feat(libmeanfield): variadic refactor

also added normaliztion operator

libmeanfield/interface/operators/prepared_stellar_equilibrium.cppm

@@ -96,6 +96,20 @@ export namespace mean_field::operators {
 
     class PreparedStellarEquilibriumOperator final : public mfem::Operator {
     public:
+        /*
+         * Privileged aggregate runtimes can inspect this complete numerical
+         * core. Keep their allow-list on the concrete core itself: a custom
+         * EOS may reuse this class, but it cannot extend the class's backend
+         * privileges. Ordinary specifications use restricted nested physics
+         * and never interact with this list.
+         */
+        using BackendSpecifications = models::ModelTypeList<
+            eos::Polytrope,
+            surface::Isobaric,
+            models::FixedTotalMass,
+            models::FixedAngularMomentum,
+            models::FixedCentralDensity>;
+
         template <models::StellarModelType Model>
             requires std::same_as<
                          typename std::remove_cvref_t<Model>::EquationOfStateType,
@@ -174,6 +188,12 @@ export namespace mean_field::operators {
         [[nodiscard]] const PreparedHydrostaticEquilibriumOperator &GetHydrostaticOperator() const noexcept;
         [[nodiscard]] const PreparedDisplacementResidualOperator &GetDisplacementOperator() const noexcept;
         [[nodiscard]] const PreparedMassNormalizationOperator &GetMassNormalizationOperator() const noexcept;
+        [[nodiscard]] double ApplyDensityVolumeIntegralDensityAction(
+            const mfem::Vector &densityDirection
+        ) const;
+        [[nodiscard]] double ApplyDensityVolumeIntegralSurfaceShapeAction(
+            const mfem::Vector &surfaceShapeDirection
+        ) const;
         [[nodiscard]] const PreparedPressureSurfaceConstraint &GetSurfaceConstraintOperator() const noexcept;
         [[nodiscard]] const deformation::PreparedDomainDeformationRuntime &GetDomainDeformation() const noexcept;
         [[nodiscard]] const mfem::Vector &GetSurfaceDeformationParameters() const;
@@ -234,5 +254,6 @@ export namespace mean_field::operators {
         mutable mfem::Vector m_fullMechanicalAction;
         mutable mfem::Vector m_surfaceShapeAction;
         mutable mfem::Vector m_pullbackDerivativeAction;
+        mutable mfem::Vector m_densityVolumeIntegralAction;
     };
 } // namespace mean_field::operators