AbstractNonlinearAssemblerSolverHybrid.hpp

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#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);
#if (PETSC_VERSION_MAJOR==3 && PETSC_VERSION_MINOR>=5)
    template<unsigned ELEMENT_DIM, unsigned SPACE_DIM, unsigned PROBLEM_DIM>
 
    PetscErrorCode AbstractNonlinearAssemblerSolverHybrid_ComputeJacobian(SNES snes,
                                                                          Vec currentGuess,
                                                                          Mat globalJacobian,
                                                                          Mat preconditioner,
                                                                          void* pContext);
#else
    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);
#endif
 
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);
 
    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)
    :  AbstractFeVolumeIntegralAssembler<ELEMENT_DIM,SPACE_DIM,PROBLEM_DIM,true,true,NONLINEAR>(pMesh),
       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!=nullptr);
    assert(pBoundaryConditions!=nullptr);
 
    mpSolver = new SimplePetscNonlinearSolver;
    mWeAllocatedSolverMemory = true;
 
    assert(mpMesh->GetNumNodes() == mpMesh->GetDistributedVectorFactory()->GetProblemSize());
 
    mpNeumannSurfaceTermsAssembler = new NaturalNeumannSurfaceTermAssembler<ELEMENT_DIM,SPACE_DIM,PROBLEM_DIM>(pMesh,pBoundaryConditions);
}
 
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, nullptr);
}
 
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, nullptr, 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;
    double near_hsquared = 1e-9;
 
    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++)
        {
            double result_entry = p_result[ global_index - lo];
            if (!CompareDoubles::IsNearZero(result_entry, near_hsquared))
            {
                PetscMatTools::SetElement(*pJacobian, global_index, global_index_outer, result_entry);
            }
        }
        PETSCEXCEPT( VecRestoreArray(result, &p_result) );
 
        PetscVecTools::AddToElement(current_guess_copy, global_index_outer, -h);
    }
 
    PetscTools::Destroy(residual);
    PetscTools::Destroy(perturbed_residual);
    PetscTools::Destroy(result);
    PetscTools::Destroy(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 != nullptr);
    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);
    PetscTools::Destroy(numerical_jacobian);
    PetscTools::Destroy(analytic_jacobian);
    PetscTools::Destroy(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>
#if (PETSC_VERSION_MAJOR==3 && PETSC_VERSION_MINOR>=5)
PetscErrorCode AbstractNonlinearAssemblerSolverHybrid_ComputeJacobian(SNES snes,
                                                                      Vec currentGuess,
                                                                      Mat globalJacobian,
                                                                      Mat preconditioner,
                                                                      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, &globalJacobian);
 
    return 0;
}
#else
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
 
#endif /*ABSTRACTNONLINEARASSEMBLERSOLVERHYBRID_HPP_*/