feat(mean_field): added initial implementation

note this implementation lacks many tests

libmeanfield/interface/integrators/advection.cppm

@@ -0,0 +1,28 @@
+module;
+#include <mfem.hpp>
+export module mean_field:integrators.advection;
+import :mapping.domain_mapper;
+
+export namespace mean_field::integrators {
+    class AdvectionIntegrator : public mfem::BlockNonlinearFormIntegrator {
+    public:
+        explicit AdvectionIntegrator(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;
+    };
+}