feat(mean_field): added initial implementation

note this implementation lacks many tests

libmeanfield/interface/fem.cppm

@@ -0,0 +1,95 @@
+module;
+
+#include <stroid/stroid.h>
+#include <memory>
+#include <mfem.hpp>
+
+export module mean_field:fem;
+export import :physics.contexts;
+export import :boundary.contexts;
+export import :mapping.domain_mapper;
+export import :utils.misc;
+export import :utils.user;
+export import :quadrature.mfem;
+
+export namespace mean_field::fem {
+    struct FEM {
+
+        stroid::StroidMesh smesh;
+        std::unique_ptr<mfem::ParMesh> mesh;
+
+        // =====================================
+        // 2. Finite Element Collections
+        // =====================================
+        // H1 (Continuous): For Gravitational Potential (Phi) and Velocity (v)
+        std::unique_ptr<mfem::FiniteElementCollection> H1_fec;
+
+        // L2 (Discontinuous): For Density (rho) to fix O-grid boundary scalloping
+        std::unique_ptr<mfem::FiniteElementCollection> L2_fec;
+
+        // H(div)/RT space for gravitational field
+        std::unique_ptr<mfem::RT_FECollection> RT_fec;
+
+
+        // =====================================
+        // 3. Finite Element Spaces
+        // =====================================
+        std::unique_ptr<mfem::ParFiniteElementSpace> H1_fes; // Scalar continuous (Gravity)
+        std::unique_ptr<mfem::ParFiniteElementSpace> Vec_H1_fes; // Vector continuous (Velocity field)
+        std::unique_ptr<mfem::ParFiniteElementSpace> L2_fes; // Scalar discontinuous (Density)
+        std::unique_ptr<mfem::ParFiniteElementSpace> RT_fes; // H(div)/RT space for gravitational field
+
+        // Preconditioning for Gravity
+        std::unique_ptr<mfem::ParLORDiscretization> H1_lor_disc;
+        const mfem::ParFiniteElementSpace *H1_lor_fes{nullptr};
+
+        // =====================================
+        // 4. Domain Mapping
+        // =====================================
+        std::unique_ptr<mapping::DomainMapper> mapping;
+
+        // =====================================
+        // 5. Global System Tracking
+        // =====================================
+        // [ Velocity | Density | Mapping Parameters (Surface) ]
+        mfem::Array<int> block_true_offsets;
+
+        mfem::Array<int> gravity_block_true_offsets;
+
+        // Essential Boundary Conditions for the fluid (e.g., surface stress-free)
+        mfem::Array<int> ess_v_tdofs;
+
+        // Elements entirely in the vacuum domain where fluid equations are not solved
+        mfem::Array<int> vacuum_tdof_rho;
+        mfem::Array<int> vacuum_tdof_v;
+
+        // =====================================
+        // 6. Multiphysics State & Integration
+        // =====================================
+        mfem::Vector com;
+        mfem::DenseMatrix Q;
+
+        int int_order{3};
+        std::unique_ptr<mfem::IntegrationRule> int_rule;
+
+        physics::GravityContext gravity_context;
+        boundary::BoundaryContext boundary_context;
+
+        std::unique_ptr<quadrature::RuleFactory> quadrature_factory;
+
+        // =====================================
+        // 7. Utilities
+        // =====================================
+        [[nodiscard]] bool okay() const {
+            return (mesh != nullptr) &&
+                (H1_fec != nullptr) && (L2_fec != nullptr) && (RT_fec != nullptr) &&
+                (H1_fes != nullptr) && (Vec_H1_fes != nullptr) && (L2_fes != nullptr) && (RT_fes != nullptr);
+        }
+
+        [[nodiscard]] bool has_mapping() const { return mapping != nullptr; }
+    };
+
+
+    FEM setup_fem(const std::string &filename, const utils::Args &args, int extra_refine = 0);
+}
+