feat(poly): moved to a block form for poly

essential dofs can be applied to both theta and phi (grad theta) if we move to a block form. I have done this derivation and made that change so that we can properly apply the central boundary condition to the slope

src/poly/utils/public/operator.h

@@ -0,0 +1,45 @@
+#ifndef POLY_UTILS_OPERATOR_H
+#define POLY_UTILS_OPERATOR_H
+
+#include "mfem.hpp"
+#include <memory>
+
+class PolytropeOperator : public mfem::Operator {
+public:
+    PolytropeOperator(
+        std::unique_ptr<mfem::MixedBilinearForm> M,
+        std::unique_ptr<mfem::MixedBilinearForm> Q,
+        std::unique_ptr<mfem::BilinearForm> D,
+        std::unique_ptr<mfem::NonlinearForm> f,
+        const mfem::Array<int> &blockOffsets);
+    ~PolytropeOperator() override = default;
+
+    void Mult(const mfem::Vector &x, mfem::Vector &y) const override;
+    mfem::Operator& GetGradient(const mfem::Vector &x) const override;
+
+    void SetEssentialTrueDofs(const mfem::Array<int> &theta_ess_tofs,
+                            const mfem::Array<int> &phi_ess_tofs);
+
+private:
+    std::unique_ptr<mfem::MixedBilinearForm> m_M;
+    std::unique_ptr<mfem::MixedBilinearForm> m_Q;
+    std::unique_ptr<mfem::BilinearForm> m_D;
+    std::unique_ptr<mfem::NonlinearForm> m_f;
+
+    const mfem::Array<int> &m_blockOffsets;
+
+    mfem::Array<int> m_theta_ess_tofs;
+    mfem::Array<int> m_phi_ess_tofs;
+
+    std::unique_ptr<mfem::SparseMatrix> m_Mmat;
+    std::unique_ptr<mfem::SparseMatrix> m_Qmat;
+    std::unique_ptr<mfem::SparseMatrix> m_Dmat;
+
+
+    std::unique_ptr<mfem::ScaledOperator> m_negM_op;
+    std::unique_ptr<mfem::ScaledOperator> m_negQ_op;
+    mutable std::unique_ptr<mfem::BlockOperator> m_jacobian;
+};
+
+
+#endif // POLY_UTILS_OPERATOR_H