feat(poly): constraint integrator

The NewtonSolver has been subclassed to try to auto enforce the zero boundary central condition by modifying the residual vector and the gradient matrix. This is a work in progress

BREAKING CHANGE:

src/poly/utils/public/polyMFEMUtils.h

@@ -3,7 +3,11 @@
 
 #include "mfem.hpp"
 #include <string>
+#include <array>
+#include <vector>
 #include "config.h"
+#include "probe.h"
+#include "quill/LogMacros.h"
 
 
 
@@ -213,6 +217,33 @@ namespace polyMFEMUtils {
    * @return The Gaussian integral.
    */
   double calculateGaussianIntegral(mfem::Mesh &mesh, polyMFEMUtils::GaussianCoefficient &gaussianCoeff);
+
+  class ZeroSlopeNewtonSolver : public mfem::NewtonSolver {
+    private:
+      Config& config = Config::getInstance();
+      Probe::LogManager& logManager = Probe::LogManager::getInstance();
+      quill::Logger* logger = logManager.getLogger("log");
+
+      double alpha; // The penalty term for the flat slope at zero
+      std::vector<double> zeroSlopeCoordinate; // The coordinate of the zero slope point
+
+      int zeroSlopeElemID = -1;
+      mfem::Array<int> zeroSlopeDofs;
+      mfem::IntegrationPoint zeroSlopeIP;
+
+      std::unique_ptr<mfem::GridFunction> u_gf;
+      mutable mfem::SparseMatrix *grad = nullptr;
+
+      void ComputeConstrainedResidual(const mfem::Vector &x, mfem::Vector &r) const;
+      void ComputeConstrainedGradient(const mfem::Vector &x) const;
+
+    public:
+      ZeroSlopeNewtonSolver(double alpha_, std::vector<double> zeroSlopeCoordinate_);
+      ~ZeroSlopeNewtonSolver();
+      // virtual void ProcessNewState(const mfem::Vector &x) const;
+      virtual void SetOperator(const mfem::Operator &op) override;
+      void Mult(const mfem::Vector &b, mfem::Vector &x) const override;
+  };
 } // namespace polyMFEMUtils
 
 #endif // POLYMFEMUTILS_H