feat(newton): first newton solver implementation

libmeanfield/interface/operators/prepared_gravity_displacement_force.cppm

@@ -2,6 +2,7 @@ module;
 
 #include <compare>
 #include <cstdint>
+#include <expected>
 #include <vector>
 
 #include <mfem.hpp>
@@ -11,6 +12,7 @@ export module mean_field:operators.prepared_gravity_displacement_force;
 export import :fem;
 export import :mapping.domain_mapper;
 export import :operators.context.gravity_field;
+export import :operators.kernels.gravity_displacement_force;
 export import :utils.blocks;
 
 export namespace mean_field::operators {
@@ -57,6 +59,11 @@ export namespace mean_field::operators {
          */
         PreparedGravityDisplacementForceReport Prepare();
 
+        [[nodiscard]] std::expected<
+            PreparedGravityDisplacementForceReport,
+            kernels::GravityDisplacementForceRejection>
+        TryPrepare();
+
         void BuildResidual(mfem::Vector &residual) const;
 
         void ApplyDensityJacobianAction(
@@ -106,7 +113,10 @@ export namespace mean_field::operators {
 
     private:
         void VerifyPrepared() const;
-        void PrepareElementData();
+        [[nodiscard]] std::expected<
+            void,
+            kernels::GravityDisplacementForceRejection>
+        TryPrepareElementData();
         void ApplyPreparedCompleteJacobianActionTrue(
             const mfem::Vector &densityVariationTrue,
             const mfem::Vector &displacementVariationTrue,