feat(mean_field): added initial implementation

note this implementation lacks many tests

libmeanfield/interface/analysis/integral.cppm

@@ -0,0 +1,41 @@
+module;
+#include "mean_field.h"
+
+export module mean_field:analysis.integral;
+export import :fem;
+export import :utils.domain;
+export import :mapping.domain_mapper;
+export import :mapping.types;
+
+export namespace mean_field::analysis {
+    double domain_integrate_grid_function(
+        const fem::FEM &fem,
+        const mfem::GridFunction &gf,
+        utils::DOMAINS domain = utils::DOMAINS::ALL,
+        mapping::COORDINATE_SPACE coord_space = mapping::COORDINATE_SPACE::PHYSICAL
+    );
+
+    mfem::Vector get_com(
+        const fem::FEM &fem,
+        const mfem::GridFunction &rho
+    );
+
+    void conserve_mass(
+        const fem::FEM &fem,
+        mfem::GridFunction &rho,
+        double target_mass
+    );
+
+    double get_moment_of_inertia(
+        const fem::FEM &fem,
+        const mfem::GridFunction &rho
+    );
+
+    double get_mesh_volume(
+        const fem::FEM& fem,
+        mapping::COORDINATE_SPACE coordinate_space = mapping::COORDINATE_SPACE::PHYSICAL,
+        utils::DOMAINS domain = utils::DOMAINS::STELLAR
+    );
+}
+
+