PreprintCC BY-NC-ND 4.0HAL
Frequency-explicit convergence analysis of a multiscale finite element method for highly heterogeneous scattering problems
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 ℓD is much larger than the wavelength, i.e., the wavenumber k is such that kℓD ≫ 1. Here, we further consider the situation where the scatterer contains different materials, with a characteristic size ε such that kε ≪ 1. We propose a high-order multiscale finite element method, and provide an error analysis that is explicit in both k and ε. 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.
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BibTeX
@misc{chaumontfrelet2026frequencyexplicit,
title = {{Frequency-explicit convergence analysis of a multiscale finite element method for highly heterogeneous scattering problems}},
author = {Théophile Chaumont-Frelet and zakaria kassali},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04930},
eprint = {2609.04930},
archivePrefix = {arXiv},
url = {https://inria.hal.science/hal-05738526v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Frequency-explicit convergence analysis of a multiscale finite element method for highly heterogeneous scattering problems
AU - Théophile Chaumont-Frelet
AU - zakaria kassali
PY - 2026
DA - 2026/09/04
PB - HAL
DO - 10.48550/arxiv.2609.04930
UR - https://inria.hal.science/hal-05738526v1
AB - 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 ℓD is much larger than the wavelength, i.e., the wavenumber k is such that kℓD ≫ 1. Here, we further consider the situation where the scatterer contains different materials, with a characteristic size ε such that kε ≪ 1. We propose a high-order multiscale finite element method, and provide an error analysis that is explicit in both k and ε. 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.
ER -