Fix inverse periodic affine transforms in the parser and FEM

[rois1995]

Proposed Changes

Periodic affine maps use an incorrect inverse when rotations and translations are combined. This PR corrects the parser inverse and the FEM caller.

A combined Euler rotation cannot be inverted by simply negating its three angles, and an affine translation must be reversed as -R^T t. The parser now stores the actual inverse rotation/translation, including gimbal cases. The FEM caller uses the same rotation helper and inverse affine offset.

Parser round trips cover translation, one/multiple angles and a gimbal layout. A tiny BOX DG regression expresses the same rotation once with an affine translation and once with a shifted center. Develop rejects the affine map at face matching; the fixed cases both complete with identical printed histories. The generated BOX mesh needs no external data. Identity/single-axis arithmetic is preserved where applicable.

Validation of the combined periodic source passes serial, partitioned MPI2, OpenMP2 and MPI2×OpenMP2 (10 cases / 3175 serial assertions). Individual branch CI and complete regression/reference checks are pending. Test configurations, meshes, logs and before/after values are in the testcase comment. New regression references are local x86 values and need CI confirmation.

Related Work

• MPI Point-to-Point Refactoring + New Periodic BC Implementation #652 introduced the current periodic implementation.
• Fixes for rotational periodic boundaries: implicit solver, multigrid and limiters #2961 lists the eight related periodic-boundary PRs. Their numbering groups the topics; it does not imply a linear dependency chain.

PR Checklist

• I am submitting my contribution to the develop branch.
• My contribution generates no new compiler warnings (complete branch CI pending).
• My contribution is commented and consistent with SU2 style.
• I ran the repository pre-commit checks on the changed files.
• I have added tests that demonstrate the contribution.
• I have updated appropriate documentation, if necessary.

[rois1995]

Test cases

Reproducers, configurations, numeric logs and scripts: transforms. Develop = 6db10127d1; BOX fixtures generate their meshes. The original B–D evidence above was recorded before the expanded follow-ups.

Check	develop	fixed
Affine parser round trips	4/5 fail; errors 0.8660254, 1.7259958 and 4	passes
Equivalent affine vs centered BOX DG map	affine stops at face matching, centered completes	both complete; identical printed histories

The two complete configurations and histories are in the evidence folder. Iteration-1 monitored values are 2.083795225, 4.631729184, 4.386282333, 3.676591706, 7.559937938 for both fixed inputs. The new periodic_affine serial regression uses a generated BOX mesh.

Combined release checks: serial and OpenMP2 pass 10 cases / 3175 assertions; partitioned MPI2 and MPI2×OpenMP2 pass on both ranks (2334 / 2238 assertions). These are combined-source checks, not standalone builds of every branch. Complete branch CI and full regression/reference checks remain pending.