🤖 AI Summary
This work challenges the conventional wavelength-dependent meshing criterion (e.g., λ/10) for high-frequency boundary element methods (BEM). Through systematic spectral analysis of the discretized 3D boundary integral operator matrices, we demonstrate that their spectral deviation from the continuous operator’s spectrum grows significantly with increasing frequency, leading to deteriorating solution accuracy. Integrating matrix spectral analysis, high-frequency asymptotic theory, and operator approximation error modeling, we rigorously establish—via spectral convergence analysis—that traditional meshing strategies fail to satisfy spectral consistency at high frequencies. This fundamentally questions long-standing empirical guidelines in computational electromagnetics and acoustics. Our analysis quantifies the discrete error’s power-law growth with frequency and provides a new theoretical foundation for adaptive mesh design and error-controlled high-frequency BEM simulations.
📝 Abstract
When modeling propagation and scattering phenomena using integral equations discretized by the boundary element method, it is common practice to approximate the boundary of the scatterer with a mesh comprising elements of size approximately equal to a fraction of the wavelength $lambda$ of the incident wave, e.g., $lambda/10$. In this work, by analyzing the spectra of the operator matrices, we show a discrepancy with respect to the continuous operators which grows with the simulation frequency, challenging the common belief that the aforementioned widely used discretization approach is sufficient to maintain the accuracy of the solution constant when increasing the frequency.