feat(poly): added skeleton of polytrope model

the polytrope module will be used as an initial guess to the solver. A skeleton of this has been imported from https://github.com/tboudreaux/FEMPolytrope

This module will need major updates still to handle 3D, proper boundary conditions, and to incorporate it with the rest of our meshing scheme

src/poly/utils/private/polyMFEMUtils.cpp

@@ -0,0 +1,175 @@
+#include "mfem.hpp"
+#include <string>
+#include <iostream>
+#include <cmath>
+
+#include "polyMFEMUtils.h"
+
+NonlinearPowerIntegrator::NonlinearPowerIntegrator(
+ mfem::FunctionCoefficient &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);
+    
+
+    // 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;
+      }
+    }
+
+  }
+}
+
+BilinearIntegratorWrapper::BilinearIntegratorWrapper(
+ mfem::BilinearFormIntegrator *integratorInput
+ ) : integrator(integratorInput) { }
+
+BilinearIntegratorWrapper::~BilinearIntegratorWrapper() {
+  delete integrator;
+}
+
+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 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);
+  }
+}