perf(allocations): reduced overall allocations by 95%, increaseed jacobian applicatin by 2x

This commit uses global pre allocated work space to dramatically reduce memory usage and allocation time

libmeanfield/interface/solver/newton.cppm

@@ -17,6 +17,7 @@ module;
 
 export module mean_field:solver.newton;
 
+export import :deformation.safe_newton_step;
 export import :solver.linear_backend;
 
 export namespace mean_field::solver::nonlinear {
@@ -264,11 +265,13 @@ export namespace mean_field::solver::nonlinear {
         double relativeResidualNorm{0.0};
         double merit{0.0};
         double iterationSeconds{0.0};
+        double geometryPreflightSeconds{0.0};
         double lineSearchSeconds{0.0};
         double trialPreparationSeconds{0.0};
         double metricEvaluationSeconds{0.0};
         double preconditionerRefreshSeconds{0.0};
         double rollbackSeconds{0.0};
+        std::optional<deformation::LargestSafeNewtonStepSizeEstimate> geometryPreflight{};
         std::optional<LinearSolveReport> linearSolve{};
         MPI_Comm communicator{MPI_COMM_NULL};
         std::span<const mfem::real_t> physicalState{};