feat(poly): added first pass implimentation of 3D constrained lane-emden solver
This has not currently been tested and this commit should not be viewed as scientifically complete
This commit is contained in:
@@ -2,174 +2,302 @@
|
||||
#include <string>
|
||||
#include <iostream>
|
||||
#include <cmath>
|
||||
#include <numbers>
|
||||
|
||||
#include "polyMFEMUtils.h"
|
||||
|
||||
NonlinearPowerIntegrator::NonlinearPowerIntegrator(
|
||||
mfem::FunctionCoefficient &coeff,
|
||||
double n) : coeff_(coeff), polytropicIndex(n) {
|
||||
namespace polyMFEMUtils {
|
||||
NonlinearPowerIntegrator::NonlinearPowerIntegrator(
|
||||
mfem::Coefficient &coeff,
|
||||
double n) : coeff_(coeff), polytropicIndex(n) {
|
||||
|
||||
}
|
||||
|
||||
void NonlinearPowerIntegrator::AssembleElementVector(
|
||||
const mfem::FiniteElement &el,
|
||||
mfem::ElementTransformation &Trans,
|
||||
const mfem::Vector &elfun,
|
||||
mfem::Vector &elvect) {
|
||||
|
||||
const mfem::IntegrationRule *ir = &mfem::IntRules.Get(el.GetGeomType(), 2 * el.GetOrder() + 3);
|
||||
int dof = el.GetDof();
|
||||
elvect.SetSize(dof);
|
||||
elvect = 0.0;
|
||||
|
||||
mfem::Vector shape(dof);
|
||||
|
||||
for (int iqp = 0; iqp < ir->GetNPoints(); iqp++) {
|
||||
mfem::IntegrationPoint ip = ir->IntPoint(iqp);
|
||||
Trans.SetIntPoint(&ip);
|
||||
double weight = ip.weight * Trans.Weight();
|
||||
|
||||
el.CalcShape(ip, shape);
|
||||
|
||||
double u_val = 0.0;
|
||||
for (int j = 0; j < dof; j++) {
|
||||
u_val += elfun(j) * shape(j);
|
||||
}
|
||||
double u_safe = std::max(u_val, 0.0);
|
||||
double u_nl = std::pow(u_safe, polytropicIndex);
|
||||
|
||||
double coeff_val = coeff_.Eval(Trans, ip);
|
||||
double x2_u_nl = coeff_val * u_nl;
|
||||
|
||||
for (int i = 0; i < dof; i++){
|
||||
elvect(i) += shape(i) * x2_u_nl * weight;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
void NonlinearPowerIntegrator::AssembleElementGrad (
|
||||
const mfem::FiniteElement &el,
|
||||
mfem::ElementTransformation &Trans,
|
||||
const mfem::Vector &elfun,
|
||||
mfem::DenseMatrix &elmat) {
|
||||
|
||||
const mfem::IntegrationRule *ir = &mfem::IntRules.Get(el.GetGeomType(), 2 * el.GetOrder() + 3);
|
||||
int dof = el.GetDof();
|
||||
elmat.SetSize(dof);
|
||||
elmat = 0.0;
|
||||
mfem::Vector shape(dof);
|
||||
|
||||
for (int iqp = 0; iqp < ir->GetNPoints(); iqp++) {
|
||||
mfem::IntegrationPoint ip = ir->IntPoint(iqp);
|
||||
Trans.SetIntPoint(&ip);
|
||||
double weight = ip.weight * Trans.Weight();
|
||||
|
||||
el.CalcShape(ip, shape);
|
||||
|
||||
double u_val = 0.0;
|
||||
|
||||
for (int j = 0; j < dof; j++) {
|
||||
u_val += elfun(j) * shape(j);
|
||||
}
|
||||
double coeff_val = coeff_.Eval(Trans, ip);
|
||||
void NonlinearPowerIntegrator::AssembleElementVector(
|
||||
const mfem::FiniteElement &el,
|
||||
mfem::ElementTransformation &Trans,
|
||||
const mfem::Vector &elfun,
|
||||
mfem::Vector &elvect) {
|
||||
|
||||
const mfem::IntegrationRule *ir = &mfem::IntRules.Get(el.GetGeomType(), 2 * el.GetOrder() + 3);
|
||||
int dof = el.GetDof();
|
||||
elvect.SetSize(dof);
|
||||
elvect = 0.0;
|
||||
|
||||
// Calculate the Jacobian
|
||||
double u_safe = std::max(u_val, 0.0);
|
||||
double d_u_nl = coeff_val * polytropicIndex * std::pow(u_safe, polytropicIndex - 1);
|
||||
double x2_d_u_nl = d_u_nl;
|
||||
mfem::Vector shape(dof);
|
||||
|
||||
for (int i = 0; i < dof; i++) {
|
||||
for (int iqp = 0; iqp < ir->GetNPoints(); iqp++) {
|
||||
mfem::IntegrationPoint ip = ir->IntPoint(iqp);
|
||||
Trans.SetIntPoint(&ip);
|
||||
double weight = ip.weight * Trans.Weight();
|
||||
|
||||
el.CalcShape(ip, shape);
|
||||
|
||||
double u_val = 0.0;
|
||||
for (int j = 0; j < dof; j++) {
|
||||
elmat(i, j) += shape(i) * x2_d_u_nl * shape(j) * weight;
|
||||
u_val += elfun(j) * shape(j);
|
||||
}
|
||||
double u_safe = std::max(u_val, 0.0);
|
||||
double u_nl = std::pow(u_safe, polytropicIndex);
|
||||
|
||||
double coeff_val = coeff_.Eval(Trans, ip);
|
||||
double x2_u_nl = coeff_val * u_nl;
|
||||
|
||||
for (int i = 0; i < dof; i++){
|
||||
elvect(i) += shape(i) * x2_u_nl * weight;
|
||||
}
|
||||
}
|
||||
|
||||
}
|
||||
}
|
||||
|
||||
BilinearIntegratorWrapper::BilinearIntegratorWrapper(
|
||||
mfem::BilinearFormIntegrator *integratorInput
|
||||
) : integrator(integratorInput) { }
|
||||
void NonlinearPowerIntegrator::AssembleElementGrad (
|
||||
const mfem::FiniteElement &el,
|
||||
mfem::ElementTransformation &Trans,
|
||||
const mfem::Vector &elfun,
|
||||
mfem::DenseMatrix &elmat) {
|
||||
|
||||
BilinearIntegratorWrapper::~BilinearIntegratorWrapper() {
|
||||
delete integrator;
|
||||
}
|
||||
const mfem::IntegrationRule *ir = &mfem::IntRules.Get(el.GetGeomType(), 2 * el.GetOrder() + 3);
|
||||
int dof = el.GetDof();
|
||||
elmat.SetSize(dof);
|
||||
elmat = 0.0;
|
||||
mfem::Vector shape(dof);
|
||||
|
||||
void BilinearIntegratorWrapper::AssembleElementVector(
|
||||
const mfem::FiniteElement &el,
|
||||
mfem::ElementTransformation &Trans,
|
||||
const mfem::Vector &elfun,
|
||||
mfem::Vector &elvect) {
|
||||
int dof = el.GetDof();
|
||||
mfem::DenseMatrix elMat(dof);
|
||||
integrator->AssembleElementMatrix(el, Trans, elMat);
|
||||
elvect.SetSize(dof);
|
||||
elvect = 0.0;
|
||||
for (int i = 0; i < dof; i++)
|
||||
{
|
||||
double sum = 0.0;
|
||||
for (int j = 0; j < dof; j++)
|
||||
{
|
||||
sum += elMat(i, j) * elfun(j);
|
||||
}
|
||||
elvect(i) = sum;
|
||||
for (int iqp = 0; iqp < ir->GetNPoints(); iqp++) {
|
||||
const mfem::IntegrationPoint &ip = ir->IntPoint(iqp);
|
||||
Trans.SetIntPoint(&ip);
|
||||
double weight = ip.weight * Trans.Weight();
|
||||
|
||||
el.CalcShape(ip, shape);
|
||||
|
||||
double u_val = 0.0;
|
||||
|
||||
for (int j = 0; j < dof; j++) {
|
||||
u_val += elfun(j) * shape(j);
|
||||
}
|
||||
double coeff_val = coeff_.Eval(Trans, ip);
|
||||
|
||||
|
||||
// Calculate the Jacobian
|
||||
double u_safe = std::max(u_val, 0.0);
|
||||
double d_u_nl = coeff_val * polytropicIndex * std::pow(u_safe, polytropicIndex - 1);
|
||||
double x2_d_u_nl = d_u_nl;
|
||||
|
||||
for (int i = 0; i < dof; i++) {
|
||||
for (int j = 0; j < dof; j++) {
|
||||
elmat(i, j) += shape(i) * x2_d_u_nl * shape(j) * weight;
|
||||
}
|
||||
}
|
||||
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
void BilinearIntegratorWrapper::AssembleElementGrad(const mfem::FiniteElement &el,
|
||||
mfem::ElementTransformation &Trans,
|
||||
const mfem::Vector &elfun,
|
||||
mfem::DenseMatrix &elmat) {
|
||||
int dof = el.GetDof();
|
||||
elmat.SetSize(dof, dof);
|
||||
elmat = 0.0;
|
||||
integrator->AssembleElementMatrix(el, Trans, elmat);
|
||||
}
|
||||
BilinearIntegratorWrapper::BilinearIntegratorWrapper(
|
||||
mfem::BilinearFormIntegrator *integratorInput
|
||||
) : integrator(integratorInput) { }
|
||||
|
||||
CompositeNonlinearIntegrator::CompositeNonlinearIntegrator() { }
|
||||
|
||||
|
||||
CompositeNonlinearIntegrator::~CompositeNonlinearIntegrator() {
|
||||
for (size_t i = 0; i < integrators.size(); i++) {
|
||||
delete integrators[i];
|
||||
BilinearIntegratorWrapper::~BilinearIntegratorWrapper() {
|
||||
delete integrator;
|
||||
}
|
||||
}
|
||||
|
||||
void CompositeNonlinearIntegrator::add_integrator(mfem::NonlinearFormIntegrator *integrator) {
|
||||
integrators.push_back(integrator);
|
||||
}
|
||||
|
||||
void CompositeNonlinearIntegrator::AssembleElementVector(
|
||||
const mfem::FiniteElement &el,
|
||||
mfem::ElementTransformation &Trans,
|
||||
const mfem::Vector &elfun,
|
||||
mfem::Vector &elvect) {
|
||||
int dof = el.GetDof();
|
||||
elvect.SetSize(dof);
|
||||
elvect = 0.0;
|
||||
mfem::Vector temp(dof);
|
||||
|
||||
for (size_t i = 0; i < integrators.size(); i++) {
|
||||
temp= 0.0;
|
||||
integrators[i]->AssembleElementVector(el, Trans, elfun, temp);
|
||||
elvect.Add(1.0, temp);
|
||||
void BilinearIntegratorWrapper::AssembleElementVector(
|
||||
const mfem::FiniteElement &el,
|
||||
mfem::ElementTransformation &Trans,
|
||||
const mfem::Vector &elfun,
|
||||
mfem::Vector &elvect) {
|
||||
int dof = el.GetDof();
|
||||
mfem::DenseMatrix elMat(dof);
|
||||
integrator->AssembleElementMatrix(el, Trans, elMat);
|
||||
elvect.SetSize(dof);
|
||||
elvect = 0.0;
|
||||
for (int i = 0; i < dof; i++)
|
||||
{
|
||||
double sum = 0.0;
|
||||
for (int j = 0; j < dof; j++)
|
||||
{
|
||||
sum += elMat(i, j) * elfun(j);
|
||||
}
|
||||
elvect(i) = sum;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
void CompositeNonlinearIntegrator::AssembleElementGrad(
|
||||
const mfem::FiniteElement &el,
|
||||
mfem::ElementTransformation &Trans,
|
||||
const mfem::Vector &elfun,
|
||||
mfem::DenseMatrix &elmat) {
|
||||
int dof = el.GetDof();
|
||||
elmat.SetSize(dof, dof);
|
||||
elmat = 0.0;
|
||||
mfem::DenseMatrix temp(dof);
|
||||
temp.SetSize(dof, dof);
|
||||
for (size_t i = 0; i < integrators.size(); i++) {
|
||||
temp = 0.0;
|
||||
integrators[i] -> AssembleElementGrad(el, Trans, elfun, temp);
|
||||
elmat.Add(1.0, temp);
|
||||
void BilinearIntegratorWrapper::AssembleElementGrad(const mfem::FiniteElement &el,
|
||||
mfem::ElementTransformation &Trans,
|
||||
const mfem::Vector &elfun,
|
||||
mfem::DenseMatrix &elmat) {
|
||||
int dof = el.GetDof();
|
||||
elmat.SetSize(dof, dof);
|
||||
elmat = 0.0;
|
||||
integrator->AssembleElementMatrix(el, Trans, elmat);
|
||||
}
|
||||
}
|
||||
|
||||
CompositeNonlinearIntegrator::CompositeNonlinearIntegrator() { }
|
||||
|
||||
|
||||
CompositeNonlinearIntegrator::~CompositeNonlinearIntegrator() {
|
||||
for (size_t i = 0; i < integrators.size(); i++) {
|
||||
delete integrators[i];
|
||||
}
|
||||
}
|
||||
|
||||
void CompositeNonlinearIntegrator::add_integrator(mfem::NonlinearFormIntegrator *integrator) {
|
||||
integrators.push_back(integrator);
|
||||
}
|
||||
|
||||
void CompositeNonlinearIntegrator::AssembleElementVector(
|
||||
const mfem::FiniteElement &el,
|
||||
mfem::ElementTransformation &Trans,
|
||||
const mfem::Vector &elfun,
|
||||
mfem::Vector &elvect) {
|
||||
int dof = el.GetDof();
|
||||
elvect.SetSize(dof);
|
||||
elvect = 0.0;
|
||||
mfem::Vector temp(dof);
|
||||
|
||||
for (size_t i = 0; i < integrators.size(); i++) {
|
||||
temp= 0.0;
|
||||
integrators[i]->AssembleElementVector(el, Trans, elfun, temp);
|
||||
elvect.Add(1.0, temp);
|
||||
}
|
||||
}
|
||||
|
||||
void CompositeNonlinearIntegrator::AssembleElementGrad(
|
||||
const mfem::FiniteElement &el,
|
||||
mfem::ElementTransformation &Trans,
|
||||
const mfem::Vector &elfun,
|
||||
mfem::DenseMatrix &elmat) {
|
||||
int dof = el.GetDof();
|
||||
elmat.SetSize(dof, dof);
|
||||
elmat = 0.0;
|
||||
mfem::DenseMatrix temp(dof);
|
||||
temp.SetSize(dof, dof);
|
||||
for (size_t i = 0; i < integrators.size(); i++) {
|
||||
temp = 0.0;
|
||||
integrators[i] -> AssembleElementGrad(el, Trans, elfun, temp);
|
||||
elmat.Add(1.0, temp);
|
||||
}
|
||||
}
|
||||
|
||||
ConstraintIntegrator::ConstraintIntegrator(mfem::Coefficient &eta_) : eta(eta_) {}
|
||||
|
||||
void ConstraintIntegrator::AssembleElementVector(const mfem::FiniteElement &el, mfem::ElementTransformation &Trans, const mfem::Vector &elfun, mfem::Vector &elvect) {
|
||||
int dof = el.GetDof();
|
||||
elvect.SetSize(dof);
|
||||
elvect = 0.0;
|
||||
|
||||
mfem::Vector shape(dof);
|
||||
const int intOrder = 2 * el.GetOrder() + 3;
|
||||
|
||||
mfem::IntegrationRule ir(el.GetGeomType(), intOrder);
|
||||
|
||||
for (int i = 0; i < ir.GetNPoints(); i++) {
|
||||
const mfem::IntegrationPoint &ip = ir.IntPoint(i);
|
||||
Trans.SetIntPoint(&ip);
|
||||
el.CalcShape(ip, shape);
|
||||
|
||||
double eta_val = eta.Eval(Trans, ip);
|
||||
|
||||
double weight = ip.weight * Trans.Weight();
|
||||
elvect.Add(eta_val * weight, shape);
|
||||
}
|
||||
}
|
||||
|
||||
void ConstraintIntegrator::AssembleElementGrad(const mfem::FiniteElement &el, mfem::ElementTransformation &Trans, const mfem::Vector &elfun, mfem::DenseMatrix &elmat) {
|
||||
int dof = el.GetDof();
|
||||
elmat.SetSize(dof);
|
||||
elmat = 0.0;
|
||||
}
|
||||
|
||||
GaussianCoefficient::GaussianCoefficient(double stdDev_)
|
||||
: stdDev(stdDev_),
|
||||
norm_coeff(1.0/(std::pow(std::sqrt(2*std::numbers::pi)*stdDev_,3))) {}
|
||||
|
||||
GaussianCoefficient::Eval(mfem::ElementTransformation &T, const mfem::IntegrationPoint &ip) {
|
||||
mfem::Vector r;
|
||||
T.Transform(ip, r);
|
||||
double r2 = r * r;
|
||||
return norm_coeff * std::exp(-r2/(2*std::pow(stdDev, 2)));
|
||||
}
|
||||
|
||||
|
||||
AugmentedOperator::AugmentedOperator(mfem::NonlinearForm &nfl_, mfem::LinearForm &C_, int lambdaDofOffset_)
|
||||
:
|
||||
mfem::Operator( // Call the base class constructor
|
||||
nfl_->FESpace()->GetTrueVSize()+1, // Sets the height attribute (+1 for the lambda component)
|
||||
nfl_->FESpace()->GetTrueVSize()+1 // Sets the width attribute (+1 for the lambda component)
|
||||
),
|
||||
nfl(&nfl_),
|
||||
C(&C_),
|
||||
lambdaDofOffset(lambdaDofOffset_),
|
||||
lastJacobian(nullptr) {}
|
||||
|
||||
void AugmentedOperator::Mult(const mfem::Vector &x, mfem::Vector &y) const {
|
||||
// Select the lambda component of the input vector and seperate it from the θ component
|
||||
mfem::Vector u(x.GetData(), lambdaDofOffset);
|
||||
double lambda = x[lambdaDofOffset];
|
||||
|
||||
// Compute the residual of the nonlinear form (F(u) - λC)
|
||||
mfem::Vector F(lambdaDofOffset);
|
||||
nfl->Mult(u, F); // This now includes the -λ∫vη(r) dΩ term
|
||||
|
||||
// Compute the transpose of C for the off diagonal terms of the augmented operator
|
||||
y.SetSize(height);
|
||||
y = 0.0;
|
||||
|
||||
y.SetBlock(0, F);
|
||||
y[lambdaDofOffset] = (*C)(u); // Cᵀ×u. This is equivalent to ∫ η(r)θ dΩ
|
||||
|
||||
// add -lambda * C to the residual
|
||||
mfem::Vector lambda_C(lambdaDofOffset);
|
||||
C->GetVector(lambda_C) // Get the coefficient vector for C. I.e. ∫ vη(r) dΩ
|
||||
lambda_C *= -lambda; // Multiply by -λ (this is now the term −λ ∫ vη(r)dΩ)
|
||||
|
||||
y.AddBlockVector(0, lambda_C); // Add the term to the residual
|
||||
}
|
||||
|
||||
mfem::Operator &AugmentedOperator::GetGradient(const mfem::Vector &x) const {
|
||||
// Select the lambda component of the input vector and seperate it from the θ component
|
||||
mfem::Vector u(x.GetData(), lambdaDofOffset);
|
||||
double lambda = x[lambdaDofOffset];
|
||||
|
||||
// --- Create the augmented Jacobian matrix ---
|
||||
mfem::Operator *Jnfl = nfl->GetGradient(u); // Get the gradient of the nonlinear form
|
||||
|
||||
mfem::SparseMatrix *J_aug = new mfem::SparseMatrix(height, width);
|
||||
|
||||
// Fill in the blocks of the augmented Jacobian matrix
|
||||
// Top-Left: Jacobian of the nonlinear form
|
||||
mfem::SparseMatrix *Jnfl_sparse = dynamic_cast<mfem::SparseMatrix*>(Jnfl);
|
||||
|
||||
// Copy the original Jacobian into the augmented Jacobian
|
||||
if (Jnfl_sparse) { // Checks if the dynamic cast was successful
|
||||
for (int i = 0; i < Jnfl_sparse->Height(); i++) {
|
||||
for (int j = 0; j < Jnfl_sparse->Width(); j++) {
|
||||
J_aug->Set(i, j, Jnfl_sparse->Get(i, j));
|
||||
}
|
||||
}
|
||||
} else {
|
||||
MFEM_ABORT("GetGradient did not return a SparseMatrix");
|
||||
}
|
||||
|
||||
// Bottom-left C (the constraint matrix)
|
||||
mfem::Vector CVec(lambdaDofOffset);
|
||||
C->GetVector(CVec);
|
||||
for (int i = 0; i < CVec.Size(); i++) {
|
||||
J_aug->Set(lambdaDofOffset, i, CVec[i]);
|
||||
}
|
||||
|
||||
// Top-right -Cᵀ (the negative transpose of the constraint matrix)
|
||||
for (int i = 0; i < CVec.Size(); i++) {
|
||||
J_aug->Set(i, lambdaDofOffset, -CVec[i]);
|
||||
}
|
||||
|
||||
J_aug->Finalize();
|
||||
|
||||
delete lastJacobian;
|
||||
lastJacobian = J_aug;
|
||||
return *lastJacobian;
|
||||
}
|
||||
|
||||
AugmentedOperator::~AugAugmentedOperator() {
|
||||
delete lastJacobian;
|
||||
}
|
||||
} // namespace polyMFEMUtils
|
||||
Reference in New Issue
Block a user