AbstractNonlinearElasticityAssembler.hpp

/*

Copyright (C) University of Oxford, 2005-2010

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
by the Free Software Foundation, either version 2.1 of the License, or
(at your option) any later version.

Chaste is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
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"

//#define MECH_VERBOSE
//#define MECH_VERY_VERBOSE
//#define MECH_USE_HYPRE

#ifdef MECH_VERBOSE
#include "Timer.hpp"
#endif

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 ComputeResidualAndGetNorm();

    double CalculateResidualNorm();

    void VectorSum(std::vector<double>& rX, ReplicatableVector& rY, double a, std::vector<double>& rZ);

    void PrintLineSearchResult(double s, double residNorm);


    double TakeNewtonStep();

    double UpdateSolutionUsingLineSearch(Vec solution);


    virtual void PostNewtonStep(unsigned counter, double normResidual);

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

    std::vector<unsigned> rows;
    if(applyToMatrix)
    {
        rows.resize(DIM*mFixedNodes.size());
    }

    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;

            if(applyToMatrix)
            {
                rows[DIM*i+j] = dof_index;
            }

            double value = mCurrentSolution[dof_index] - mFixedNodeDisplacements[i](j);
            mpLinearSystem->SetRhsVectorElement(dof_index, value);
        }
    }

    if(applyToMatrix)
    {
        mpLinearSystem->ZeroMatrixRowsWithValueOnDiagonal(rows, 1.0);
        mpPreconditionMatrixLinearSystem->ZeroMatrixRowsWithValueOnDiagonal(rows, 1.0);
    }
}

template<unsigned DIM>
double AbstractNonlinearElasticityAssembler<DIM>::ComputeResidualAndGetNorm()
{
      AssembleSystem(true, false);

//    if(!allowException /* argument */)
//    {
//        // assemble the residual
//        AssembleSystem(true, false);
//    }
//    else
//    {
//        try
//        {
//            // try to assemble the residual using this current solution
//            AssembleSystem(true, false);
//        }
//        catch(Exception& e)
//        {
//            // if fail (because eg ODEs fail to solve), return infinity
//            return DBL_MAX;
//        }
//    }

    // return the scaled norm of the residual
    return CalculateResidualNorm();
}

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

template<unsigned DIM>
void AbstractNonlinearElasticityAssembler<DIM>::VectorSum(std::vector<double>& rX,
                                                          ReplicatableVector& rY,
                                                          double a,
                                                          std::vector<double>& rZ)
{
    assert(rX.size()==rY.GetSize());
    assert(rY.GetSize()==rZ.size());
    for(unsigned i=0; i<rX.size(); i++)
    {
        rZ[i] = rX[i] + a*rY[i];
    }
}


template<unsigned DIM>
double AbstractNonlinearElasticityAssembler<DIM>::TakeNewtonStep()
{
    #ifdef MECH_VERBOSE
    Timer::Reset();
    #endif

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

    // 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(PETSC_COMM_WORLD,&solver);

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

    double ksp_relative_error_tol = 1e-6;
    unsigned num_restarts = 100;
    // set max iterations
    KSPSetTolerances(solver, ksp_relative_error_tol, PETSC_DEFAULT, PETSC_DEFAULT, 10000); //hopefully with the preconditioner this max is way too high
    KSPSetType(solver,KSPGMRES);
    KSPGMRESSetRestart(solver,num_restarts); // gmres num restarts

    KSPSetFromOptions(solver);
    KSPSetUp(solver);
    #ifdef MECH_VERBOSE
    Timer::PrintAndReset("KSP Setup");
    #endif

    PC pc;
    KSPGetPC(solver, &pc);

    #ifndef MECH_USE_HYPRE    
        PCSetType(pc, PCJACOBI);
    #else
        // Speed up linear solve time massively for larger simulations (in fact GMRES may stagnate without
        // this for larger problems), by using a AMG preconditioner -- needs HYPRE installed 
        PCSetType(pc, PCHYPRE);
        KSPSetPreconditionerSide(solver, PC_RIGHT);
    #endif     

    KSPSetFromOptions(solver);
    
    KSPSolve(solver,mpLinearSystem->rGetRhsVector(),solution);
    
    #ifdef MECH_VERBOSE
    Timer::PrintAndReset("KSP Solve");
    int num_iters;
    KSPGetIterationNumber(solver, &num_iters);
    std::cout << "[" << PetscTools::GetMyRank() << "]: Num iterations = " << num_iters << "\n" << std::flush;
    #endif


    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);
    double new_norm_resid = UpdateSolutionUsingLineSearch(solution);
    MechanicsEventHandler::EndEvent(MechanicsEventHandler::UPDATE);

    VecDestroy(solution);
    KSPDestroy(solver);

    return new_norm_resid;
}

template<unsigned DIM>
void AbstractNonlinearElasticityAssembler<DIM>::PrintLineSearchResult(double s, double residNorm)
{
    #ifdef MECH_VERBOSE
    std::cout << "\tTesting s = " << s << ", |f| = " << residNorm << "\n" << std::flush;
    #endif
}

template<unsigned DIM>
double AbstractNonlinearElasticityAssembler<DIM>::UpdateSolutionUsingLineSearch(Vec solution)
{
    double initial_norm_resid = CalculateResidualNorm();
    #ifdef MECH_VERBOSE
    std::cout << "\tInitial |f| [corresponding to s=0] is " << initial_norm_resid << "\n"  << std::flush;
    #endif

    ReplicatableVector update(solution);

    std::vector<double> old_solution = mCurrentSolution;

    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);


    // let mCurrentSolution = old_solution - damping_val[0]*update; and compute residual
    unsigned index = 0;
    VectorSum(old_solution, update, -damping_values[index], mCurrentSolution);
    double current_resid_norm = ComputeResidualAndGetNorm();
    PrintLineSearchResult(damping_values[index], current_resid_norm);

    // let mCurrentSolution = old_solution - damping_val[1]*update; and compute residual
    index = 1;
    VectorSum(old_solution, update, -damping_values[index], mCurrentSolution);
    double next_resid_norm = ComputeResidualAndGetNorm();
    PrintLineSearchResult(damping_values[index], next_resid_norm);

    index = 2;
    // While f(s_next) < f(s_current), [f = residnorm], keep trying new damping values,
    // ie exit thus loop when next norm of the residual first increases
    while ( (next_resid_norm < current_resid_norm)  && index<damping_values.size())
    {
        current_resid_norm = next_resid_norm;

        // let mCurrentSolution = old_solution - damping_val*update; and compute residual
        VectorSum(old_solution, update, -damping_values[index], mCurrentSolution);
        next_resid_norm = ComputeResidualAndGetNorm();
        PrintLineSearchResult(damping_values[index], next_resid_norm);

        index++;
    }

    unsigned best_index;

    if(index==damping_values.size() && (next_resid_norm < current_resid_norm))
    {
        // Difficult to come up with large forces/tractions such that it had to
        // test right down to s=0.05, but overall doesn't fail.
        // The possible damping values have been manually temporarily altered to
        // get this code to be called, it appears to work correctly. Even if it
        // didn't tests wouldn't fail, they would just be v. slightly less efficient.
        #define COVERAGE_IGNORE
        // if we exited because we got to the end of the possible damping values, the
        // best one was the last one (excl the final index++ at the end)
        current_resid_norm = next_resid_norm;
        best_index = index-1;
        #undef COVERAGE_IGNORE
    }
    else
    {
        // else the best one must have been the second last one (excl the final index++ at the end)
        // (as we would have exited when the resid norm first increased)
        best_index = index-2;
    }

    // check out best was better than the original residual-norm
    if (initial_norm_resid < current_resid_norm)
    {
        #define COVERAGE_IGNORE
        // Have to use an assert/exit here as the following exception causes a seg fault (in cardiac mech problems?)
        // Don't know why
        std::cout << "CHASTE ERROR: (AbstractNonlinearElasticityAssembler.hpp): Residual does not appear to decrease in newton direction, quitting.\n" << std::flush;
        exit(0);
        //EXCEPTION("Residual does not appear to decrease in newton direction, quitting");
        #undef COVERAGE_IGNORE
    }

    #ifdef MECH_VERBOSE
    std::cout << "\tBest s = " << damping_values[best_index] << "\n"  << std::flush;
    #endif
    VectorSum(old_solution, update, -damping_values[best_index], mCurrentSolution);

    return current_resid_norm;

//        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
//            double norm_resid = ComputeResidualAndGetNorm();
//
//            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];
//        }
}



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 != "");
}


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 != "");
}


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
    double norm_resid = this->ComputeResidualAndGetNorm();
    #ifdef MECH_VERBOSE
    std::cout << "\nNorm of residual is " << norm_resid << "\n";
    #endif

    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
    }

    #ifdef MECH_VERBOSE
    std::cout << "Solving with tolerance " << tol << "\n";
    #endif

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

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

        #ifdef MECH_VERBOSE
        std::cout << "Norm of residual is " << norm_resid << "\n";
        #endif
        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
    }
}


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-7;

template<unsigned DIM>
const double AbstractNonlinearElasticityAssembler<DIM>::MIN_NEWTON_ABS_TOL = 1e-10;

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


#endif /*ABSTRACTNONLINEARELASTICITYASSEMBLER_HPP_*/