A Topology-Aware Mixed Finite-Element Formulation for Flux-Free Beltrami Modes in an Annular-Cylinder Domain

Abstract

Version 1.1 adds the boundary-trace justification and direct source-level verification of the discrete boundary construction. This technical note reports a reproducible five-mesh numerical study of flux-free signed Beltrami modes on an annular-cylinder domain with solid-torus topology. For a nonzero Beltrami eigenfield, curl J = lambda J implies J = (1/lambda) curl J, so imposing (curl J) dot n = 0 recovers J dot n = 0. The archived Phase B2 source verifies that L_boundarycurl = D1[F_boundary, :], meaning each constraint is the signed circulation around a boundary triangle rather than an individual boundary-edge mask. The topology pipeline also distinguishes the complementary meridional cycle gamma from the longitudinal H1 generator and removes the surviving harmonic zero mode exactly once in Phase C2. Across five meshes, the final principal cosines reached 0.943205 and 0.942553, mean absolute eigenvalue changes fell to 1.516% and 1.594%, and tracked normalized strong defects decreased to 0.175226 and 0.174585. The numerical values are unchanged from Version 1.0. These results provide numerical validation under stated practical gates, not a proof of continuum spectral convergence.