AdvDiffSolver flow-solver upgrade + alternating-Schwarz ROM for SteadyNS

[dreamer2368]

This PR bundles two related lines of work that have been developed sequentially. Both target the component-wise solver stack; the second sits on top of the first. Together they reflect the methodology demonstrated in our recent paper: https://onlinelibrary.wiley.com/doi/full/10.1002/nme.70314.

1. AdvDiffSolver update (originally branch advdiff_update)

Generalizes the flow solver inside AdvDiffSolver and hardens the sampling workflow so that failed parameter choices no longer abort sample generation.

Flow solver generalization

• AdvDiffSolver now accepts either StokesSolver or SteadyNSSolver as its flow solver, selected by adv-diff/flow_solver/type (stokes or steady-ns). The member stokes_solver is renamed flow_solver.
• New adv-diff/flow_solver/order option lets the flow solver use a different discretization order from the advection-diffusion solver.
• GetFlowField now returns whether the flow solver converged, so the caller can react.

SetParameterizedProblem returns success

• MultiBlockSolver::SetParameterizedProblem and all overrides (PoissonSolver, StokesSolver, LinElastSolver, UnsteadyNSSolver, AdvDiffSolver) now return bool.
• GenerateSamples uses this signal: on random sampling, if SetParameterizedProblem fails, the workflow draws a new parameter set and retries instead of crashing. On non-random sampling, the failure is fatal as before. BuildROM, SingleRun, and PrintEQPCoords assert success.

Separate ROM solver tolerances

• ROM linear/nonlinear solver options moved from the solver/... namespace to rom_solver/... (max_iter, relative_tolerance, absolute_tolerance, print_level, use_restart, initial_random_perturbation, jacobian/...). This decouples ROM and FOM solver settings, which were previously coupled and forced compromises during testing. Test inputs (steady_ns.base.yml, steady_ns.component.yml) updated to provide the new keys.

Misc

• utils/gmsh2mfem: added -rs/--refine-serial option for serial uniform refinement at conversion time.

2. Alternating-Schwarz ROM for SteadyNS (branch schwarz)

Adds an alternating-Schwarz solve mode for the component-wise SteadyNS ROM, where the global N×N array is solved as overlapping M×M subdomain ROM problems iterated to convergence.

Subset topology

• New ComponentTopologyHandler(global, i0, j0, N, M, subset_to_orig) constructor extracts an M×M subset starting at (i0, j0) from an N×N global component topology, preserving internal ports and promoting subset-facing internal interfaces to boundaries. Tracks a subset→original mesh mapping.
• Mesh subset constructor also stores the subset-to-original mapping.

Solver-side hooks

• MultiBlockSolver, StokesSolver, SteadyNSSolver, LinElastSolver constructors now accept an optional pre-built TopologyHandler*, enabling sub-solvers to share/own a subset topology.
• New MultiBlockSolver::IsBdrTypeDefined() and PrintConfiguration() helpers.
• StokesSolver::SetSubsetComplementaryFlux enforces incompressibility on a subset when all boundaries are velocity-Dirichlet (uses new subset_flux coefficient namespace).
• LinElastSolver BC handling rewritten to switch explicitly on BoundaryType (now supports ZERO and treats undefined boundaries as homogeneous Neumann).

Schwarz driver

• New src/steady_ns_solver_schwarz.cpp implementing SteadyNSSolver::SchwarzROM(M, N, problem, …, maxIter, threshold, plateau_track, plateau_range, use_restart, initial_tol). Builds (N-M+1)² overlapping sub-solvers, sets internal sub-boundaries to Dirichlet from the latest global iterate, and iterates with plateau detection. Optional relaxed initial_tol on the first iterations to avoid early stagnation.
• New SingleSchwarzRun workflow entry point, gated on main/solver: steady-ns. Configured via new schwarz/ input section (local_size, global_size, maximum_iteration, threshold, plateau_track, plateau_range, initial_tolerance).
• SteadyNSTensorROM::SaveOperator added for diagnostics (writes linear op + per-subdomain tensor to HDF5).

Misc

• PrintBoundaryType() helper added to parameterized_problem.
• New reference Poisson sketch sketches/phyml_poisson.cpp for the PhyML demo (piecewise-kappa diffusion with Gaussian forcing).

Test plan

• Existing tests pass with updated rom_solver/* keys in test/inputs/steady_ns.*.yml.
• AdvDiffSolver with flow_solver/type: stokes reproduces previous behavior.
• AdvDiffSolver with flow_solver/type: steady-ns runs end-to-end.
• GenerateSamples random mode recovers from a SetParameterizedProblem failure.
• SingleSchwarzRun converges on the SteadyNS component-wise example used during development; record converged error and iteration count.
• phyml_poisson sketch builds.

[dylan-copeland]

lay -> lie