feat(mean_field): added initial implementation

note this implementation lacks many tests

libmeanfield/interface/integrators/mass_continuity.cppm

@@ -0,0 +1,62 @@
+module;
+#include <mfem.hpp>
+export module mean_field:integrators.mass_continuity;
+import :mapping.domain_mapper;
+
+export namespace mean_field::integrators {
+   class ContinuityVolumeIntegrator : public mfem::BlockNonlinearFormIntegrator {
+    public:
+        explicit ContinuityVolumeIntegrator(const mapping::DomainMapper& map);
+
+        void AssembleElementVector(
+            const mfem::Array<const mfem::FiniteElement *> &el,
+            mfem::ElementTransformation &Tr,
+            const mfem::Array<const mfem::Vector *> &elfun,
+            const mfem::Array<mfem::Vector *> &elvec
+        ) override;
+
+        void AssembleElementGrad(
+            const mfem::Array<const mfem::FiniteElement *> &el,
+            mfem::ElementTransformation &Tr,
+            const mfem::Array<const mfem::Vector *> &elfun,
+            const mfem::Array2D<mfem::DenseMatrix *> &elmats
+        ) override;
+    private:
+        const mapping::DomainMapper& m_map;
+    };
+
+    class ContinuityFaceIntegrator : public mfem::BlockNonlinearFormIntegrator {
+    public:
+        explicit ContinuityFaceIntegrator(const mapping::DomainMapper& map);
+
+        void AssembleFaceVector(
+            const mfem::Array<const mfem::FiniteElement *> &el1,
+            const mfem::Array<const mfem::FiniteElement *> &el2,
+            mfem::FaceElementTransformations &Tr,
+            const mfem::Array<const mfem::Vector *> &elfun,
+            const mfem::Array<mfem::Vector *> &elvect
+        ) override;
+
+        void AssembleFaceGrad(
+            const mfem::Array<const mfem::FiniteElement *> &el1,
+            const mfem::Array<const mfem::FiniteElement *> &el2,
+            mfem::FaceElementTransformations &Tr,
+            const mfem::Array<const mfem::Vector *> &elfun,
+            const mfem::Array2D<mfem::DenseMatrix *> &elmats
+        ) override;
+    private:
+        static bool skip_face(const mfem::FaceElementTransformations& Tr);
+
+        static double compute_u_n(
+            const mfem::Vector& v_dofs,
+            const mfem::Vector& shape_v_minus,
+            const mfem::Vector& n_unit,
+            int dof_v_minus,
+            int dim
+        );
+
+    private:
+        const mapping::DomainMapper& m_map;
+    };
+
+}