %d at t=%e (step size= %e)\n",i_substeps+1,t+dt2,dt2); |
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Paso_FCT_setUp(fctp,dt2,sourceN,sourceP,b_n,uTilde_n,uTilde_n_coupler,QN_n,QN_n_coupler,QP_n,QP_n_coupler, |
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options,&pp); |
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/* now the iteration starts */ |
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m=0; |
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converged=FALSE; |
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max_m_reached=FALSE; |
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/* tolerance? */ |
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while ( (!converged) && (! max_m_reached) && Paso_noError()) { |
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/* set z_m */ |
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Paso_FCT_setUpRightHandSide(fctp,dt2,u,u_m_coupler,z_m,flux_matrix_m,uTilde_n_coupler,b_n, |
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QN_n_coupler,QP_n_coupler,RN_m,RN_m_coupler,RP_m,RP_m_coupler,sourceN,&pp); |
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/* |
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* now we solve the linear system to get the correction dt: |
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* |
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*/ |
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if (fctp->theta > 0) { |
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omega=1./(dt2*fctp->theta); |
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Paso_Solver_solvePreconditioner(fctp->iteration_matrix,du_m,z_m); |
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Paso_Update(n,1.,u,omega,du_m); |
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} else { |
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omega=1; |
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#pragma omp parallel for private(i,mass,rtmp) |
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for (i = 0; i < n; ++i) { |
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mass=fctp->lumped_mass_matrix[i]; |
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if (ABS(mass)>0.) { |
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rtmp=z_m[i]/mass; |
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} else { |
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rtmp=0; |
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} |
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du_m[i]=rtmp; |
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u[i]+=rtmp; |
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} |
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} |
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norm_u_m=Paso_lsup(n,u, fctp->mpi_info); |
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norm_du_m=Paso_lsup(n,du_m, fctp->mpi_info)*omega; |
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printf("iteration step %d completed: norm increment= %e (tolerance = %e)\n",m+1, norm_du_m, rtol * norm_u_m + atol); |
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|
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max_m_reached=(m>max_m); |
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converged=(norm_du_m <= rtol * norm_u_m + atol); |
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m++; |
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} |
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if (converged) { |
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Failed=0; |
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/* #pragma omp parallel for schedule(static) private(i) */ |
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Paso_Copy(n,fctp->u,u); |
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i_substeps++; |
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t+=dt2; |
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if (fctp->dt_max < LARGE_POSITIVE_FLOAT) { |
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dt2=MIN3(dt_max,dt2*1.5,dt-t); |
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} else { |
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dt2=MIN(dt2*1.5,dt-t); |
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} |
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} else if (max_m_reached) { |
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/* if FAILURES_MAX failures in a row: give up */ |
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if (Failed > FAILURES_MAX) { |
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Paso_setError(VALUE_ERROR,"Paso_SolverFCT_solve: no convergence after time step reduction."); |
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} else { |
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printf("no convergence in Paso_Solver_NewtonGMRES: Trying smaller time step size."); |
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dt2=dt*0.5; |
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Failed++; |
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} |
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} |
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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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MEMFREE(z_m); |
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MEMFREE(du_m); |
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TMPMEMFREE(b_n); |
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Paso_SystemMatrix_free(flux_matrix_m); |
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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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Paso_Coupler_free(QN_n_coupler); |
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Paso_Coupler_free(QP_n_coupler); |
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Paso_Coupler_free(RN_m_coupler); |
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Paso_Coupler_free(RP_m_coupler); |
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Paso_Coupler_free(uTilde_n_coupler); |
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Paso_Coupler_free(u_m_coupler); |
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options->absolute_tolerance=atol; |
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options->tolerance=rtol; |
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} |
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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; |
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double dt_max, dt_max_loc; |
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register double l_ii,m; |
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n=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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/* 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,l_ii,m) |
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for (i=0;i<n;++i) { |
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l_ii=fctp->main_diagonal_low_order_transport_matrix[i]; |
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m=fctp->lumped_mass_matrix[i]; |
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if ( (l_ii<0 && m>0.) || (l_ii>0 && m<0) ) { |
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dt_max_loc=MIN(dt_max_loc,-m/l_ii); |
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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) |
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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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void Paso_FCT_setUp(Paso_FCTransportProblem* fctp, const double dt, const double *sourceN, const double *sourceP, double* b, double* uTilde, |
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Paso_Coupler* uTilde_coupler, double *QN, Paso_Coupler* QN_coupler, double *QP, Paso_Coupler* QP_coupler, |
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Paso_Options* options, Paso_Performance* pp) |
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{ |
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dim_t i; |
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const dim_t n=Paso_SystemMatrix_getTotalNumRows(fctp->transport_matrix); |
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double omega, factor; |
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register double m, u_tilde_i, rtmp4; |
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/* distribute u */ |
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Paso_Coupler_startCollect(fctp->u_coupler,fctp->u); |
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Paso_Coupler_finishCollect(fctp->u_coupler); |
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/* |
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* b^n[i]=m u^n[i] + dt*(1-theta) sum_{j <> i} l_{ij}*(u^n[j]-u^n[i]) + dt*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=-dt*(1-fctp->theta) is used. |
| 342 |
* |
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*/ |
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Paso_SolverFCT_setMuPaLuPbQ(b,fctp->lumped_mass_matrix,fctp->u_coupler, |
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-dt*(1-fctp->theta),fctp->iteration_matrix,dt,sourceP); |
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/* |
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* uTilde[i]=b[i]/m[i] |
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* |
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* fctp->iteration_matrix[i,i]=m[i]/(dt theta) + \frac{1}{\theta} \frac{q^-[i]}-l[i,i] |
| 350 |
* |
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*/ |
| 352 |
if (fctp->theta > 0) { |
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Paso_solve_free(fctp->iteration_matrix); |
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omega=1./(dt*fctp->theta); |
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factor=dt*omega; |
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#pragma omp parallel for private(i,m,u_tilde_i,rtmp4) |
| 357 |
for (i = 0; i < n; ++i) { |
| 358 |
m=fctp->lumped_mass_matrix[i]; |
| 359 |
if (ABS(m)>0.) { |
| 360 |
u_tilde_i=b[i]/m; |
| 361 |
} else { |
| 362 |
u_tilde_i=fctp->u[i]; |
| 363 |
} |
| 364 |
rtmp4=m*omega-fctp->main_diagonal_low_order_transport_matrix[i]; |
| 365 |
if (ABS(u_tilde_i)>0) rtmp4+=sourceN[i]*factor/u_tilde_i; |
| 366 |
fctp->iteration_matrix->mainBlock->val[fctp->main_iptr[i]]=rtmp4; |
| 367 |
uTilde[i]=u_tilde_i; |
| 368 |
} |
| 369 |
Performance_startMonitor(pp,PERFORMANCE_PRECONDITIONER_INIT); |
| 370 |
Paso_Solver_setPreconditioner(fctp->iteration_matrix,options); |
| 371 |
Performance_stopMonitor(pp,PERFORMANCE_PRECONDITIONER_INIT); |
| 372 |
} else { |
| 373 |
#pragma omp parallel for private(i,m,u_tilde_i) |
| 374 |
for (i = 0; i < n; ++i) { |
| 375 |
m=fctp->lumped_mass_matrix[i]; |
| 376 |
if (ABS(m)>0.) { |
| 377 |
u_tilde_i=b[i]/m; |
| 378 |
} else { |
| 379 |
u_tilde_i=fctp->u[i]; |
| 380 |
} |
| 381 |
uTilde[i]=u_tilde_i; |
| 382 |
} |
| 383 |
/* no update of iteration_matrix required! */ |
| 384 |
} /* end (fctp->theta > 0) */ |
| 385 |
|
| 386 |
/* distribute uTilde: */ |
| 387 |
Paso_Coupler_startCollect(uTilde_coupler,uTilde); |
| 388 |
Paso_Coupler_finishCollect(uTilde_coupler); |
| 389 |
/* |
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* calculate QP[i] max_{j} (\tilde{u}[j]- \tilde{u}[i] ) |
| 391 |
* QN[i] min_{j} (\tilde{u}[j]- \tilde{u}[i] ) |
| 392 |
* |
| 393 |
*/ |
| 394 |
Paso_SolverFCT_setQs(uTilde_coupler,QN,QP,fctp->iteration_matrix); |
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Paso_Coupler_startCollect(QN_coupler,QN); |
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Paso_Coupler_startCollect(QP_coupler,QP); |
| 397 |
Paso_Coupler_finishCollect(QN_coupler); |
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Paso_Coupler_finishCollect(QP_coupler); |
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} |
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