SERiF/src/poly/solver/private/polySolver.cpp

/* ***********************************************************************
//
//   Copyright (C) 2025 -- The 4D-STAR Collaboration
//   File Author: Emily Boudreaux
//   Last Modified: April 21, 2025
//
//   4DSSE is free software; you can use it and/or modify
//   it under the terms and restrictions the GNU General Library Public
//   License version 3 (GPLv3) as published by the Free Software Foundation.
//
//   4DSSE 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 Library General Public License for more details.
//
//   You should have received a copy of the GNU Library General Public License
//   along with this software; if not, write to the Free Software
//   Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
//
// *********************************************************************** */
#include "polySolver.h"

#include <memory>
#include <stdexcept>
#include <string>
#include <utility>

#include "mfem.hpp"

#include "4DSTARTypes.h"
#include "config.h"
#include "integrators.h"
#include "mfem.hpp"
#include "operator.h"
#include "polyCoeff.h"
#include "probe.h"
#include "resourceManager.h"
#include "resourceManagerTypes.h"
#include "quill/LogMacros.h"


namespace laneEmden {

    double a (const int k, const double n) { // NOLINT(*-no-recursion)
        if ( k == 0 ) { return 1; }
        if ( k == 1 ) { return 0; }
        else { return -(c(k-2, n)/(std::pow(k, 2)+k)); }

    }

    double c(const int m, const double n) { // NOLINT(*-no-recursion)
        if ( m == 0 ) { return std::pow(a(0, n), n); }
        else {
            double termOne = 1.0/(m*a(0, n));
            double acc = 0;
            for (int k = 1; k <= m; k++) {
                acc += (k*n-m+k)*a(k, n)*c(m-k, n);
            }
            return termOne*acc;
        }
    }

    double thetaSeriesExpansion(const double xi, const double n, const int order) {
        double acc = 0;
        for (int k = 0; k < order; k++) {
            acc += a(k, n) * std::pow(xi, k);
        }
        return acc;
    }
}


PolySolver::PolySolver(const double n, const double order) {

    // --- Check the polytropic index ---
    if (n > 4.99 || n < 0.0) {
        LOG_ERROR(m_logger, "The polytropic index n must be less than 5.0 and greater than 0.0. Currently it is {}", m_polytropicIndex);
        throw std::runtime_error("The polytropic index n must be less than 5.0 and greater than 0.0. Currently it is " + std::to_string(m_polytropicIndex));
    }

    m_polytropicIndex = n;
    m_feOrder = order;

    // Load and rescale the mesh
    const ResourceManager& rm = ResourceManager::getInstance();
    const Resource& genericResource = rm.getResource("mesh:polySphere");
    const auto &meshIO = std::get<std::unique_ptr<MeshIO>>(genericResource);
    meshIO->LinearRescale(polycoeff::x1(m_polytropicIndex));
    m_mesh = std::make_unique<mfem::Mesh>(meshIO->GetMesh());

    // Use feOrder - 1 for the RT space to satisfy Brezzi-Babuska condition
    // for the H1 and RT [H(div)] spaces
    m_fecH1 = std::make_unique<mfem::H1_FECollection>(m_feOrder, m_mesh->SpaceDimension());
    m_fecRT = std::make_unique<mfem::RT_FECollection>(m_feOrder - 1, m_mesh->SpaceDimension());

    m_feTheta = std::make_unique<mfem::FiniteElementSpace>(m_mesh.get(), m_fecH1.get());
    m_fePhi = std::make_unique<mfem::FiniteElementSpace>(m_mesh.get(), m_fecRT.get());

    m_theta = std::make_unique<mfem::GridFunction>(m_feTheta.get());
    m_phi = std::make_unique<mfem::GridFunction>(m_fePhi.get());

    assembleBlockSystem();

}

PolySolver::~PolySolver() = default;

void PolySolver::assembleBlockSystem() {
    mfem::Array<int> blockOffsets = computeBlockOffsets();

    const std::unique_ptr<formBundle> forms = buildIndividualForms(blockOffsets);

    // --- Build the BlockOperator ---
    m_polytropOperator = std::make_unique<PolytropeOperator>(
        std::move(forms->M),
        std::move(forms->Q),
        std::move(forms->D),
        std::move(forms->f),
        blockOffsets);
}

mfem::Array<int> PolySolver::computeBlockOffsets() const {
    mfem::Array<int> blockOffsets;
    blockOffsets.SetSize(3);
    blockOffsets[0] = 0;
    blockOffsets[1] = m_feTheta->GetVSize(); // Get actual number of dofs *before* applying BCs
    blockOffsets[2] = m_fePhi->GetVSize();
    blockOffsets.PartialSum(); // Cumulative sum to get the offsets
    return blockOffsets;
}

std::unique_ptr<formBundle> PolySolver::buildIndividualForms(const mfem::Array<int> &blockOffsets) {
    // --- Assemble the MixedBilinear and Bilinear forms (M, D, and Q) ---
    auto forms = std::make_unique<formBundle>(
        std::make_unique<mfem::MixedBilinearForm>(m_fePhi.get(), m_feTheta.get()),
        std::make_unique<mfem::MixedBilinearForm>(m_feTheta.get(), m_fePhi.get()),
        std::make_unique<mfem::BilinearForm>(m_fePhi.get()),
        std::make_unique<mfem::NonlinearForm>(m_feTheta.get())
    );

    // --- -M negation -> M ---
    mfem::Vector negOneVec(m_mesh->SpaceDimension());
    negOneVec = -1.0;

    m_negationCoeff = std::make_unique<mfem::VectorConstantCoefficient>(negOneVec);

    // --- Add the integrators to the forms ---
    forms->M->AddDomainIntegrator(new mfem::MixedVectorWeakDivergenceIntegrator(*m_negationCoeff));
    forms->Q->AddDomainIntegrator(new mfem::MixedVectorGradientIntegrator());
    forms->D->AddDomainIntegrator(new mfem::VectorFEMassIntegrator());

    // --- Assemble and Finalize the forms ---
    assembleAndFinalizeForm(forms->M);
    assembleAndFinalizeForm(forms->Q);
    assembleAndFinalizeForm(forms->D);

    forms->f->AddDomainIntegrator(new polyMFEMUtils::NonlinearPowerIntegrator(m_polytropicIndex));

    return std::move(forms);
}

void PolySolver::assembleAndFinalizeForm(auto &f) {
    // This constructs / ensures the matrix representation for each form
    // Assemble => Computes the local element matrices across the domain. Adds these to the global matrix . Adds these to the global matrix.
    // Finalize => Builds the sparsity pattern and allows the SparseMatrix representation to be extracted.
    f->Assemble();
    f->Finalize();
}

void PolySolver::solve() const {
    // --- Set the initial guess for the solution ---
    setInitialGuess();

    setOperatorEssentialTrueDofs();
    const auto thetaVec = static_cast<mfem::Vector>(*m_theta); // NOLINT(*-slicing)
    const auto phiVec = static_cast<mfem::Vector>(*m_phi); // NOLINT(*-slicing)

    // --- Finalize the operator ---
    // Finalize with the initial state of theta for the initial jacobian calculation
    m_polytropOperator->finalize(thetaVec);

    if (!m_polytropOperator->isFinalized()) {
        LOG_ERROR(m_logger, "PolytropeOperator is not finalized. Cannot solve.");
        throw std::runtime_error("PolytropeOperator is not finalized. Cannot solve.");
    }

    // It's safer to get the offsets directly from the operator after finalization
    const mfem::Array<int>& block_offsets = m_polytropOperator->GetBlockOffsets(); // Assuming a getter exists or accessing member if public/friend
    mfem::BlockVector state_vector(block_offsets);
    state_vector.GetBlock(0) = thetaVec; // NOLINT(*-slicing)
    state_vector.GetBlock(1) = phiVec; // NOLINT(*-slicing)


    mfem::Vector zero_rhs(block_offsets.Last()); // TODO: Is this right?
    zero_rhs = 0.0;

    const solverBundle sb = setupNewtonSolver();
    sb.newton.Mult(zero_rhs, state_vector);

    // Ax = b for x

    // --- Save and view the solution ---
    saveAndViewSolution(state_vector);
}

SSE::MFEMArrayPairSet PolySolver::getEssentialTrueDof() const {
    mfem::Array<int> theta_ess_tdof_list;
    mfem::Array<int> phi_ess_tdof_list;

    mfem::Array<int> thetaCenterDofs, phiCenterDofs; // phiCenterDofs are not used
    mfem::Array<double> thetaCenterVals;
    std::tie(thetaCenterDofs, phiCenterDofs) = findCenterElement();
    thetaCenterVals.SetSize(thetaCenterDofs.Size());

    thetaCenterVals = 1.0;

    mfem::Array<int> ess_brd(m_mesh->bdr_attributes.Max());
    ess_brd = 1;

    mfem::Array<double> thetaSurfaceVals, phiSurfaceVals;
    m_feTheta->GetEssentialTrueDofs(ess_brd, theta_ess_tdof_list);
    m_fePhi->GetEssentialTrueDofs(ess_brd, phi_ess_tdof_list);

    thetaSurfaceVals.SetSize(theta_ess_tdof_list.Size());
    thetaSurfaceVals = 0.0;
    phiSurfaceVals.SetSize(phi_ess_tdof_list.Size());
    phiSurfaceVals = polycoeff::thetaSurfaceFlux(m_polytropicIndex);

    // combine the essential dofs with the center dofs
    theta_ess_tdof_list.Append(thetaCenterDofs);
    thetaSurfaceVals.Append(thetaCenterVals);

    SSE::MFEMArrayPair thetaPair = std::make_pair(theta_ess_tdof_list, thetaSurfaceVals);
    SSE::MFEMArrayPair phiPair = std::make_pair(phi_ess_tdof_list, phiSurfaceVals);
    SSE::MFEMArrayPairSet pairSet = std::make_pair(thetaPair, phiPair);

    return pairSet;
}

std::pair<mfem::Array<int>, mfem::Array<int>> PolySolver::findCenterElement() const {
    mfem::Array<int> thetaCenterDofs;
    mfem::Array<int> phiCenterDofs;
    mfem::DenseMatrix centerPoint(m_mesh->SpaceDimension(), 1);
    centerPoint(0, 0) = 0.0;
    centerPoint(1, 0) = 0.0;
    centerPoint(2, 0) = 0.0;

    mfem::Array<int> elementIDs;
    mfem::Array<mfem::IntegrationPoint> ips;
    m_mesh->FindPoints(centerPoint, elementIDs, ips);
    mfem::Array<int> tempDofs;
    for (int i = 0; i < elementIDs.Size(); i++) {
        m_feTheta->GetElementDofs(elementIDs[i], tempDofs);
        thetaCenterDofs.Append(tempDofs);
        m_fePhi->GetElementDofs(elementIDs[i], tempDofs);
        phiCenterDofs.Append(tempDofs);
    }
    return std::make_pair(thetaCenterDofs, phiCenterDofs);
}

void PolySolver::setInitialGuess() const {
    // --- Set the initial guess for the solution ---
    mfem::FunctionCoefficient thetaInitGuess (
        [this](const mfem::Vector &x) {
            const double r = x.Norml2();
            const double radius = Probe::getMeshRadius(*m_mesh);
            const double u = 1/radius;

            // return (-1.0/radius) * r + 1;
            // return -std::pow((u*r), 2)+1.0; // The series expansion is a better guess; however, this is cheaper and ensures that the value at the surface is very close to zero in a way that the series expansion does not
            return laneEmden::thetaSeriesExpansion(r, m_polytropicIndex, 5);
        }
    );

    mfem::VectorFunctionCoefficient phiSurfaceVectors (m_mesh->SpaceDimension(),
        [this](const mfem::Vector &x, mfem::Vector &y) {
            const double r = x.Norml2();
            mfem::Vector xh(x);
            xh /= r; // Normalize the vector
            y.SetSize(m_mesh->SpaceDimension());
            y = xh;
            y *= polycoeff::thetaSurfaceFlux(m_polytropicIndex);
        }
    );
    // We want to apply specific boundary conditions to the surface
    mfem::Array<int> ess_brd(m_mesh->bdr_attributes.Max());
    ess_brd = 1;

    // θ = 0 at surface
    mfem::ConstantCoefficient surfacePotential(0);

    m_theta->ProjectCoefficient(thetaInitGuess);
    m_theta->ProjectBdrCoefficient(surfacePotential, ess_brd);

    mfem::GradientGridFunctionCoefficient phiInitGuess (m_theta.get());
    m_phi->ProjectCoefficient(phiInitGuess);
    m_phi->ProjectBdrCoefficientNormal(phiSurfaceVectors, ess_brd);

    if (m_config.get<bool>("Poly:Solver:ViewInitialGuess", false)) {
        Probe::glVisView(*m_theta, *m_mesh, "θ init");
        Probe::glVisView(*m_phi, *m_mesh, "φ init");
    }

}

void PolySolver::saveAndViewSolution(const mfem::BlockVector& state_vector) const {
    mfem::BlockVector x_block(const_cast<mfem::BlockVector&>(state_vector), m_polytropOperator->GetBlockOffsets());
    mfem::Vector& x_theta = x_block.GetBlock(0);
    mfem::Vector& x_phi = x_block.GetBlock(1);

    if (m_config.get<bool>("Poly:Output:View", false)) {
        Probe::glVisView(x_theta, *m_feTheta, "θ Solution");
        Probe::glVisView(x_phi, *m_fePhi, "ɸ Solution");
    }

    // --- Extract the Solution ---
    if (m_config.get<bool>("Poly:Output:1D:Save", true)) {
        auto solutionPath = m_config.get<std::string>("Poly:Output:1D:Path", "polytropeSolution_1D.csv");
        auto derivSolPath = "d" + solutionPath;

        auto rayCoLatitude = m_config.get<double>("Poly:Output:1D:RayCoLatitude", 0.0);
        auto rayLongitude = m_config.get<double>("Poly:Output:1D:RayLongitude", 0.0);
        auto raySamples = m_config.get<int>("Poly:Output:1D:RaySamples", 100);

        std::vector rayDirection = {rayCoLatitude, rayLongitude};

        Probe::getRaySolution(x_theta, *m_feTheta, rayDirection, raySamples, solutionPath);
        // Probe::getRaySolution(x_phi, *m_fePhi, rayDirection, raySamples, derivSolPath);
    }
}

void PolySolver::setOperatorEssentialTrueDofs() const {
    const SSE::MFEMArrayPairSet ess_tdof_pair_set = getEssentialTrueDof();
    m_polytropOperator->SetEssentialTrueDofs(ess_tdof_pair_set);
}

void PolySolver::LoadSolverUserParams(double &newtonRelTol, double &newtonAbsTol, int &newtonMaxIter, int &newtonPrintLevel, double &gmresRelTol, double &gmresAbsTol, int &gmresMaxIter, int &gmresPrintLevel) const {
    newtonRelTol = m_config.get<double>("Poly:Solver:Newton:RelTol", 1e-7);
    newtonAbsTol = m_config.get<double>("Poly:Solver:Newton:AbsTol", 1e-7);
    newtonMaxIter = m_config.get<int>("Poly:Solver:Newton:MaxIter", 200);
    newtonPrintLevel = m_config.get<int>("Poly:Solver:Newton:PrintLevel", 1);

    gmresRelTol = m_config.get<double>("Poly:Solver:GMRES:RelTol", 1e-10);
    gmresAbsTol = m_config.get<double>("Poly:Solver:GMRES:AbsTol", 1e-12);
    gmresMaxIter = m_config.get<int>("Poly:Solver:GMRES:MaxIter", 2000);
    gmresPrintLevel = m_config.get<int>("Poly:Solver:GMRES:PrintLevel", 0);

    LOG_DEBUG(m_logger, "Newton Solver (relTol: {:0.2E}, absTol: {:0.2E}, maxIter: {}, printLevel: {})", newtonRelTol, newtonAbsTol, newtonMaxIter, newtonPrintLevel);
    LOG_DEBUG(m_logger, "GMRES Solver (relTol: {:0.2E}, absTol: {:0.2E}, maxIter: {}, printLevel: {})", gmresRelTol, gmresAbsTol, gmresMaxIter, gmresPrintLevel);
}

void PolySolver::GetDofCoordinates(const mfem::FiniteElementSpace &fes, const std::string& filename) {
    mfem::Mesh *mesh = fes.GetMesh();
    double r = Probe::getMeshRadius(*mesh);
    std::ofstream outputFile(filename, std::ios::out | std::ios::trunc);
    outputFile << "dof,R,r,x,y,z" << '\n';

    const int nElements = mesh->GetNE();

    mfem::Vector coords;
    mfem::IntegrationPoint ipZero;
    double p[3] = {0.0, 0.0, 0.0};
    int actual_idx;
    ipZero.Set3(p);
    for (int i = 0; i < nElements; i++) {
        mfem::Array<int> elemDofs;
        fes.GetElementDofs(i, elemDofs);
        mfem::ElementTransformation* T = mesh->GetElementTransformation(i);
        mfem::Vector physCoord(3);
        T->Transform(ipZero, physCoord);
        for (int dofID = 0; dofID < elemDofs.Size(); dofID++) {
            if (elemDofs[dofID] < 0) {
                actual_idx = -elemDofs[dofID] - 1;
            } else {
                actual_idx = elemDofs[dofID];
            }
            outputFile << actual_idx;
            if (dofID != elemDofs.Size() - 1) {
                outputFile << "|";
            } else {
                outputFile << ",";
            }
        }
        outputFile << r << "," << physCoord.Norml2() << "," << physCoord[0] << "," << physCoord[1] << "," << physCoord[2] << '\n';
    }
    outputFile.close();
}

solverBundle PolySolver::setupNewtonSolver() const {
    // --- Load configuration parameters ---
    double newtonRelTol, newtonAbsTol, gmresRelTol, gmresAbsTol;
    int newtonMaxIter, newtonPrintLevel, gmresMaxIter, gmresPrintLevel;
    LoadSolverUserParams(newtonRelTol, newtonAbsTol, newtonMaxIter, newtonPrintLevel, gmresRelTol, gmresAbsTol,
                         gmresMaxIter, gmresPrintLevel);

    solverBundle solver; // Use this solver bundle to ensure lifetime safety
    solver.solver.SetRelTol(gmresRelTol);
    solver.solver.SetAbsTol(gmresAbsTol);
    solver.solver.SetMaxIter(gmresMaxIter);
    solver.solver.SetPrintLevel(gmresPrintLevel);

    solver.solver.SetPreconditioner(m_polytropOperator->GetPreconditioner());
    // --- Set up the Newton solver ---
    solver.newton.SetRelTol(newtonRelTol);
    solver.newton.SetAbsTol(newtonAbsTol);
    solver.newton.SetMaxIter(newtonMaxIter);
    solver.newton.SetPrintLevel(newtonPrintLevel);
    solver.newton.SetOperator(*m_polytropOperator);

    // --- Created the linear solver which is used to invert the jacobian ---
    solver.newton.SetSolver(solver.solver);

    return solver;
}