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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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// Finite Elements for Life Sciences and Engineering |
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// |
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// License: LGL2.1 License |
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// FELiScE default license: LICENSE in root folder |
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// |
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// Main authors: Julien Castelneau, Dominique Chapelle, Miguel Fernandez |
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// |
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// System includes |
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// External includes |
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#ifdef FELISCE_WITH_SLEPC |
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#include "Core/NoThirdPartyWarning/Slepc/slepceps.hpp" |
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#endif |
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// Project includes |
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#include "Solver/steklovBanner.hpp" |
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#include "Solver/linearProblem.hpp" |
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#include "InputOutput/io.hpp" |
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#include "Core/filesystemUtil.hpp" |
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namespace felisce { |
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//! The constructor |
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template<class volumeProblem> |
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ReducedSteklov<volumeProblem>::ReducedSteklov(PetscMatrix& mass, PetscMatrix& laplacian, MPI_Comm comm, LinearProblemReducedSteklov<volumeProblem>* pb, typename LinearProblemReducedSteklov<volumeProblem>::imgType imType, ChronoInstance::Pointer chrono): |
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m_comm(comm), m_mass(mass), m_laplacian(laplacian), m_lpb(pb),m_chronoRS(chrono) |
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{ |
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//! We need to know if we are going to extract the Dirichlet data or the Neumann data from the volume problem solution |
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m_imgType=imType; |
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//! We try to load the off-line basis from file. |
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//! The quantities: rank, nlap, numberofstekloveigenfunctions determine the folder where we hope to find the off-line basis |
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//! The folder will be SteklovDataDir/NUMPROC_NBLAP_LOWRANK |
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//! By default steklovDataDir = ./ |
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//! This folder should be a symbolic link to another folder. |
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std::stringstream folder; |
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folder<<FelisceParam::instance().steklovDataDir |
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<<MpiInfo::numProc()<<"_" |
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<<FelisceParam::instance().nbOfLaplacianEigenFunction<<"_" |
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<<FelisceParam::instance().lowRank<<"/"; |
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//! if the reading fails, it mains that the off-line basis is not available! |
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m_loaded = this->loadFromFile(folder.str()); |
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} |
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template<class volumeProblem> |
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bool |
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ReducedSteklov<volumeProblem>::loadFromFile(std::string folder) { |
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//! We try to load the following files |
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//! 1. Steklov eigenVectors: |
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//! eigenVectorsStreklov{0,1,2,...}.mb |
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//! |
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//! 2. Steklov eigenvalues: |
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//! steklovEigenvalues.txt |
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//! |
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//! To compute these quantities you have to run the code once with some flags std::set to true (TODO) |
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//! (1) steklov eigenVectors |
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for ( int i = 0; i < FelisceParam::instance().lowRank; ++i ) { |
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PetscVector tmp; |
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if (m_lpb->dofBD(/*iBD*/0).hasDofsOnBoundary() ) { |
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m_laplacian.getVecs(FELISCE_PETSC_NULLPTR,tmp); |
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} |
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std::stringstream filename; |
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filename<<"eigenVectorsSteklov"<<i; |
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std::stringstream filenameBin; |
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filenameBin<< folder << filename.str() << ".mb"; |
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if ( !filesystemUtil::fileExists(filenameBin.str()) ) { |
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std::stringstream msg; |
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msg<<"Off-line basis not found in folder: "<<folder<<std::endl; |
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PetscPrintf(m_comm,"%s",msg.str().c_str()); |
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m_eVecW.clear(); |
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return false; |
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} |
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if (m_lpb->dofBD(/*iBD*/0).hasDofsOnBoundary() ) { |
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tmp.loadFromBinaryFormat(m_comm, filename.str(), folder); |
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} |
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m_eVecW.push_back(tmp); |
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} |
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m_offLineBasisDim = m_eVecW.size(); |
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std::stringstream msg; |
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msg<<"Correctly loaded "<<m_offLineBasisDim<<" basis function."<<std::endl; |
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PetscPrintf(m_comm,"%s",msg.str().c_str()); |
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//! (2) loading the eigenvalues |
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if ( ! Tools::loadVectorFromFile(m_eValues,"steklovEigenvalues.txt",folder) ) |
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return false; |
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if ( m_eValues.size() != std::size_t(FelisceParam::instance().lowRank) ) |
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return false; |
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//! Finally a scaling is needed for compatibility with the rest of the code. |
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for ( int i(0); i < FelisceParam::instance().lowRank; ++i ) |
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m_eVecW[i].scale( std::sqrt(m_eValues[i]) ); |
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return true; |
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} |
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/*! \brief method that uses slepc to compute the eigenvalues/eigenvectors of the laplace-beltrami |
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* operator at the interface. |
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* |
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* the generalized Neumann eigenproblem is solved \f[Av=\lambda Bv\f], |
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* where A is neumann laplacian on the boundary, and B is the corresponding mass matrix. |
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*/ |
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template<class volumeProblem> |
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void |
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ReducedSteklov<volumeProblem>::solveLaplacianEP() { |
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// Necessary to compile felisce with Slepc |
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#ifdef FELISCE_WITH_SLEPC |
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FEL_ASSERT(m_laplacianEVec.size()==0); |
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m_laplacianEVec.resize( FelisceParam::instance().nbOfLaplacianEigenFunction ); |
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//! We require more eigenpairs than necessary because Slepc does not always return enough of them |
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int requestedNumberOfEigen = static_cast<int>( ceil( FelisceParam::instance().nbOfLaplacianEigenFunction * ( 1. + FelisceParam::instance().percentageOfExtraEig/100. ) ) ); |
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//! We create an EPS object |
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EPS laplacianEigenProblem; |
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EPSCreate(m_comm,&laplacianEigenProblem); |
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EPSSetOperators(laplacianEigenProblem,m_laplacian.toPetsc(),m_mass.toPetsc()); //<! We std::set the laplacian and the mass matrix as the two operators of the generalized problem |
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EPSSetProblemType(laplacianEigenProblem,EPS_GHEP); //<! We tell Slepc that the problem is GHEP: Generalized Hermitian Problem. |
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EPSSetDimensions(laplacianEigenProblem,requestedNumberOfEigen,PETSC_DEFAULT,PETSC_DEFAULT); |
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EPSSetWhichEigenpairs(laplacianEigenProblem,EPS_SMALLEST_MAGNITUDE); |
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//! Necessary only when using Petsc-3.6 and only in parallel |
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ST st; KSP ksp; PC pc; |
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EPSGetST ( laplacianEigenProblem, &st); |
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STGetKSP ( st, &ksp); |
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KSPGetPC ( ksp, &pc); |
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PCSetType ( pc, PCREDUNDANT); |
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EPSSetFromOptions(laplacianEigenProblem); //<! more options can be std::set in the command line. |
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//! We solve the eigen problem. |
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EPSSolve(laplacianEigenProblem); |
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if ( FelisceParam::verbose() > 2 ) { |
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EPSView(laplacianEigenProblem, PETSC_VIEWER_STDOUT_(m_comm) ); |
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} |
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// We get the number of eigenpairs there were actually computed. |
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PetscInt nconv; |
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EPSGetConverged(laplacianEigenProblem,&nconv); |
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PetscPrintf( m_comm," Number of converged eigenpairs: %d \n", nconv); |
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if ( FelisceParam::instance().nbOfLaplacianEigenFunction > nconv ) |
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FEL_ERROR("Number of converged eigenpairs is no enough!"); |
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std::vector<double> eigenvalues; |
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for ( int iEig(0); iEig < FelisceParam::instance().nbOfLaplacianEigenFunction; ++iEig ) { |
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// The parallel layout of the eigen functions is taken from the laplacian matrix. |
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m_laplacian.getVecs(FELISCE_PETSC_NULLPTR,m_laplacianEVec[iEig]); |
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// We extract the result of the EPS object |
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double eigenValue(0); |
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EPSGetEigenpair(laplacianEigenProblem,iEig,&eigenValue,nullptr,m_laplacianEVec[iEig].toPetsc(),nullptr); |
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eigenvalues.push_back(eigenValue); |
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if ( FelisceParam::verbose() > 1 ) { |
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std::stringstream master; |
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master<<"Laplacian eigenValues: k="<<iEig<<": "<< eigenValue << std::endl; |
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PetscPrintf(m_comm,"%s",master.str().c_str()); |
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MPI_Barrier(m_comm); |
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} |
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// The eigenvector related to zero is badly approximated by Slepc: we std::set it by hand |
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if ( eigenValue< 1e-7 ) { |
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std::stringstream master; |
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master<<"****************** Setting the "<<iEig<<" laplacian eigenValue to zero and the corresponding eigenVector to the correct std::vector."<<std::endl; |
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PetscPrintf(m_comm,"%s",master.str().c_str()); |
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MPI_Barrier(m_comm); |
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m_lpb->userSetNullSpace( m_laplacianEVec[iEig], iEig ); |
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// Normalization |
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PetscVector aus; |
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aus.duplicateFrom( m_laplacianEVec[iEig]); |
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mult(m_mass, m_laplacianEVec[iEig], aus); |
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double L2norm; |
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dot(aus,m_laplacianEVec[iEig],&L2norm); |
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m_laplacianEVec[iEig].scale(1./std::sqrt(L2norm) ); |
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} |
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if ( FelisceParam::instance().exportLaplacianEigenVectors ) { |
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std::stringstream filename; |
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filename<<"laplacianEigenVector"<<iEig; |
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m_laplacianEVec[iEig].saveInBinaryFormat(m_comm,filename.str(),FelisceParam::instance().resultDir); |
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} |
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} |
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// Destruction of the EPS object. |
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EPSDestroy(&laplacianEigenProblem); |
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if ( FelisceParam::instance().exportLaplacianEigenValues ) { |
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Tools::saveVectorInFile(eigenvalues,"laplacianEigenValues",FelisceParam::instance().resultDir); |
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} |
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#endif |
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} |
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/*! \brief For each eigenvector of the surface laplacian its image through the steklov operator is computed |
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* |
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* The result is stored in m_imgLaplacianEVec |
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*/ |
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template<class volumeProblem> |
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void |
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ReducedSteklov<volumeProblem>::applySteklovOperatorOnLEV(felInt imesh) { |
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std::vector<IO::Pointer> io(1); |
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if ( FelisceParam::instance().exportOffLineVolumeSolution ) { |
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io[0] = felisce::make_shared<IO>(FelisceParam::instance().inputDirectory, FelisceParam::instance().inputFile, FelisceParam::instance().inputMesh[imesh], |
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FelisceParam::instance().outputMesh[imesh], FelisceParam::instance().meshDir, FelisceParam::instance().resultDir, |
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"offLineSteklovSolution"); |
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io[0]->writeMesh(*m_lpb->mesh(imesh)); |
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io[0]->initializeOutput(); |
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} |
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m_lpb->useSteklovDataBegin(); |
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FelisceParam::linearSolverVerboseOFF(); |
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// Banner to improve communications on the screen |
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steklovBanner banner(m_lpb->m_dofBD[0/*iBD*/].numLocalDofInterface(), MpiInfo::rankProc(), m_comm, m_laplacianEVec.size() ); |
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//The matrix 0 is cleared |
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m_lpb->clearMatrixRHS( FlagMatrixRHS::only_matrix ); |
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if ( m_lpb->numberOfMatrices() == 2 ) { |
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//Also matrix 1 is cleared if there is one. |
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m_lpb->clearMatrix(1); |
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} |
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// Matrix 0 and 1 are computed and summed toghter into matrix 0. |
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m_lpb->assembleVolumeSystem( FlagMatrixRHS::only_matrix ); |
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banner.initComputation(); |
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for ( int iLap(0); iLap < FelisceParam::instance().nbOfLaplacianEigenFunction; ++iLap, ++banner) { |
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m_lpb->clearMatrixRHS(FlagMatrixRHS::only_rhs); |
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m_lpb->setSteklovData(m_laplacianEVec[iLap]); |
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m_lpb->assembleVolumeSystem(FlagMatrixRHS::only_rhs); |
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m_chronoRS->start(); |
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m_lpb->solve(MpiInfo::rankProc(),MpiInfo::numProc()); |
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m_chronoRS->stop(); |
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m_lpb->gatherSolution(); |
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double time=iLap; |
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if ( FelisceParam::instance().exportOffLineVolumeSolution ) { |
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m_lpb->writeSolutionFromVec(m_lpb->sequentialSolution(), MpiInfo::rankProc(), io, time, iLap, std::string("offLineVolumeSolution")); |
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} |
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FEL_ASSERT(io[0] != nullptr) |
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m_imgLaplacianEVec.push_back( m_lpb->getSteklovImg() ); |
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if (MpiInfo::rankProc() == 0 && FelisceParam::instance().exportOffLineVolumeSolution && io[0]->typeOutput == 1 ) { //TODO and what if proc 0 has no dofs on the boundary? |
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io[0]->postProcess(time/*, !m_sameGeometricMeshForVariable*/); |
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} |
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} |
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banner.finalizeComputation(); |
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// restoring the normal state |
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FelisceParam::linearSolverVerboseON(); |
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m_lpb->useSteklovDataEnd(); |
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} |
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template<class volumeProblem> |
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void |
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ReducedSteklov<volumeProblem>::steklovEVecEstimate() { |
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//! The Laplacian EigenVectors are realigned to be the eigenVectors. |
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double coeff; |
| 263 |
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std::vector<PetscVector> coefficients; |
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this->approximateSteklovEigenVec(coefficients); |
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//! The approximated eigenVectors are computed |
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for ( std::size_t j(0); j < coefficients.size(); ++j ) { |
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PetscVector currentEigenVec; |
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currentEigenVec.duplicateFrom( m_laplacianEVec[0]); |
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currentEigenVec.set(0.0); |
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for ( int i(0); std::size_t(i) < m_laplacianEVec.size(); ++i ) { |
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coefficients[j].getValues(1,&i,&coeff); |
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currentEigenVec.axpy(coeff,m_laplacianEVec[i]); |
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} |
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if ( FelisceParam::instance().exportSteklovEigenVectors ) { |
| 275 |
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std::stringstream filename; |
| 276 |
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filename<<"eigenVectorsSteklov"<<j; |
| 277 |
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currentEigenVec.saveInBinaryFormat(m_comm,filename.str(),FelisceParam::instance().resultDir); |
| 278 |
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} |
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currentEigenVec.scale( std::sqrt(m_eValues[j]) ); |
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m_eVecW.push_back(currentEigenVec); |
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coefficients[j].destroy(); |
| 282 |
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} |
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m_offLineBasisDim = m_eVecW.size(); |
| 284 |
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m_onLineBasisDim = 0; |
| 285 |
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m_currentBasisDim = m_offLineBasisDim; |
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| 287 |
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//! for future loading of the off-line bais: |
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| 289 |
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//! rank, nlap, numberofstekloveigenfunctions determine the folder where we hope to find the off-line basis |
| 290 |
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std::stringstream folder; |
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folder<<FelisceParam::instance().steklovDataDir |
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<<MpiInfo::numProc()<<"_" |
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<<FelisceParam::instance().nbOfLaplacianEigenFunction<<"_" |
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|
✗ |
<<FelisceParam::instance().lowRank; |
| 295 |
|
|
|
| 296 |
|
✗ |
std::stringstream createdir; |
| 297 |
|
✗ |
createdir<<"mkdir -p "<<FelisceParam::instance().steklovDataDir; |
| 298 |
|
|
|
| 299 |
|
✗ |
std::stringstream createlink; |
| 300 |
|
✗ |
std::stringstream aus; |
| 301 |
|
✗ |
if( FelisceParam::instance().resultDir.c_str()[0] != '/' ) |
| 302 |
|
✗ |
aus<<"../"<<FelisceParam::instance().resultDir; |
| 303 |
|
|
else |
| 304 |
|
✗ |
aus<<FelisceParam::instance().resultDir; |
| 305 |
|
✗ |
createlink<<"ln -s "<<aus.str() <<" "<<folder.str(); |
| 306 |
|
|
|
| 307 |
|
✗ |
if ( MpiInfo::rankProc() == 0 ) { |
| 308 |
|
|
|
| 309 |
|
✗ |
int ierr=system(createdir.str().c_str()); |
| 310 |
|
✗ |
if ( ierr>0 ) |
| 311 |
|
✗ |
std::cout<<"problems with: "<<createdir.str()<<std::endl; |
| 312 |
|
✗ |
std::cout<<createlink.str()<<std::endl; |
| 313 |
|
✗ |
ierr=system(createlink.str().c_str()); |
| 314 |
|
✗ |
if ( ierr>0 ) |
| 315 |
|
✗ |
std::cout<<"problems with: "<<createlink.str()<<std::endl; |
| 316 |
|
|
|
| 317 |
|
|
} |
| 318 |
|
|
} |
| 319 |
|
|
template<class volumeProblem> |
| 320 |
|
|
void |
| 321 |
|
✗ |
ReducedSteklov<volumeProblem>::assembleReducedMatrix( PetscMatrix& ReducedEigenMatrix ) { |
| 322 |
|
✗ |
if ( m_lpb->dofBD(/*iBD*/0).hasDofsOnBoundary() ) { |
| 323 |
|
|
|
| 324 |
|
|
//int lowRank = FelisceParam::instance().lowRank; |
| 325 |
|
✗ |
int nbOfLapEV = m_laplacianEVec.size(); |
| 326 |
|
✗ |
PetscVector tmpVec; |
| 327 |
|
|
|
| 328 |
|
|
// This matrix is supposed to be small we do not care too much about the efficiency of this code. |
| 329 |
|
|
//! The entries of this symmetric matrix are: (M lev_i)^T(S lev_j) |
| 330 |
|
✗ |
ReducedEigenMatrix.createSeqDense( PETSC_COMM_SELF, nbOfLapEV, nbOfLapEV, nullptr ); |
| 331 |
|
✗ |
tmpVec.duplicateFrom(m_laplacianEVec[0]); |
| 332 |
|
✗ |
for ( int i(0); i < nbOfLapEV; ++i ) { |
| 333 |
|
✗ |
std::vector<double> valuesOfCurrentRow(nbOfLapEV-i,0.0); |
| 334 |
|
✗ |
std::vector<int> id(nbOfLapEV-i,0); |
| 335 |
|
✗ |
if ( m_imgType == LinearProblemReducedSteklov<volumeProblem>::dirichlet) { |
| 336 |
|
|
//! M lev_i |
| 337 |
|
✗ |
mult(m_mass,m_laplacianEVec[i],tmpVec ); |
| 338 |
|
|
} else {// We do not need it in the Neumann case since it is embedded in the residual |
| 339 |
|
✗ |
tmpVec=m_laplacianEVec[i]; |
| 340 |
|
|
} |
| 341 |
|
|
|
| 342 |
|
✗ |
for ( int j(i); j < nbOfLapEV; ++j ) { |
| 343 |
|
✗ |
double value(0); |
| 344 |
|
|
//! (M lev_i)^T(S lev_j) |
| 345 |
|
✗ |
dot(tmpVec, m_imgLaplacianEVec[j], &value); |
| 346 |
|
✗ |
valuesOfCurrentRow[j-i]=value; |
| 347 |
|
✗ |
id[j-i]=j; |
| 348 |
|
|
} |
| 349 |
|
|
//! the matrix is symmetric: we first std::set the row and then the column |
| 350 |
|
✗ |
ReducedEigenMatrix.setValues( 1 , &i , nbOfLapEV-i, &id[0], &valuesOfCurrentRow[0], INSERT_VALUES); |
| 351 |
|
✗ |
ReducedEigenMatrix.setValues( nbOfLapEV-i-1 , &id[1] , 1, &i, &valuesOfCurrentRow[1], INSERT_VALUES); |
| 352 |
|
|
} |
| 353 |
|
✗ |
ReducedEigenMatrix.assembly(MAT_FINAL_ASSEMBLY); |
| 354 |
|
|
|
| 355 |
|
✗ |
if (FelisceParam::instance().exportReducedEigenMatrix) { |
| 356 |
|
✗ |
std::stringstream filename; filename<<"reducedEigenMatrix"<<MpiInfo::rankProc(); |
| 357 |
|
✗ |
ReducedEigenMatrix.saveInBinaryFormat(PETSC_COMM_SELF,filename.str(),FelisceParam::instance().resultDir); |
| 358 |
|
|
} |
| 359 |
|
|
|
| 360 |
|
|
} |
| 361 |
|
|
} |
| 362 |
|
|
/*! |
| 363 |
|
|
*/ |
| 364 |
|
|
template<class volumeProblem> |
| 365 |
|
|
void |
| 366 |
|
✗ |
ReducedSteklov<volumeProblem>::approximateSteklovEigenVec(std::vector<PetscVector> &coefficients) { |
| 367 |
|
|
(void) coefficients; |
| 368 |
|
|
#ifdef FELISCE_WITH_SLEPC |
| 369 |
|
✗ |
if (m_lpb->dofBD(/*iBD*/0).hasDofsOnBoundary() ) { |
| 370 |
|
✗ |
int lowRank = FelisceParam::instance().lowRank; |
| 371 |
|
|
//int nbOfLapEV = m_laplacianEVec.size(); |
| 372 |
|
|
|
| 373 |
|
|
|
| 374 |
|
|
// This matrix is supposed to be small we do not care too much about the efficiency of this code. |
| 375 |
|
|
//! The entries of this symmetric matrix are: (M lev_i)^T(S lev_j) |
| 376 |
|
✗ |
PetscMatrix ReducedEigenMatrix; |
| 377 |
|
✗ |
this->assembleReducedMatrix(ReducedEigenMatrix); |
| 378 |
|
|
|
| 379 |
|
|
//! We create an EPS object using the sub-comunicator of the procs that have at least on dof on the boundary. |
| 380 |
|
|
//! The matrix is supposed to be small: we do it in serial. |
| 381 |
|
|
EPS reducedEigenProblem; |
| 382 |
|
✗ |
EPSCreate(PETSC_COMM_SELF,&reducedEigenProblem); |
| 383 |
|
|
//! We std::set that matrix as the only operator of the eigenproblem. |
| 384 |
|
✗ |
EPSSetOperators(reducedEigenProblem,ReducedEigenMatrix.toPetsc(), nullptr ); |
| 385 |
|
|
//! We inform slepc that the problem is HEP: Hermitian Problem. |
| 386 |
|
✗ |
EPSSetProblemType(reducedEigenProblem,EPS_HEP); |
| 387 |
|
|
//! We require the eigenparis associated with the N largest eigenvalues, N=lowRank |
| 388 |
|
✗ |
EPSSetDimensions(reducedEigenProblem,lowRank,PETSC_DEFAULT,PETSC_DEFAULT); |
| 389 |
|
✗ |
if ( m_imgType == LinearProblemReducedSteklov<volumeProblem>::dirichlet) { |
| 390 |
|
✗ |
EPSSetWhichEigenpairs(reducedEigenProblem,EPS_LARGEST_MAGNITUDE); |
| 391 |
|
|
} else { |
| 392 |
|
✗ |
EPSSetWhichEigenpairs(reducedEigenProblem,EPS_SMALLEST_MAGNITUDE); |
| 393 |
|
|
} |
| 394 |
|
|
//EPSKrylovSchurSetRestart(reducedEigenProblem,0.5); |
| 395 |
|
|
//EPSSetTolerances(reducedEigenProblem,1e-8,500); |
| 396 |
|
✗ |
EPSSetFromOptions(reducedEigenProblem); |
| 397 |
|
|
|
| 398 |
|
|
//! We solve the eigen problem. |
| 399 |
|
✗ |
EPSSolve(reducedEigenProblem); |
| 400 |
|
✗ |
if ( FelisceParam::verbose() > 1 ) { |
| 401 |
|
✗ |
EPSView(reducedEigenProblem,PETSC_VIEWER_STDOUT_SELF ); |
| 402 |
|
|
} |
| 403 |
|
|
|
| 404 |
|
|
// We get the number of eigenpairs there were actually computed. |
| 405 |
|
✗ |
PetscInt nconv; EPSGetConverged(reducedEigenProblem,&nconv); |
| 406 |
|
✗ |
PetscPrintf(m_comm," Number of converged eigenpairs for the small eigenvalue problem: %d \n",nconv); |
| 407 |
|
✗ |
FEL_ASSERT( lowRank <= nconv ); |
| 408 |
|
✗ |
coefficients.resize(lowRank); |
| 409 |
|
✗ |
m_eValues.resize(lowRank); |
| 410 |
|
✗ |
for ( int iEig(0); iEig < lowRank; ++iEig ) { |
| 411 |
|
|
// The parallel layout of the eigen functions is taken from the operator of the problem. |
| 412 |
|
✗ |
ReducedEigenMatrix.getVecs(FELISCE_PETSC_NULLPTR,coefficients[iEig]); |
| 413 |
|
|
|
| 414 |
|
|
// We extract the result of the EPS object |
| 415 |
|
✗ |
EPSGetEigenpair(reducedEigenProblem,iEig,&m_eValues[iEig],nullptr,coefficients[iEig].toPetsc(),nullptr); |
| 416 |
|
✗ |
if ( FelisceParam::verbose() > 1) { |
| 417 |
|
✗ |
std::stringstream master; |
| 418 |
|
✗ |
master<<"Eigen Values: "<<iEig<<" , "<< m_eValues[iEig] << std::endl; |
| 419 |
|
✗ |
PetscPrintf(m_comm,"%s",master.str().c_str()); |
| 420 |
|
✗ |
MPI_Barrier(m_comm); |
| 421 |
|
|
} |
| 422 |
|
✗ |
if (FelisceParam::instance().exportFTOfSteklovEigenVectors && MpiInfo::rankProc() == 0 ) { |
| 423 |
|
✗ |
std::stringstream filename; filename<<"fourierTransformOfSteklovEigenVectors"<<iEig; |
| 424 |
|
✗ |
coefficients[iEig].saveInBinaryFormat(PETSC_COMM_SELF,filename.str(),FelisceParam::instance().resultDir); |
| 425 |
|
|
} |
| 426 |
|
|
} |
| 427 |
|
|
// destruction of the EPS object. |
| 428 |
|
✗ |
EPSDestroy(&reducedEigenProblem); |
| 429 |
|
✗ |
ReducedEigenMatrix.destroy(); |
| 430 |
|
✗ |
if (FelisceParam::instance().exportSteklovEigenValues) { |
| 431 |
|
✗ |
Tools::saveVectorInFile(m_eValues,"steklovEigenvalues.txt",FelisceParam::instance().resultDir); |
| 432 |
|
|
} |
| 433 |
|
|
} |
| 434 |
|
|
#else |
| 435 |
|
|
std::cerr<<"You have to compile this program with the flag FELISCE_WITH_SLEPC"<< std::endl; |
| 436 |
|
|
#endif |
| 437 |
|
|
} |
| 438 |
|
|
|
| 439 |
|
|
|
| 440 |
|
|
/*! \brief The action of the low rank steklov on an a given input std::vector |
| 441 |
|
|
* |
| 442 |
|
|
* \param[in] in, the given std::vector |
| 443 |
|
|
* \param[out] out, the outcome: it is supposed to be already allocated. |
| 444 |
|
|
* |
| 445 |
|
|
* We use the formula \f[ S = V L V^T M \f], where V is matrix with the eigenvectors, L of the eigenvalues and M is the mass. |
| 446 |
|
|
* If the tryAcceleration parameter is on: |
| 447 |
|
|
* First we check if the input is well represented on the current basis, if not it is added to the basis after having solved the volume problem |
| 448 |
|
|
*/ |
| 449 |
|
|
template<class volumeProblem> |
| 450 |
|
|
void |
| 451 |
|
✗ |
ReducedSteklov<volumeProblem>::applyLowRankSteklov(PetscVector& in, PetscVector& out) { |
| 452 |
|
✗ |
m_chronoRS->start(); |
| 453 |
|
|
// Initialization phase, out reset to zero since we comulate on it in the different for loops |
| 454 |
|
✗ |
out.set(0.0); |
| 455 |
|
|
|
| 456 |
|
|
// Auxiliary double |
| 457 |
|
✗ |
double partialResult(0); |
| 458 |
|
|
|
| 459 |
|
✗ |
PetscVector tmpVec,ausForNeu; |
| 460 |
|
✗ |
tmpVec.duplicateFrom(in); |
| 461 |
|
✗ |
ausForNeu.duplicateFrom(in); |
| 462 |
|
|
// The quantity M*in is stored since it will used several times |
| 463 |
|
✗ |
mult(m_mass,in,tmpVec ); |
| 464 |
|
|
|
| 465 |
|
|
|
| 466 |
|
✗ |
if ( ! FelisceParam::instance().tryAcceleration ) { |
| 467 |
|
✗ |
for ( std::size_t i(0); i < m_offLineBasisDim; ++i ) { |
| 468 |
|
✗ |
if ( ! FelisceParam::instance().onlyConstResp ) { |
| 469 |
|
|
//! \f[ partialResult = q_i \cdot M in \f] |
| 470 |
|
✗ |
dot( m_eVecW[i], tmpVec, &partialResult); |
| 471 |
|
✗ |
if ( m_imgType == LinearProblemReducedSteklov<volumeProblem>::neumann) { |
| 472 |
|
|
// We pre-multiply the result by -M because we want to pass the equivalent of a residual to the coupled problem |
| 473 |
|
✗ |
partialResult *= -1; |
| 474 |
|
✗ |
mult(m_mass, m_eVecW[i], ausForNeu); |
| 475 |
|
✗ |
out.axpy( partialResult, ausForNeu); //out = - pr M q (we want the residual not the traction ) //DEBUG |
| 476 |
|
|
} else { |
| 477 |
|
|
//! \f[ out += partialResult q_i \f] |
| 478 |
|
✗ |
out.axpy( partialResult, m_eVecW[i]); |
| 479 |
|
|
} |
| 480 |
|
|
} |
| 481 |
|
|
} |
| 482 |
|
|
} else { |
| 483 |
|
✗ |
if ( m_imgType == LinearProblemReducedSteklov<volumeProblem>::neumann) { |
| 484 |
|
✗ |
std::cout<<"WARNING: this part has not been checked for dirichlet 2 neumann problem"<<std::endl; |
| 485 |
|
✗ |
std::cout<<__FILE__<<":"<<__LINE__<<std::endl; |
| 486 |
|
|
} |
| 487 |
|
✗ |
std::size_t curOnLineDim = m_onLineBasisDim; |
| 488 |
|
|
//! 1) COMPUTATION OF THE TRUE L2-NORM OF THE INPUT |
| 489 |
|
|
// L2 norm of the input std::vector |
| 490 |
|
✗ |
double L2Norm(0); |
| 491 |
|
✗ |
dot(in,tmpVec, &L2Norm); |
| 492 |
|
✗ |
L2Norm=std::sqrt(L2Norm); |
| 493 |
|
|
|
| 494 |
|
|
//! 2) COMPUTATION OF THE FOURIER COEFFICIENTS |
| 495 |
|
|
//! 2bis) COMPUTATION OF THE L2-NORM OF THE INPUT'S PROJECTION |
| 496 |
|
|
// now we compute the norm of the projection onto the basis |
| 497 |
|
✗ |
double projNorm(0); |
| 498 |
|
|
// Vector that'll contains all the scalar product w.r.t. the vectors of the basis |
| 499 |
|
✗ |
std::vector<double> partialResults( m_currentBasisDim ); |
| 500 |
|
|
// loop on the offline basis |
| 501 |
|
✗ |
for ( std::size_t i(0); i < m_offLineBasisDim; ++i ) { |
| 502 |
|
|
// be careful: the eigenVector contains the square root of the eigenValue |
| 503 |
|
✗ |
dot(m_eVecW[i], tmpVec, &partialResult); |
| 504 |
|
✗ |
partialResults[i]=partialResult; |
| 505 |
|
✗ |
projNorm += std::pow( partialResult / std::sqrt( m_eValues[i] ), 2 ); |
| 506 |
|
|
} |
| 507 |
|
✗ |
for ( std::size_t i(0); i< m_onLineBasisDim; ++i ) { |
| 508 |
|
✗ |
dot(m_onlineInputs[i],tmpVec, &partialResult); |
| 509 |
|
✗ |
partialResults[ i + m_offLineBasisDim ] = partialResult; |
| 510 |
|
✗ |
projNorm += std::pow( partialResult, 2 ); |
| 511 |
|
|
} |
| 512 |
|
✗ |
projNorm=std::sqrt(projNorm); |
| 513 |
|
|
|
| 514 |
|
|
//! 3) COMPUTATION OF THE RATIO: ||P(X_in)||/|| X_in || |
| 515 |
|
✗ |
double ratio(projNorm/L2Norm); |
| 516 |
|
✗ |
if( MpiInfo::rankProc() == 0 ) |
| 517 |
|
✗ |
std::cout<<"percentage of input vectors that is taken into account by the approximation: "<<ratio*100<<std::endl; |
| 518 |
|
|
|
| 519 |
|
✗ |
if ( ratio < FelisceParam::instance().projOnlineRatio )//0.995 |
| 520 |
|
|
{ |
| 521 |
|
✗ |
if( MpiInfo::rankProc() == 0 ) |
| 522 |
|
✗ |
std::cout<<"Too complicated input, the volume problem will be solved!"<<std::endl; |
| 523 |
|
|
//! 4) CONSTRUCTION OF A NEW BASIS VECTOR |
| 524 |
|
|
// Reconstruct the projection of in, compute in - P(in) |
| 525 |
|
✗ |
PetscVector newBasisVector; |
| 526 |
|
|
// first we take In and then we remove its projections on the current basis |
| 527 |
|
✗ |
newBasisVector.duplicateFrom(in); |
| 528 |
|
✗ |
newBasisVector.copyFrom(in); |
| 529 |
|
✗ |
for ( std::size_t i(0); i< m_offLineBasisDim; ++i ) { |
| 530 |
|
✗ |
newBasisVector.axpy( - partialResults[i] / m_eValues[i], m_eVecW[i]); |
| 531 |
|
|
} |
| 532 |
|
✗ |
for ( std::size_t i(0); i<m_onLineBasisDim; ++i ) { |
| 533 |
|
✗ |
newBasisVector.axpy( - partialResults[ i + m_eVecW.size() ], m_onlineInputs[i] ); |
| 534 |
|
|
} |
| 535 |
|
|
// renormalize it, with respect to Mass (we know the norm by difference) |
| 536 |
|
✗ |
newBasisVector.scale( 1./( std::sqrt(L2Norm*L2Norm - projNorm*projNorm) ) ); |
| 537 |
|
|
|
| 538 |
|
|
// DEBUG |
| 539 |
|
|
#ifdef FELISCE_DEBUG |
| 540 |
|
|
double check; |
| 541 |
|
✗ |
PetscVector tmpVec2; |
| 542 |
|
|
//Computing L2-norm |
| 543 |
|
✗ |
tmpVec2.duplicateFrom(newBasisVector); |
| 544 |
|
✗ |
mult(m_mass,newBasisVector,tmpVec2 ); |
| 545 |
|
✗ |
dot(tmpVec2, newBasisVector, &check); |
| 546 |
|
✗ |
tmpVec2.destroy(); |
| 547 |
|
|
//checking that it has been normalized |
| 548 |
|
✗ |
if ( MpiInfo::rankProc() == 0 ) |
| 549 |
|
✗ |
std::cout<<"added a new input Vector, norm should be one and it is: "<< check << std::endl; |
| 550 |
|
✗ |
FEL_ASSERT( Tools::almostEqual(check,1.,1.e-12) ); |
| 551 |
|
|
#endif |
| 552 |
|
|
//! 5) ADDITION OF THE NEW VECTOR TO THE ONLINE BASIS |
| 553 |
|
✗ |
m_onlineInputs.push_back(newBasisVector); |
| 554 |
|
✗ |
++m_onLineBasisDim; |
| 555 |
|
✗ |
++m_currentBasisDim; |
| 556 |
|
|
|
| 557 |
|
|
//! 6) COMPUTATION OF THE IMAGE OF THE NEW VECTOR |
| 558 |
|
✗ |
m_lpb->useSteklovDataBegin(); |
| 559 |
|
✗ |
m_lpb->setSteklovData( newBasisVector ); |
| 560 |
|
✗ |
m_lpb->clearMatrixRHS(FlagMatrixRHS::matrix_and_rhs); |
| 561 |
|
✗ |
m_lpb->assembleVolumeSystem(FlagMatrixRHS::matrix_and_rhs); |
| 562 |
|
✗ |
m_lpb->solve(MpiInfo::rankProc(),MpiInfo::numProc()); |
| 563 |
|
✗ |
out = m_lpb->getSteklovImg(); |
| 564 |
|
✗ |
m_lpb->useSteklovDataEnd(); |
| 565 |
|
|
//! 7) SAVING OF THE IMAGE OF THE NEW VECTOR |
| 566 |
|
|
// save in a list along with its image. |
| 567 |
|
✗ |
PetscVector imageOfNewBasisVec; |
| 568 |
|
✗ |
imageOfNewBasisVec.duplicateFrom(out); |
| 569 |
|
✗ |
imageOfNewBasisVec.copyFrom(out); |
| 570 |
|
✗ |
m_onlineOutputs.push_back(imageOfNewBasisVec); |
| 571 |
|
|
//! 8) COMPUTATION OF THE CURRENT IMAGE ON THE NEW BASIS |
| 572 |
|
|
// the output is rescaled with the correct norm |
| 573 |
|
✗ |
out.scale(std::sqrt(L2Norm*L2Norm - projNorm*projNorm)); |
| 574 |
|
|
} |
| 575 |
|
|
//! 9) COMPUTATION OF THE CURRENT IMAGE WITH THE REST OF THE BASIS |
| 576 |
|
✗ |
for ( std::size_t i(0); i < m_offLineBasisDim; ++i ) { |
| 577 |
|
✗ |
out.axpy( partialResults[i], m_eVecW[i]); |
| 578 |
|
|
} |
| 579 |
|
✗ |
for ( std::size_t i(0); i < curOnLineDim; ++i ) { |
| 580 |
|
✗ |
out.axpy( partialResults[ i + m_offLineBasisDim ], m_onlineOutputs[i]); |
| 581 |
|
|
} |
| 582 |
|
|
} |
| 583 |
|
✗ |
if ( m_constantResponse.size() == 1) { |
| 584 |
|
|
//TODO: case with multiple constant responses |
| 585 |
|
✗ |
double coeff = m_lpb->userInletPressure() * ( ( m_imgType == LinearProblemReducedSteklov<volumeProblem>::neumann ) ? -1 : 1 ); |
| 586 |
|
✗ |
out.axpy( coeff,m_constantResponse[0]); |
| 587 |
|
|
} |
| 588 |
|
✗ |
m_chronoRS->stop(); |
| 589 |
|
|
} |
| 590 |
|
|
|
| 591 |
|
|
template<class volumeProblem> |
| 592 |
|
|
void |
| 593 |
|
✗ |
ReducedSteklov<volumeProblem>::exportAllEig( felInt imesh ) { |
| 594 |
|
|
|
| 595 |
|
✗ |
std::vector<IO::Pointer> ioSteklov = {felisce::make_shared<IO>(FelisceParam::instance().inputDirectory, FelisceParam::instance().inputFile, FelisceParam::instance().inputMesh[imesh], |
| 596 |
|
✗ |
FelisceParam::instance().outputMesh[imesh], FelisceParam::instance().meshDir, FelisceParam::instance().resultDir, |
| 597 |
|
|
"steklovEigen")}; |
| 598 |
|
|
|
| 599 |
|
✗ |
std::vector<IO::Pointer> ioLaplacian = {felisce::make_shared<IO>(FelisceParam::instance().inputDirectory, FelisceParam::instance().inputFile, FelisceParam::instance().inputMesh[imesh], |
| 600 |
|
✗ |
FelisceParam::instance().outputMesh[imesh], FelisceParam::instance().meshDir, FelisceParam::instance().resultDir, |
| 601 |
|
|
"laplacianEigen")}; |
| 602 |
|
|
|
| 603 |
|
✗ |
ioSteklov[0] ->writeMesh(*m_lpb->m_mesh[0]); |
| 604 |
|
✗ |
ioLaplacian[0] ->writeMesh(*m_lpb->m_mesh[0]); |
| 605 |
|
|
|
| 606 |
|
✗ |
ioSteklov[0] ->initializeOutput(); |
| 607 |
|
✗ |
ioLaplacian[0] ->initializeOutput(); |
| 608 |
|
|
|
| 609 |
|
✗ |
PetscVector ausPara,ausSeq; |
| 610 |
|
✗ |
ausPara.duplicateFrom(m_lpb->solution()); |
| 611 |
|
✗ |
ausSeq.duplicateFrom(m_lpb->sequentialSolution()); |
| 612 |
|
|
|
| 613 |
|
✗ |
int nEVECWl = m_eVecW.size(); |
| 614 |
|
✗ |
int nEVECW(0); |
| 615 |
|
✗ |
MPI_Allreduce( &nEVECWl,&nEVECW,1,MPI_INT,MPI_MAX,MpiInfo::petscComm()); |
| 616 |
|
|
|
| 617 |
|
✗ |
if ( m_eValues.size() < (std::size_t)nEVECW ) |
| 618 |
|
✗ |
m_eValues.resize(nEVECW); |
| 619 |
|
|
|
| 620 |
|
✗ |
for ( std::size_t k(0); k<(std::size_t)nEVECW; ++k) { |
| 621 |
|
✗ |
m_lpb->dofBD(/*iBD*/0).extendOnVolume( ausPara, m_eVecW[k]); |
| 622 |
|
✗ |
m_lpb->gatherVector(ausPara,ausSeq); |
| 623 |
|
✗ |
ausSeq.scale( 1./std::sqrt( m_eValues[k] ) ); |
| 624 |
|
✗ |
double time=k; |
| 625 |
|
✗ |
m_lpb->writeSolutionFromVec(ausSeq, MpiInfo::rankProc(), ioSteklov, time, k, std::string("steklovEigenVec")); |
| 626 |
|
✗ |
if (MpiInfo::rankProc() == 0) { |
| 627 |
|
✗ |
if ( ioSteklov[0]->typeOutput == 1 ) // 1 : ensight{ |
| 628 |
|
✗ |
ioSteklov[0]->postProcess(time/*, !m_sameGeometricMeshForVariable*/); |
| 629 |
|
|
} |
| 630 |
|
|
} |
| 631 |
|
|
|
| 632 |
|
|
|
| 633 |
|
✗ |
int nLAPl = m_laplacianEVec.size(); |
| 634 |
|
✗ |
int nLAP(0); |
| 635 |
|
✗ |
MPI_Allreduce( &nLAPl,&nLAP,1,MPI_INT,MPI_MAX,MpiInfo::petscComm()); |
| 636 |
|
|
|
| 637 |
|
✗ |
for ( std::size_t k(0); k<(std::size_t)nLAP; ++k) { |
| 638 |
|
✗ |
m_lpb->dofBD(/*iBD*/0).extendOnVolume( ausPara, m_laplacianEVec[k]); |
| 639 |
|
✗ |
m_lpb->gatherVector(ausPara,ausSeq); |
| 640 |
|
✗ |
double time=k; |
| 641 |
|
✗ |
m_lpb->writeSolutionFromVec(ausSeq, MpiInfo::rankProc(), ioLaplacian, time, k, std::string("laplacianEigenVec")); |
| 642 |
|
✗ |
if (MpiInfo::rankProc() == 0) { |
| 643 |
|
✗ |
if ( ioLaplacian[0]->typeOutput == 1 ) // 1 : ensight{ |
| 644 |
|
✗ |
ioLaplacian[0]->postProcess(time/*, !m_sameGeometricMeshForVariable*/); |
| 645 |
|
|
} |
| 646 |
|
|
} |
| 647 |
|
|
} |
| 648 |
|
|
} |
| 649 |
|
|
|
| 650 |
|
|
|