362 lines
14 KiB
C++
362 lines
14 KiB
C++
/* ***********************************************************************
|
|
//
|
|
// 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 (int k, 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(int m, 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(double xi, double n, int order) {
|
|
double acc = 0;
|
|
for (int k = 0; k < order; k++) {
|
|
acc += a(k, n) * std::pow(xi, k);
|
|
}
|
|
return acc;
|
|
}
|
|
}
|
|
|
|
|
|
PolySolver::PolySolver(double n, 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;
|
|
|
|
ResourceManager& rm = ResourceManager::getInstance();
|
|
const Resource& resource = rm.getResource("mesh:polySphere");
|
|
const auto &meshIO = std::get<std::unique_ptr<MeshIO>>(resource);
|
|
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 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() {
|
|
|
|
// Start by defining the block structure of the system
|
|
// Block 0: Theta (scalar space, uses m_feTheta)
|
|
// Block 1: Phi (vector space, uses m_fePhi)
|
|
mfem::Array<mfem::FiniteElementSpace*> feSpaces;
|
|
feSpaces.Append(m_feTheta.get());
|
|
feSpaces.Append(m_fePhi.get());
|
|
|
|
// Create the block offsets. These define the start of each block in the combined vector.
|
|
// Block offsets will be [0, thetaDofs, thetaDofs + phiDofs]
|
|
mfem::Array<int> blockOffsets;
|
|
blockOffsets.SetSize(3);
|
|
blockOffsets[0] = 0;
|
|
blockOffsets[1] = feSpaces[0]->GetVSize();
|
|
blockOffsets[2] = feSpaces[1]->GetVSize();
|
|
blockOffsets.PartialSum();
|
|
|
|
// Add integrators to block form one by one
|
|
// We add integrators corresponding to each term in the weak form
|
|
// The block form of the residual matrix
|
|
// ⎡ 0 -M ⎤ ⎡ θ ⎤ + ⎡f(θ)⎤ = ⎡ 0 ⎤ = R(X)
|
|
// ⎣ -Q D ⎦ ⎣ Φ ⎦ ⎣ 0 ⎦ ⎣ 0 ⎦
|
|
// This then simplifies to
|
|
// ⎡f(θ) - MΘ ⎤ = ⎡ 0 ⎤ = R
|
|
// ⎣ -Qɸ Dθ ⎦ ⎣ 0 ⎦
|
|
// Here M, Q, and D are
|
|
// M = ∫∇ψᶿ·Nᵠ dV (MixedVectorWeakDivergenceIntegrator)
|
|
// D = ∫ψᵠ·Nᵠ dV (VectorFEMassIntegrator)
|
|
// Q = ∫ψᵠ·∇Nᶿ dV (MixedVectorGradientIntegrator)
|
|
// f(θ) = ∫ψᶿ·θⁿ dV (NonlinearPowerIntegrator)
|
|
// Here ψᶿ and ψᵠ are the test functions for the theta and phi spaces, respectively
|
|
// Nᵠ and Nᶿ are the basis functions for the theta and phi spaces, respectively
|
|
// A full derivation of the weak form can be found in the 4DSSE documentation
|
|
|
|
// --- Assemble the MixedBilinear and Bilinear forms (M, D, and Q) ---
|
|
auto Mform = std::make_unique<mfem::MixedBilinearForm>(m_fePhi.get(), m_feTheta.get());
|
|
auto Qform = std::make_unique<mfem::MixedBilinearForm>(m_feTheta.get(), m_fePhi.get());
|
|
auto Dform = std::make_unique<mfem::BilinearForm>(m_fePhi.get());
|
|
|
|
// TODO: Check the sign on all of the integrators
|
|
Mform->AddDomainIntegrator(new mfem::MixedVectorWeakDivergenceIntegrator());
|
|
Qform->AddDomainIntegrator(new mfem::MixedVectorGradientIntegrator());
|
|
Dform->AddDomainIntegrator(new mfem::VectorFEMassIntegrator());
|
|
|
|
Mform->Assemble();
|
|
Mform->Finalize();
|
|
|
|
Qform->Assemble();
|
|
Qform->Finalize();
|
|
|
|
Dform->Assemble();
|
|
Dform->Finalize();
|
|
|
|
// --- Assemble the NonlinearForm (f) ---
|
|
auto fform = std::make_unique<mfem::NonlinearForm>(m_feTheta.get());
|
|
fform->AddDomainIntegrator(new polyMFEMUtils::NonlinearPowerIntegrator(m_polytropicIndex));
|
|
// TODO: Add essential boundary conditions to the nonlinear form
|
|
|
|
// -- Build the BlockOperator --
|
|
m_polytropOperator = std::make_unique<PolytropeOperator>(
|
|
std::move(Mform),
|
|
std::move(Qform),
|
|
std::move(Dform),
|
|
std::move(fform),
|
|
blockOffsets
|
|
);
|
|
|
|
}
|
|
|
|
void PolySolver::solve() const {
|
|
// --- Set the initial guess for the solution ---
|
|
setInitialGuess();
|
|
|
|
setupOperator();
|
|
|
|
// 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) = static_cast<mfem::Vector>(*m_theta);
|
|
state_vector.GetBlock(1) = static_cast<mfem::Vector>(*m_phi);
|
|
|
|
mfem::Vector zero_rhs(block_offsets.Last());
|
|
zero_rhs = 0.0;
|
|
|
|
solverBundle sb = setupNewtonSolver();
|
|
|
|
// EMB 2025: Calling Mult gets the gradient of the operator for the NewtonSolver
|
|
// This then is set as the operator for the solver for NewtonSolver
|
|
// The solver (assuming it is an iterative solver) then sets the
|
|
// operator for its preconditioner to this.
|
|
// What this means is that there is no need to manually deal
|
|
// with updating the preconditioner at every newton step as the
|
|
// changes to the jacobian are automatically propagated through the
|
|
// solving chain. This is at least true with MFEM 4.8-rc0
|
|
sb.newton.Mult(zero_rhs, state_vector);
|
|
|
|
// --- 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;
|
|
mfem::Array<double> thetaCenterVals, phiCenterVals;
|
|
std::tie(thetaCenterDofs, phi_ess_tdof_list) = findCenterElement();
|
|
thetaCenterVals.SetSize(thetaCenterDofs.Size());
|
|
phiCenterVals.SetSize(phi_ess_tdof_list.Size());
|
|
|
|
thetaCenterVals = 1.0;
|
|
phiCenterVals = 0.0;
|
|
|
|
mfem::Array<int> ess_brd(m_mesh->bdr_attributes.Max());
|
|
ess_brd = 1;
|
|
|
|
mfem::Array<double> thetaSurfaceVals;
|
|
m_feTheta->GetEssentialTrueDofs(ess_brd, theta_ess_tdof_list);
|
|
thetaSurfaceVals.SetSize(theta_ess_tdof_list.Size());
|
|
thetaSurfaceVals = 0.0;
|
|
// 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, phiCenterVals);
|
|
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) {
|
|
double r = x.Norml2();
|
|
double radius = Probe::getMeshRadius(*m_mesh);
|
|
double u = 1/radius;
|
|
|
|
return -std::pow((u*r), 2)+1.0;
|
|
}
|
|
);
|
|
m_theta->ProjectCoefficient(thetaInitGuess);
|
|
mfem::GradientGridFunctionCoefficient phiInitGuess (m_theta.get());
|
|
m_phi->ProjectCoefficient(phiInitGuess);
|
|
if (m_config.get<bool>("Poly:Solver:ViewInitialGuess", false)) {
|
|
Probe::glVisView(*m_theta, *m_mesh, "θ init");
|
|
Probe::glVisView(*m_phi, *m_mesh, "ɸ 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::setupOperator() const {
|
|
|
|
SSE::MFEMArrayPairSet ess_tdof_pair_set = getEssentialTrueDof();
|
|
m_polytropOperator->SetEssentialTrueDofs(ess_tdof_pair_set);
|
|
|
|
// -- Finalize the operator --
|
|
m_polytropOperator->finalize();
|
|
|
|
if (!m_polytropOperator->isFinalized()) {
|
|
LOG_ERROR(m_logger, "PolytropeOperator is not finalized. Cannot solve.");
|
|
throw std::runtime_error("PolytropeOperator is not finalized. Cannot solve.");
|
|
}
|
|
}
|
|
|
|
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);
|
|
}
|
|
|
|
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;
|
|
}
|