This work presents a high-precision numerical benchmark for wave propagation in heterogeneous media using Cherenkov radiation as a canonical test case. A combined framework based on Leue Modulation Coefficients (LMC) and Resonant Operator Calculus (ROC) is validated against analytically predictable Cherenkov emission angles. The LMC construction enables smooth, spatially varying refractive index fields while maintaining uniform ellipticity, and ROC provides exact spectral partitioning into forward, resonant, and backward propagation channels. Numerical results demonstrate machine-precision agreement with analytical emission angles, complete suppression of spurious backward modes (residual energy < 10⁻³²), and dispersion-free propagation even in spatially heterogeneous media. The benchmark confirms the suitability of the LMC–ROC framework for high-fidelity simulations of wave phenomena in complex media, with applications in photonics, metamaterials, acoustics, and spectral signal processing.
Jeanette Leue (Sun,) studied this question.