Kovac Spectral Horizon (KSH): Spectral Horizon of the Maxwell Operator on 2D and 3D Domains

Abstract

The Kovac Spectral Horizon (KSH) is introduced as a global spectral invariant for the Maxwell operator on general 2D and 3D domains. This work presents a comprehensive experimental study based on 23 independent geometries, including symmetric and asymmetric regions, porous structures, degenerate shapes, domains with interior cavities, extreme aspect ratios, geometric singularities, highly deformed boundaries, and non‑orientable manifolds such as the Möbius strip and the Klein bottle. Across all tested configurations, KSH demonstrates exceptional robustness, consistently converging to the normalized value h(λ)=1.0 regardless of domain shape, topology, mesh quality, penalized volumes, or degenerate tetrahedra. The results show that KSH is a dimensionless, scale‑independent, topology‑independent spectral invariant, suitable for comparing Maxwell spectra across heterogeneous geometries. This dataset includes complete eigenvalue tables, normalized spectral horizons, and graphical outputs for all 23 tests, providing a unified reference for spectral analysis on extreme geometric and topological configurations.