feat(newton): first newton solver implementation

libmeanfield/interface/operators/prepared_pressure_force.cppm

@@ -3,6 +3,7 @@ module;
 #include <compare>
 #include <cstddef>
 #include <cstdint>
+#include <expected>
 #include <optional>
 #include <vector>
 
@@ -18,6 +19,18 @@ export import :operators.context.pressure_force;
 export import :utils.blocks;
 
 export namespace mean_field::operators {
+    enum class PressureForcePreparationRejectionReason : std::uint8_t {
+        equation_of_state,
+        invalid_mapping,
+        non_finite_arithmetic
+    };
+
+    struct PressureForcePreparationRejection final {
+        PressureForcePreparationRejectionReason reason{PressureForcePreparationRejectionReason::equation_of_state};
+        eos::EvaluationErrorCode equationOfStateCode{eos::EvaluationErrorCode::nonfinite_result};
+        mapping::MappingStatus mappingStatus{mapping::MappingStatus::valid};
+    };
+
     struct PreparedPressureForceReport final {
         context::pressure_force::PressureForcePreparationReport contextReport;
 
@@ -92,6 +105,14 @@ export namespace mean_field::operators {
             const context::pressure_force::PressureForceDependencies &dependencies
         );
 
+        [[nodiscard]] std::expected<
+            PreparedPressureForceReport,
+            PressureForcePreparationRejection>
+        TryPrepare(
+            const context::pressure_force::PressureForceStateView &state,
+            const context::pressure_force::PressureForceDependencies &dependencies
+        );
+
         void BuildResidual(mfem::Vector &residual) const;
 
         void ApplyEnthalpyJacobianAction(
@@ -206,12 +227,12 @@ export namespace mean_field::operators {
         };
 
         void PrepareStaticPlan();
-        void PrepareGeometry();
-        void PrepareMaterialState();
+        [[nodiscard]] std::optional<PressureForcePreparationRejection> PrepareGeometry();
+        [[nodiscard]] std::optional<PressureForcePreparationRejection> PrepareMaterialState();
 
         void FinalizeDisplacementJacobianPreparation();
 
-        void AssembleCachedResidual();
+        [[nodiscard]] std::optional<PressureForcePreparationRejection> AssembleCachedResidual();
 
         void VerifyPrepared() const;
 
@@ -301,4 +322,4 @@ export namespace mean_field::operators {
 
         const PreparedPressureForceOperator &m_preparedOperator;
     };
-} // namespace mean_field::operators
+} // namespace mean_field::operators