Frequency-explicit convergence analysis of a multiscale finite element method for highly heterogeneous scattering problems
Year: 2026
Type: preprint
Abstract: We analyze the numerical approximation of time-harmonic scattering by highly heterogeneous penetrable obstacles. These problems are especially challenging in the high-frequency regime, where the size of the scatterer $L$ is much larger than the wavelength, i.e., the wavenumber $k$ is such that $kL \gg 1$. Here, we further consider the situation where the scatterer contains different materials, with a characteristic size $\varepsilon$ such that $k\varepsilon \ll 1$. We propose a high-order multiscale finite element method, and provide an error analysis that is explicit in both $k$ and $\varepsilon$. Crucially, our error estimates suggest that using a high-order method should reduce the computational cost for large frequencies, which is corroborated by numerical examples.
Source: arXiv (Cornell University)
Authors: Chaumont-Frelet, T., Kassali, Z.
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7210893762
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