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Spherical Perfectly Matched Layer Method for Electromagnetic Scattering Problems with Large Wave Number
Abstract
We study a spherical perfectly matched layer (PML) method for the time-harmonic Maxwell scattering problem with large wavenumber. Using vector spherical harmonics and a modal transformation for the coupled transverse magnetic components, we establish the sharp wavenumber-explicit stability estimate for the truncated PML problem and prove that its inf-sup constant is of order O(κ−1). We then analyze the first-order Nédélec edge element method and its continuous interior penalty counterpart. Under the condition that κ3h2 is sufficiently small, the preasymptotic errors in the energy norm and the κ-scaled L2 norm are of orders O(κh+κ3h2) and O(κ2h2+κ3h2), respectively. Numerical experiments confirm the theoretical results.
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BibTeX
@misc{shi2026spherical,
title = {{Spherical Perfectly Matched Layer Method for Electromagnetic Scattering Problems with Large Wave Number}},
author = {Jian Shi and Yonglin Li and Haijun Wu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.19982},
eprint = {2610.19982},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.19982},
}
RIS
TY - UNPB
TI - Spherical Perfectly Matched Layer Method for Electromagnetic Scattering Problems with Large Wave Number
AU - Jian Shi
AU - Yonglin Li
AU - Haijun Wu
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.19982
UR - https://arxiv.org/abs/2610.19982
AB - We study a spherical perfectly matched layer (PML) method for the time-harmonic Maxwell scattering problem with large wavenumber. Using vector spherical harmonics and a modal transformation for the coupled transverse magnetic components, we establish the sharp wavenumber-explicit stability estimate for the truncated PML problem and prove that its inf-sup constant is of order O(κ^−1). We then analyze the first-order Nédélec edge element method and its continuous interior penalty counterpart. Under the condition that κ^3h^2 is sufficiently small, the preasymptotic errors in the energy norm and the κ-scaled L^2 norm are of orders O(κh+κ^3h^2) and O(κ^2h^2+κ^3h^2), respectively. Numerical experiments confirm the theoretical results.
ER -