feat(mean_field): added initial implementation

note this implementation lacks many tests

libmeanfield/interface/physics/gravity.cppm

@@ -0,0 +1,45 @@
+module;
+#include <mfem.hpp>
+
+export module mean_field:physics.gravity;
+
+export import :fem;
+
+export namespace mean_field::physics {
+    struct GravitySolution {
+        mfem::ParGridFunction gradPhi;
+        mfem::ParGridFunction phi;
+
+        explicit GravitySolution(fem::FEM& fem): gradPhi(fem.RT_fes.get()), phi(fem.L2_fes.get()) {}
+    };
+
+    GravitySolution grav_potential(
+        fem::FEM &f,
+        const utils::Args &args,
+        const mfem::GridFunction &rho,
+        bool phi_warm = false
+    );
+
+    mfem::GridFunction get_potential(
+        fem::FEM &fem,
+        const utils::Args &args,
+        const mfem::GridFunction &rho,
+        bool warm = false
+    );
+
+    mfem::DenseMatrix compute_quadrupole_moment_tensor(
+        const fem::FEM &fem,
+        const mfem::GridFunction &rho,
+        const mfem::Vector &com
+    );
+
+    double l2_multipole_potential(
+        const fem::FEM &fem,
+        double total_mass,
+        const mfem::Vector &phys_x
+    );
+
+    void update_stiffness_matrix(fem::FEM &fem);
+}
+
+