AbstractNonlinearAssemblerSolverHybrid.hpp

/*

Copyright (C) University of Oxford, 2005-2011

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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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(at your option) any later version.

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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 ABSTRACTNONLINEARASSEMBLERSOLVERHYBRID_HPP_
#define ABSTRACTNONLINEARASSEMBLERSOLVERHYBRID_HPP_

#include "BoundaryConditionsContainer.hpp"
#include "AbstractNonlinearEllipticPde.hpp"
#include "AbstractNonlinearSolver.hpp"
#include "PetscTools.hpp"
#include "PetscMatTools.hpp"
#include "PetscVecTools.hpp"
#include "AbstractFeVolumeIntegralAssembler.hpp"
#include "LinearSystem.hpp"
#include "SimplePetscNonlinearSolver.hpp"
#include "NaturalNeumannSurfaceTermAssembler.hpp"

/*
 * Definitions of GLOBAL functions used by PETSc nonlinear solver
 * (implementations are at the bottom of this file).
 */

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM>
PetscErrorCode AbstractNonlinearAssemblerSolverHybrid_ComputeResidual(SNES snes,
                                                                      Vec currentGuess,
                                                                      Vec residualVector,
                                                                      void* pContext);

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM>
PetscErrorCode AbstractNonlinearAssemblerSolverHybrid_ComputeJacobian(SNES snes,
                                                                      Vec currentGuess,
                                                                      Mat* pGlobalJacobian,
                                                                      Mat* pPreconditioner,
                                                                      MatStructure* pMatStructure,
                                                                      void* pContext);

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM>
class AbstractNonlinearAssemblerSolverHybrid : public AbstractFeVolumeIntegralAssembler<ELEMENT_DIM,SPACE_DIM,PROBLEM_DIM,true,true,NONLINEAR>
{
protected:

    AbstractTetrahedralMesh<ELEMENT_DIM,SPACE_DIM>* mpMesh;

    BoundaryConditionsContainer<ELEMENT_DIM,SPACE_DIM,PROBLEM_DIM>* mpBoundaryConditions;

    AbstractNonlinearSolver* mpSolver;

    bool mWeAllocatedSolverMemory;

    bool mUseAnalyticalJacobian;

    NaturalNeumannSurfaceTermAssembler<ELEMENT_DIM,SPACE_DIM,PROBLEM_DIM>* mpNeumannSurfaceTermsAssembler;

    void ApplyDirichletConditions(Vec currentGuess, Vec residual, Mat* pMat);

    void ComputeJacobianNumerically(const Vec currentGuess, Mat* pJacobian);

public:

    void ComputeResidual(const Vec currentGuess, Vec residualVector);

    void ComputeJacobian(const Vec currentGuess, Mat* pJacobian);

    AbstractNonlinearAssemblerSolverHybrid(AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>* pMesh,
                                           BoundaryConditionsContainer<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM>* pBoundaryConditions,
                                           unsigned numQuadPoints = 2);

    virtual ~AbstractNonlinearAssemblerSolverHybrid();

    virtual Vec Solve(Vec initialGuess, bool useAnalyticalJacobian=false);

    void SetNonlinearSolver(AbstractNonlinearSolver* pNonlinearSolver);

    bool VerifyJacobian(double tol);
};

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM>
AbstractNonlinearAssemblerSolverHybrid<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM>::AbstractNonlinearAssemblerSolverHybrid(
            AbstractTetrahedralMesh<ELEMENT_DIM, SPACE_DIM>* pMesh,
            BoundaryConditionsContainer<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM>* pBoundaryConditions,
            unsigned numQuadPoints)
    :  AbstractFeVolumeIntegralAssembler<ELEMENT_DIM,SPACE_DIM,PROBLEM_DIM,true,true,NONLINEAR>(pMesh,numQuadPoints),
       mpMesh(pMesh),
       mpBoundaryConditions(pBoundaryConditions)
{
    /*
     * Note: if this is run with SPACE_DIM != ELEMENT_DIM the class has to be checked:
     * there may be lots of places where we should be using SPACE_DIM not ELEMENT_DIM.
     */
    assert(SPACE_DIM==ELEMENT_DIM);
    assert(pMesh!=NULL);
    assert(pBoundaryConditions!=NULL);

   // mpAssembler = new SimpleNonlinearEllipticPdeAssembler<ELEMENT_DIM,SPACE_DIM>(mpMesh,pPde,numQuadPoints);
    mpSolver = new SimplePetscNonlinearSolver;
    mWeAllocatedSolverMemory = true;

    assert(mpMesh->GetNumNodes() == mpMesh->GetDistributedVectorFactory()->GetProblemSize());

    mpNeumannSurfaceTermsAssembler = new NaturalNeumannSurfaceTermAssembler<ELEMENT_DIM,SPACE_DIM,PROBLEM_DIM>(pMesh,pBoundaryConditions,numQuadPoints);
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM>
AbstractNonlinearAssemblerSolverHybrid<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM>::~AbstractNonlinearAssemblerSolverHybrid()
{
    if (mWeAllocatedSolverMemory)
    {
        delete mpSolver;
    }
    delete mpNeumannSurfaceTermsAssembler;
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM>
void AbstractNonlinearAssemblerSolverHybrid<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM>::ApplyDirichletConditions(Vec currentGuess, Vec residual, Mat* pJacobian)
{
    if (residual)
    {
        mpBoundaryConditions->ApplyDirichletToNonlinearResidual(currentGuess,
                                                                residual,
                                                                *(mpMesh->GetDistributedVectorFactory()));
    }
    if (pJacobian)
    {
        mpBoundaryConditions->ApplyDirichletToNonlinearJacobian(*pJacobian);
    }
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM>
void AbstractNonlinearAssemblerSolverHybrid<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM>::ComputeResidual(const Vec currentGuess, Vec residualVector)
{
    // Add the volume integral part of the residual. This will call ComputeVectorTerm, which needs to be
    // implemented in the concrete class.
    this->SetVectorToAssemble(residualVector,true);
    this->SetCurrentSolution(currentGuess);
    this->AssembleVector();

    // Add the surface integral contribution - note the negative sign (scale factor).
    // This contribution is, for example for a 1 unknown problem
    // -integral(g\phi_id dS), where g is the specfied neumann boundary condition
    mpNeumannSurfaceTermsAssembler->SetVectorToAssemble(residualVector, false);
    mpNeumannSurfaceTermsAssembler->SetScaleFactor(-1.0);
    mpNeumannSurfaceTermsAssembler->Assemble();

    PetscVecTools::Finalise(residualVector);

    ApplyDirichletConditions(currentGuess, residualVector, NULL);
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM>
void AbstractNonlinearAssemblerSolverHybrid<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM>::ComputeJacobian(const Vec currentGuess, Mat* pJacobian)
{
    if (mUseAnalyticalJacobian)
    {
        this->SetMatrixToAssemble(*pJacobian);
        this->SetCurrentSolution(currentGuess);
        this->AssembleMatrix();

        PetscMatTools::SwitchWriteMode(*pJacobian);

        ApplyDirichletConditions(currentGuess, NULL, pJacobian);

        PetscMatTools::Finalise(*pJacobian);
    }
    else
    {
        ComputeJacobianNumerically(currentGuess, pJacobian);
    }
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM>
void AbstractNonlinearAssemblerSolverHybrid<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM>::ComputeJacobianNumerically(const Vec currentGuess, Mat* pJacobian)
{
    unsigned num_unknowns = PROBLEM_DIM * this->mpMesh->GetNumNodes();

    // Set up working vectors
    Vec residual;
    Vec perturbed_residual;
    Vec result;
    residual = PetscTools::CreateVec(num_unknowns);
    result = PetscTools::CreateVec(num_unknowns);
    perturbed_residual = PetscTools::CreateVec(num_unknowns);

    // Copy the currentGuess vector; we perturb the copy
    Vec current_guess_copy;
    PETSCEXCEPT( VecDuplicate(currentGuess, &current_guess_copy) );
    PETSCEXCEPT( VecCopy(currentGuess, current_guess_copy) );

    // Compute the current residual
    ComputeResidual(currentGuess, residual);

    // Amount to perturb each input element by
    double h = 1e-5;

    PetscInt ilo, ihi;
    VecGetOwnershipRange(current_guess_copy, &ilo, &ihi);
    unsigned lo = ilo;
    unsigned hi = ihi;

    // Iterate over entries in the input vector
    for (unsigned global_index_outer = 0; global_index_outer < num_unknowns; global_index_outer++)
    {
        // Only perturb if we own it
        PetscVecTools::AddToElement(current_guess_copy, global_index_outer, h);
        ComputeResidual(current_guess_copy, perturbed_residual);

        // result = (perturbed_residual - residual) / h
        PetscVecTools::WAXPY(result, -1.0, residual, perturbed_residual);
        PetscVecTools::Scale(result, 1.0/h);

        double* p_result;
        PETSCEXCEPT( VecGetArray(result, &p_result) );
        for (unsigned global_index=lo; global_index < hi; global_index++)
        {
            unsigned local_index = global_index - lo;
            PetscMatTools::SetElement(*pJacobian, global_index, global_index_outer, p_result[local_index]);
        }
        PETSCEXCEPT( VecRestoreArray(result, &p_result) );

        PetscVecTools::AddToElement(current_guess_copy, global_index_outer, -h);
    }

    VecDestroy(residual);
    VecDestroy(perturbed_residual);
    VecDestroy(result);
    VecDestroy(current_guess_copy);

    PetscMatTools::Finalise(*pJacobian);
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM>
Vec AbstractNonlinearAssemblerSolverHybrid<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM>::Solve(Vec initialGuess,
                                                                                       bool useAnalyticalJacobian)
{
    assert(initialGuess != NULL);
    mUseAnalyticalJacobian = useAnalyticalJacobian;

    PetscInt size_of_init_guess;
    VecGetSize(initialGuess, &size_of_init_guess);
    PetscInt problem_size = PROBLEM_DIM * this->mpMesh->GetNumNodes();
    if (size_of_init_guess != problem_size)
    {
        EXCEPTION("Size of initial guess vector, " << size_of_init_guess
                      << ", does not match size of problem, " << problem_size);
    }

    // Run the solver, telling it which global functions to call in order to assemble the residual or jacobian
    return mpSolver->Solve(&AbstractNonlinearAssemblerSolverHybrid_ComputeResidual<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM>,
                           &AbstractNonlinearAssemblerSolverHybrid_ComputeJacobian<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM>,
                           initialGuess,
                           PROBLEM_DIM * this->mpMesh->CalculateMaximumNodeConnectivityPerProcess(),
                           this);
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM>
void AbstractNonlinearAssemblerSolverHybrid<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM>::SetNonlinearSolver(AbstractNonlinearSolver* pNonlinearSolver)
{
    if (mWeAllocatedSolverMemory)
    {
        delete mpSolver;
    }
    mpSolver = pNonlinearSolver;
    mWeAllocatedSolverMemory = false;
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM>
bool AbstractNonlinearAssemblerSolverHybrid<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM>::VerifyJacobian(double tol)
{
    unsigned size = PROBLEM_DIM * this->mpMesh->GetNumNodes();

    Vec initial_guess = PetscTools::CreateAndSetVec(size, 0.0);

    Mat analytic_jacobian;
    Mat numerical_jacobian;

    PetscTools::SetupMat(analytic_jacobian, size, size, size);
    PetscTools::SetupMat(numerical_jacobian, size, size, size);

    mUseAnalyticalJacobian = true;
    ComputeJacobian(initial_guess, &analytic_jacobian);

    mUseAnalyticalJacobian = false;
    ComputeJacobian(initial_guess, &numerical_jacobian);

    bool ok = PetscMatTools::CheckEquality(numerical_jacobian, analytic_jacobian, tol);
    MatDestroy(numerical_jacobian);
    MatDestroy(analytic_jacobian);
    VecDestroy(initial_guess);

    return ok;
}

// Implementations of GLOBAL functions called by PETSc nonlinear solver

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM>
PetscErrorCode AbstractNonlinearAssemblerSolverHybrid_ComputeResidual(SNES snes,
                                                                      Vec currentGuess,
                                                                      Vec residualVector,
                                                                      void* pContext)
{
    // Extract the solver from the void*
    AbstractNonlinearAssemblerSolverHybrid<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM>* p_solver =
        (AbstractNonlinearAssemblerSolverHybrid<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM>*) pContext;

    p_solver->ComputeResidual(currentGuess, residualVector);

    return 0;
}

template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM>
PetscErrorCode AbstractNonlinearAssemblerSolverHybrid_ComputeJacobian(SNES snes,
                                                                      Vec currentGuess,
                                                                      Mat* pGlobalJacobian,
                                                                      Mat* pPreconditioner,
                                                                      MatStructure* pMatStructure,
                                                                      void* pContext)
{
    // Extract the solver from the void*
    AbstractNonlinearAssemblerSolverHybrid<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM>* p_solver =
        (AbstractNonlinearAssemblerSolverHybrid<ELEMENT_DIM, SPACE_DIM, PROBLEM_DIM>*) pContext;

    p_solver->ComputeJacobian(currentGuess, pGlobalJacobian);

    return 0;
}

#endif /*ABSTRACTNONLINEARASSEMBLERSOLVERHYBRID_HPP_*/