Allow fully traction-free boundaries for elasticity problem

[masterleinad]

Restricting translation modes seems to be sufficient for MueLU/ML to converge.

[gemini-code-assist]

Summary of Changes

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This pull request introduces a crucial enhancement to the elasticity problem solver by automatically handling fully traction-free boundary conditions. It ensures the stability and convergence of numerical methods, particularly for multigrid solvers like MueLU/ML, by implicitly restricting rigid body translation modes when no explicit boundary constraints are defined.

Highlights

• Traction-Free Boundaries: Implemented logic to automatically apply affine constraints for translation modes when no explicit boundary conditions are provided, addressing fully traction-free elasticity problems.
• Solver Convergence: Enhanced the robustness of the elasticity solver by ensuring convergence for cases with unconstrained boundaries, specifically benefiting multigrid solvers like MueLU/ML.

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[gemini-code-assist]

Code Review

This pull request introduces logic to automatically apply affine constraints to a boundary node when no explicit boundary IDs are provided, executed on MPI rank 0, to prevent rigid body modes. The current method for selecting and constraining a node on the boundary is identified as potentially fragile and difficult to maintain due to its reliance on internal deal.II DoF ordering, and a more robust approach by explicitly selecting a vertex for constraints has been suggested.

[gemini-code-assist]

The logic to select a node on the boundary for constraining is difficult to follow. It relies on implementation details of DoF ordering on a face, which makes it fragile and hard to maintain.

A more direct and robust approach is to explicitly select a vertex on the boundary face and constrain its degrees of freedom. This makes the code's intent clear and is less dependent on internal deal.II orderings.

            // Pin the first vertex of the face to remove translational rigid body modes.
            const unsigned int vertex_on_face = 0;
            const unsigned int vertex_on_cell =
                cell->face_vertex_index(face, vertex_on_face);
            for (unsigned int c = 0; c < dim; ++c)
              _affine_constraints.add_line(
                  cell->vertex_dof_index(vertex_on_cell, c));