PreprintarXiv licencearXiv
Cartesian PML truncation for the Helmholtz equation is exponentially accurate at high frequency
Abstract
For a wide class of Helmholtz scattering problems (namely, those fitting in the black-box framework of Sjöstrand--Zworski) we prove that the error incurred by approximating the radiation condition by a Cartesian perfectly-matched layer (PML) decreases exponentially in the width of the PML, the strength of the PML scaling, and the frequency.
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BibTeX
@misc{averseng2026cartesian,
title = {{Cartesian PML truncation for the Helmholtz equation is exponentially accurate at high frequency}},
author = {Martin Averseng and Jeffrey Galkowski and Euan A. Spence},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11343},
eprint = {2609.11343},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11343},
}
RIS
TY - UNPB
TI - Cartesian PML truncation for the Helmholtz equation is exponentially accurate at high frequency
AU - Martin Averseng
AU - Jeffrey Galkowski
AU - Euan A. Spence
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11343
UR - https://arxiv.org/abs/2609.11343
AB - For a wide class of Helmholtz scattering problems (namely, those fitting in the black-box framework of Sjöstrand--Zworski) we prove that the error incurred by approximating the radiation condition by a Cartesian perfectly-matched layer (PML) decreases exponentially in the width of the PML, the strength of the PML scaling, and the frequency.
ER -