AbstractNonlinearElasticityAssembler.hpp

/*

Copyright (C) University of Oxford, 2005-2009

University of Oxford means the Chancellor, Masters and Scholars of the
University of Oxford, having an administrative office at Wellington
Square, Oxford OX1 2JD, UK.

This file is part of Chaste.

Chaste is free software: you can redistribute it and/or modify it
under the terms of the GNU Lesser General Public License as published
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ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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License for more details. The offer of Chaste under the terms of the
License is subject to the License being interpreted in accordance with
English Law and subject to any action against the University of Oxford
being under the jurisdiction of the English Courts.

You should have received a copy of the GNU Lesser General Public License
along with Chaste. If not, see <http://www.gnu.org/licenses/>.

*/

#ifndef ABSTRACTNONLINEARELASTICITYASSEMBLER_HPP_
#define ABSTRACTNONLINEARELASTICITYASSEMBLER_HPP_

#include <vector>
#include <cmath>
#include "LinearSystem.hpp"
#include "AbstractIncompressibleMaterialLaw.hpp"
#include "OutputFileHandler.hpp"
#include "LogFile.hpp"
#include "PetscTools.hpp"
#include "MechanicsEventHandler.hpp"
#include "ReplicatableVector.hpp"
//#include "Timer.hpp" 

template<unsigned DIM>
class AbstractNonlinearElasticityAssembler
{
protected:

    static const double MAX_NEWTON_ABS_TOL;

    static const double MIN_NEWTON_ABS_TOL;

    static const double NEWTON_REL_TOL;

    unsigned mNumDofs;

    std::vector<AbstractIncompressibleMaterialLaw<DIM>*> mMaterialLaws;

    LinearSystem *mpLinearSystem;

    LinearSystem *mpPreconditionMatrixLinearSystem;

    c_vector<double,DIM> mBodyForce;

    double mDensity;

    std::string mOutputDirectory;

    std::vector<unsigned> mFixedNodes;

    std::vector<c_vector<double,DIM> > mFixedNodeDisplacements;

    bool mWriteOutput;

    std::vector<double> mCurrentSolution;

    FourthOrderTensor<DIM> dTdE;

    unsigned mNumNewtonIterations;

    std::vector<c_vector<double,DIM> > mDeformedPosition;

    std::vector<double> mPressures;

    std::vector<c_vector<double,DIM> > mSurfaceTractions;

    c_vector<double,DIM> (*mpBodyForceFunction)(c_vector<double,DIM>&);

    c_vector<double,DIM> (*mpTractionBoundaryConditionFunction)(c_vector<double,DIM>&);

    bool mUsingBodyForceFunction;

    bool mUsingTractionBoundaryConditionFunction;

    virtual void FormInitialGuess()=0;

    virtual void AssembleSystem(bool assembleResidual, bool assembleJacobian)=0;

    virtual std::vector<c_vector<double,DIM> >& rGetDeformedPosition()=0;

    void ApplyBoundaryConditions(bool applyToMatrix);

    double CalculateResidualNorm();

    double TakeNewtonStep();

    virtual void PostNewtonStep(unsigned counter, double normResidual);

    void AllocateMatrixMemory();

public:

    AbstractNonlinearElasticityAssembler(unsigned numDofs,
                                         AbstractIncompressibleMaterialLaw<DIM>* pMaterialLaw,
                                         c_vector<double,DIM> bodyForce,
                                         double density,
                                         std::string outputDirectory,
                                         std::vector<unsigned>& fixedNodes);

    AbstractNonlinearElasticityAssembler(unsigned numDofs,
                                         std::vector<AbstractIncompressibleMaterialLaw<DIM>*>& rMaterialLaws,
                                         c_vector<double,DIM> bodyForce,
                                         double density,
                                         std::string outputDirectory,
                                         std::vector<unsigned>& fixedNodes);

    virtual ~AbstractNonlinearElasticityAssembler();

    void Solve(double tol=-1.0,
               unsigned offset=0,
               unsigned maxNumNewtonIterations=INT_MAX,
               bool quitIfNoConvergence=true);

    void WriteOutput(unsigned counter);

    unsigned GetNumNewtonIterations();

    void SetFunctionalBodyForce(c_vector<double,DIM> (*pFunction)(c_vector<double,DIM>&));

    void SetWriteOutput(bool writeOutput=true);

};


// Implementation


template<unsigned DIM>
void AbstractNonlinearElasticityAssembler<DIM>::ApplyBoundaryConditions(bool applyToMatrix)
{
    assert(mFixedNodeDisplacements.size()==mFixedNodes.size());

    // The boundary conditions on the NONLINEAR SYSTEM are x=boundary_values
    // on the boundary nodes. However:
    // The boundary conditions on the LINEAR SYSTEM  Ju=f, where J is the
    // u the negative update vector and f is the residual is
    // u=current_soln-boundary_values on the boundary nodes
    for (unsigned i=0; i<mFixedNodes.size(); i++)
    {
        unsigned node_index = mFixedNodes[i];
        for (unsigned j=0; j<DIM; j++)
        {
            unsigned dof_index = DIM*node_index+j;
            double value = mCurrentSolution[dof_index] - mFixedNodeDisplacements[i](j);
            if (applyToMatrix)
            {
                mpLinearSystem->ZeroMatrixRow(dof_index);
                mpLinearSystem->SetMatrixElement(dof_index,dof_index,1);

                // apply same bcs to preconditioner matrix
                mpPreconditionMatrixLinearSystem->ZeroMatrixRow(dof_index);
                mpPreconditionMatrixLinearSystem->SetMatrixElement(dof_index,dof_index,1);
            }
            mpLinearSystem->SetRhsVectorElement(dof_index, value);
        }
    }
}

template<unsigned DIM>
double AbstractNonlinearElasticityAssembler<DIM>::CalculateResidualNorm()
{
    double norm;
    VecNorm(mpLinearSystem->rGetRhsVector(), NORM_2, &norm);
    return norm/mNumDofs;
}

template<unsigned DIM>
void AbstractNonlinearElasticityAssembler<DIM>::AllocateMatrixMemory()
{
    mpLinearSystem = new LinearSystem(mNumDofs, (MatType)MATAIJ); // default Mat tyype is MATMPIAIJ, see below
    mpPreconditionMatrixLinearSystem = new LinearSystem(mNumDofs, (MatType)MATAIJ); //MATAIJ is needed for precond to work

    // 2D: N elements around a point => 7N+3 non-zeros in that row? Assume N<=10 (structured mesh would have N_max=6) => 73.  
    // 3D: N elements around a point. nz < (3*10+6)N (lazy estimate). Better estimate is 23N+4?. Assume N<20 => 500ish
    unsigned num_non_zeros = DIM < 3 ? 75 : 500;

    // without leaking memory. This is the call to preallocate an MPI AIJ matrix: 
    // MatSeqAIJSetPreallocation(mpLinearSystem->rGetLhsMatrix(), num_non_zeros, PETSC_NULL, (PetscInt) (num_non_zeros*0.5), PETSC_NULL);

    MatSeqAIJSetPreallocation(mpLinearSystem->rGetLhsMatrix(),                   num_non_zeros, PETSC_NULL);
    MatSeqAIJSetPreallocation(mpPreconditionMatrixLinearSystem->rGetLhsMatrix(), num_non_zeros, PETSC_NULL);
}

template<unsigned DIM>
double AbstractNonlinearElasticityAssembler<DIM>::TakeNewtonStep()
{
    //Timer::Reset();

    // Assemble Jacobian (and preconditioner)
    MechanicsEventHandler::BeginEvent(MechanicsEventHandler::ASSEMBLE);
    AssembleSystem(true, true);
    MechanicsEventHandler::EndEvent(MechanicsEventHandler::ASSEMBLE);
    //Timer::PrintAndReset("AssembleSystem");

    // Solve the linear system using Petsc GMRES and an LU
    // factorisation of the preconditioner. Note we
    // don't call Solve on the linear_system as we want to
    // set Petsc options..
    MechanicsEventHandler::BeginEvent(MechanicsEventHandler::SOLVE);


    KSP solver;
    Vec solution;
    VecDuplicate(mpLinearSystem->rGetRhsVector(),&solution);

    Mat& r_jac = mpLinearSystem->rGetLhsMatrix();
    Mat& r_precond_jac = mpPreconditionMatrixLinearSystem->rGetLhsMatrix();

    KSPCreate(MPI_COMM_SELF,&solver);

    KSPSetOperators(solver, r_jac, r_precond_jac, DIFFERENT_NONZERO_PATTERN /*in precond between successive solves*/);

    // set max iterations
    KSPSetTolerances(solver, PETSC_DEFAULT, PETSC_DEFAULT, PETSC_DEFAULT, 10000); //hopefully with the preconditioner this max is way too high
    KSPSetType(solver,KSPGMRES);
    KSPGMRESSetRestart(solver,100); // gmres num restarts

    KSPSetFromOptions(solver);
    KSPSetUp(solver);

    PC pc;
    KSPGetPC(solver, &pc);
    PCSetType(pc, PCLU);         // Note: ILU factorisation doesn't have much effect, but LU works well.

    KSPSetFromOptions(solver);
    KSPSolve(solver,mpLinearSystem->rGetRhsVector(),solution);

    //Timer::PrintAndReset("KSP Solve");
    ReplicatableVector update(solution);

    MechanicsEventHandler::EndEvent(MechanicsEventHandler::SOLVE);

    // Update the solution
    //  Newton method:       sol = sol - update, where update=Jac^{-1}*residual
    //  Newton with damping: sol = sol - s*update, where s is chosen
    //   such that |residual(sol)| is minimised. Damping is important to
    //   avoid initial divergence.
    //
    // Normally, finding the best s from say 0.05,0.1,0.2,..,1.0 is cheap,
    // but this is not the case in cardiac electromechanics calculations.
    // Therefore, we initially check s=1 (expected to be the best most of the
    // time, then s=0.9. If the norm of the residual increases, we assume
    // s=1 is the best. Otherwise, check s=0.8 to see if s=0.9 is a local min.
    MechanicsEventHandler::BeginEvent(MechanicsEventHandler::UPDATE);
    std::vector<double> old_solution(mNumDofs);
    for (unsigned i=0; i<mNumDofs; i++)
    {
        old_solution[i] = mCurrentSolution[i];
    }

    std::vector<double> damping_values; // = {1.0, 0.9, .., 0.2, 0.1, 0.05} ie size 11
    for (unsigned i=10; i>=1; i--)
    {
        damping_values.push_back((double)i/10.0);
    }
    damping_values.push_back(0.05);
    assert(damping_values.size()==11);

    double initial_norm_resid = CalculateResidualNorm();
    unsigned index = 0;
    for (unsigned j=0; j<mNumDofs; j++)
    {
        mCurrentSolution[j] = old_solution[j] - damping_values[index]*update[j];
    }

    // compute residual
    AssembleSystem(true, false);
    double norm_resid = CalculateResidualNorm();
    std::cout << "\tTesting s = " << damping_values[index] << ", |f| = " << norm_resid << "\n" << std::flush;

    double next_norm_resid = -DBL_MAX;
    index = 1;

    // exit loop when next norm of the residual first increases
    while (next_norm_resid < norm_resid  && index<damping_values.size())
    {
        if (index!=1)
        {
            norm_resid = next_norm_resid;
        }

        for (unsigned j=0; j<mNumDofs; j++)
        {
           mCurrentSolution[j] = old_solution[j] - damping_values[index]*update[j];
        }

        // compute residual
        AssembleSystem(true, false);
        next_norm_resid = CalculateResidualNorm();
        std::cout << "\tTesting s = " << damping_values[index] << ", |f| = " << next_norm_resid << "\n" << std::flush;
        index++;
    }

    if (initial_norm_resid < norm_resid)
    {
        #define COVERAGE_IGNORE
        assert(0); // assert here as sometimes the following causes a seg fault - don't know why
        EXCEPTION("Residual does not appear to decrease in newton direction, quitting");
        #undef COVERAGE_IGNORE
    }
    else
    {
        index-=2;
        std::cout << "\tBest s = " << damping_values[index] << "\n"  << std::flush;
        for (unsigned j=0; j<mNumDofs; j++)
        {
            mCurrentSolution[j] = old_solution[j] - damping_values[index]*update[j];
        }
    }

//        double best_norm_resid = DBL_MAX;
//        double best_damping_value = 0.0;
//
//        std::vector<double> damping_values;
//        damping_values.reserve(12);
//        damping_values.push_back(0.0);
//        damping_values.push_back(0.05);
//        for (unsigned i=1; i<=10; i++)
//        {
//            damping_values.push_back((double)i/10.0);
//        }
//
//        for (unsigned i=0; i<damping_values.size(); i++)
//        {
//            for (unsigned j=0; j<mNumDofs; j++)
//            {
//                mCurrentSolution[j] = old_solution[j] - damping_values[i]*update[j];
//            }
//
//            // compute residual
//            AssembleSystem(true, false);
//            double norm_resid = CalculateResidualNorm();
//
//            std::cout << "\tTesting s = " << damping_values[i] << ", |f| = " << norm_resid << "\n" << std::flush;
//            if (norm_resid < best_norm_resid)
//            {
//                best_norm_resid = norm_resid;
//                best_damping_value = damping_values[i];
//            }
//        }
//
//        if (best_damping_value == 0.0)
//        {
//            #define COVERAGE_IGNORE
//            assert(0);
//            EXCEPTION("Residual does not decrease in newton direction, quitting");
//            #undef COVERAGE_IGNORE
//        }
//        else
//        {
//            std::cout << "\tBest s = " << best_damping_value << "\n"  << std::flush;
//        }
//        //Timer::PrintAndReset("Find best damping");
//
//        // implement best update and recalculate residual
//        for (unsigned j=0; j<mNumDofs; j++)
//        {
//            mCurrentSolution[j] = old_solution[j] - best_damping_value*update[j];
//        }
    MechanicsEventHandler::EndEvent(MechanicsEventHandler::UPDATE);

    VecDestroy(solution);
    KSPDestroy(solver);

    return norm_resid;
}


template<unsigned DIM>
void AbstractNonlinearElasticityAssembler<DIM>::PostNewtonStep(unsigned counter, double normResidual)
{
}


template<unsigned DIM>
AbstractNonlinearElasticityAssembler<DIM>::AbstractNonlinearElasticityAssembler(unsigned numDofs,
                                         AbstractIncompressibleMaterialLaw<DIM>* pMaterialLaw,
                                         c_vector<double,DIM> bodyForce,
                                         double density,
                                         std::string outputDirectory,
                                         std::vector<unsigned>& fixedNodes)
    : mNumDofs(numDofs),
      mBodyForce(bodyForce),
      mDensity(density),
      mOutputDirectory(outputDirectory),
      mFixedNodes(fixedNodes),
      mNumNewtonIterations(0),
      mUsingBodyForceFunction(false),
      mUsingTractionBoundaryConditionFunction(false)
{
    assert(pMaterialLaw != NULL);
    mMaterialLaws.push_back(pMaterialLaw);

    assert(DIM==2 || DIM==3);
    assert(density > 0);
    assert(fixedNodes.size() > 0);
    mWriteOutput = (mOutputDirectory != "");
    
    AllocateMatrixMemory();
}


template<unsigned DIM>
AbstractNonlinearElasticityAssembler<DIM>::AbstractNonlinearElasticityAssembler(unsigned numDofs,
                                         std::vector<AbstractIncompressibleMaterialLaw<DIM>*>& rMaterialLaws,
                                         c_vector<double,DIM> bodyForce,
                                         double density,
                                         std::string outputDirectory,
                                         std::vector<unsigned>& fixedNodes)
    : mNumDofs(numDofs),
      mBodyForce(bodyForce),
      mDensity(density),
      mOutputDirectory(outputDirectory),
      mFixedNodes(fixedNodes),
      mUsingBodyForceFunction(false),
      mUsingTractionBoundaryConditionFunction(false)
{
    mMaterialLaws.resize(rMaterialLaws.size(), NULL);
    for (unsigned i=0; i<mMaterialLaws.size(); i++)
    {
        assert(rMaterialLaws[i] != NULL);
        mMaterialLaws[i] = rMaterialLaws[i];
    }

    assert(DIM==2 || DIM==3);
    assert(density > 0);
    assert(fixedNodes.size() > 0);
    mWriteOutput = (mOutputDirectory != "");

    AllocateMatrixMemory();
}


template<unsigned DIM>
AbstractNonlinearElasticityAssembler<DIM>::~AbstractNonlinearElasticityAssembler()
{
    delete mpLinearSystem;
    delete mpPreconditionMatrixLinearSystem;
}


template<unsigned DIM>
void AbstractNonlinearElasticityAssembler<DIM>::Solve(double tol,
           unsigned offset,
           unsigned maxNumNewtonIterations,
           bool quitIfNoConvergence)
{
    if (mWriteOutput)
    {
        WriteOutput(0+offset);
    }

    // compute residual
    AssembleSystem(true, false);
    double norm_resid = this->CalculateResidualNorm();
    std::cout << "\nNorm of residual is " << norm_resid << "\n";

    mNumNewtonIterations = 0;
    unsigned counter = 1;

    if (tol < 0) // ie if wasn't passed in as a parameter
    {
        tol = NEWTON_REL_TOL*norm_resid;

        #define COVERAGE_IGNORE // not going to have tests in cts for everything
        if (tol > MAX_NEWTON_ABS_TOL)
        {
            tol = MAX_NEWTON_ABS_TOL;
        }
        if (tol < MIN_NEWTON_ABS_TOL)
        {
            tol = MIN_NEWTON_ABS_TOL;
        }
        #undef COVERAGE_IGNORE
    }

    std::cout << "Solving with tolerance " << tol << "\n";

    while (norm_resid > tol && counter<=maxNumNewtonIterations)
    {
        std::cout <<  "\n-------------------\n"
                  <<   "Newton iteration " << counter
                  << ":\n-------------------\n";

        // take newton step (and get returned residual)
        norm_resid = TakeNewtonStep();

        std::cout << "Norm of residual is " << norm_resid << "\n";
        if (mWriteOutput)
        {
            WriteOutput(counter+offset);
        }

        mNumNewtonIterations = counter;

        PostNewtonStep(counter,norm_resid);

        counter++;
        if (counter==20)
        {
            #define COVERAGE_IGNORE
            EXCEPTION("Not converged after 20 newton iterations, quitting");
            #undef COVERAGE_IGNORE
        }
    }

    if ((norm_resid > tol) && quitIfNoConvergence)
    {
        #define COVERAGE_IGNORE
        EXCEPTION("Failed to converge");
        #undef COVERAGE_IGNORE
    }

    // we have solved for a deformation so note this
    //mADeformedHasBeenSolved = true;
}


template<unsigned DIM>
void AbstractNonlinearElasticityAssembler<DIM>::WriteOutput(unsigned counter)
{
    // only write output if the flag mWriteOutput has been set
    if (!mWriteOutput)
    {
        return;
    }

    OutputFileHandler output_file_handler(mOutputDirectory, (counter==0));
    std::stringstream file_name;
    file_name << "/solution_" << counter << ".nodes";

    out_stream p_file = output_file_handler.OpenOutputFile(file_name.str());

    std::vector<c_vector<double,DIM> >& r_deformed_position = rGetDeformedPosition();
    for (unsigned i=0; i<r_deformed_position.size(); i++)
    {
        for (unsigned j=0; j<DIM; j++)
        {
            *p_file << r_deformed_position[i](j) << " ";
        }
        *p_file << "\n";
    }
    p_file->close();
}


template<unsigned DIM>
unsigned AbstractNonlinearElasticityAssembler<DIM>::GetNumNewtonIterations()
{
    return mNumNewtonIterations;
}


template<unsigned DIM>
void AbstractNonlinearElasticityAssembler<DIM>::SetFunctionalBodyForce(c_vector<double,DIM> (*pFunction)(c_vector<double,DIM>&))
{
    mUsingBodyForceFunction = true;
    mpBodyForceFunction = pFunction;
}


template<unsigned DIM>
void AbstractNonlinearElasticityAssembler<DIM>::SetWriteOutput(bool writeOutput)
{
    if (writeOutput && (mOutputDirectory==""))
    {
        EXCEPTION("Can't write output if no output directory was given in constructor");
    }
    mWriteOutput = writeOutput;
}

//
// Constant setting definitions
//
template<unsigned DIM>
const double AbstractNonlinearElasticityAssembler<DIM>::MAX_NEWTON_ABS_TOL = 1e-8;

template<unsigned DIM>
const double AbstractNonlinearElasticityAssembler<DIM>::MIN_NEWTON_ABS_TOL = 1e-12;

template<unsigned DIM>
const double AbstractNonlinearElasticityAssembler<DIM>::NEWTON_REL_TOL = 1e-4;


#endif /*ABSTRACTNONLINEARELASTICITYASSEMBLER_HPP_*/

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