feat(newton): first newton solver implementation

libmeanfield/impl/operators/gravity_field.cpp

@@ -4,6 +4,7 @@ module;
 #include <cstdint>
 #include <limits>
 #include <mfem.hpp>
+#include <utility>
 
 module mean_field;
 import :operators.gravity_field;
@@ -273,6 +274,18 @@ namespace mean_field::operators {
     context::gravity_field::GravityFieldPreparationReport GravityFieldOperator::Prepare(
         const mfem::Vector &state,
         const context::gravity_field::GravityFieldRevisions &revisions
+    ) {
+        auto result = TryPrepare(state, revisions);
+        if (!result.has_value()) {
+            context::gravity_field::throwGravityFieldPreparationRejection(result.error());
+        }
+        return std::move(result).value();
+    }
+
+    context::gravity_field::GravityFieldPreparationResult<context::gravity_field::GravityFieldPreparationReport>
+    GravityFieldOperator::TryPrepare(
+        const mfem::Vector &state,
+        const context::gravity_field::GravityFieldRevisions &revisions
     ) {
         using form                   = utils::blocks::gravity_field_form;
 
@@ -295,7 +308,7 @@ namespace mean_field::operators {
         const mfem::Vector gravity_potential =
             make_read_only_value_view(state, m_state_offsets, gravity_potential_block);
 
-        return m_linearization_context.Prepare(
+        return m_linearization_context.TryPrepare(
             {.density           = density,
              .displacement      = displacement,
              .gravity_gradient  = gravity_gradient,