feat(poly): lagrangian constrained weak form of 3D lane-Emden

added a basic implimentation of the 3D lane emden equation using a lagrangian multiplier to constrain the value at the center of a spherical domain

src/poly/utils/private/polyMFEMUtils.cpp

@@ -132,11 +132,7 @@ namespace polyMFEMUtils {
   CompositeNonlinearIntegrator::CompositeNonlinearIntegrator() { }
 
 
-  CompositeNonlinearIntegrator::~CompositeNonlinearIntegrator() {
-    for (size_t i = 0; i < integrators.size(); i++) {
-      delete integrators[i];
-    }
-  }
+  CompositeNonlinearIntegrator::~CompositeNonlinearIntegrator() { }
 
   void CompositeNonlinearIntegrator::add_integrator(mfem::NonlinearFormIntegrator *integrator) {
     integrators.push_back(integrator);
@@ -186,7 +182,7 @@ namespace polyMFEMUtils {
     mfem::Vector shape(dof);
     const int intOrder = 2 * el.GetOrder() + 3;
 
-    mfem::IntegrationRule ir(el.GetGeomType(), intOrder);
+    const mfem::IntegrationRule &ir = mfem::IntRules.Get(el.GetGeomType(), intOrder);
 
     for (int i = 0; i < ir.GetNPoints(); i++) {
       const mfem::IntegrationPoint &ip = ir.IntPoint(i);
@@ -210,7 +206,7 @@ namespace polyMFEMUtils {
    : 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) {
+  double GaussianCoefficient::Eval(mfem::ElementTransformation &T, const mfem::IntegrationPoint &ip) {
     mfem::Vector r;
     T.Transform(ip, r);
     double r2 = r * r;
@@ -221,11 +217,11 @@ namespace polyMFEMUtils {
   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_.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_), 
+    nfl(nfl_),
+    C(C_), 
     lambdaDofOffset(lambdaDofOffset_),
     lastJacobian(nullptr) {}
 
@@ -236,51 +232,59 @@ namespace polyMFEMUtils {
 
     // 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
+    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
+    for (int i = 0; i < lambdaDofOffset; i++) {
+      y[i] = F[i];
+    }
+    mfem::GridFunction u_gf(C.FESpace());
+    u_gf.SetData(u);
+    y[lambdaDofOffset] = C.operator()(u_gf);
 
     // 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)
+    mfem::GridFunction constraint_gf(C.FESpace());
+    constraint_gf = 0.0;
 
-    y.AddBlockVector(0, lambda_C); // Add the term to the residual
+    mfem::Vector constraint_tdofs;
+    C.Assemble();
+    lambda_C = C.GetData();
+    lambda_C *= -lambda;  // Multiply by -λ (this is now the term −λ ∫ vη(r)dΩ)
+
+    for (int i = 0; i < lambdaDofOffset; i++) {
+      y[i] += lambda_C[i];
+    }
   }
 
   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::SparseMatrix *Jnfl_sparse = dynamic_cast<mfem::SparseMatrix*>(&nfl.GetGradient(u));
+    if (!Jnfl_sparse) {
       MFEM_ABORT("GetGradient did not return a SparseMatrix");
     }
 
+    mfem::SparseMatrix *J_aug = new mfem::SparseMatrix(height, width);
+    // Copy the original Jacobian into the augmented Jacobian
+    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->Elem(i, j));
+      }
+    }
+
     // Bottom-left C (the constraint matrix)
     mfem::Vector CVec(lambdaDofOffset);
-    C->GetVector(CVec);
+    mfem::GridFunction tempCGrid(C.FESpace());
+    C.Assemble();
+    CVec = C.GetData();
     for (int i = 0; i < CVec.Size(); i++) {
       J_aug->Set(lambdaDofOffset, i, CVec[i]);
     }
@@ -297,7 +301,7 @@ namespace polyMFEMUtils {
     return *lastJacobian;
   }
 
-  AugmentedOperator::~AugAugmentedOperator() {
+  AugmentedOperator::~AugmentedOperator() {
     delete lastJacobian;
   }
 } // namespace polyMFEMUtils