Work

Cartesian PML truncation for the Helmholtz equation is exponentially accurate at high frequency

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.11343

Authors: Averseng, Martin, Galkowski, Jeffrey, Spence, Euan A.

Institutions: Centre National de la Recherche Scientifique, Laboratoire Angevin de Recherche en Mathématiques, Université d'Angers, University College London, University of Bath

Language: English

Topic: Electromagnetic Simulation and Numerical Methods

Subfield: Electrical and Electronic Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: Leverhulme Trust, Engineering and Physical Sciences Research Council, HORIZON EUROPE European Research Council

Awards: Phase-space-inspired numerical methods for high-frequency wave scattering: from semiclassical analysis through numerical analysis to open-source software, High energy spectral and scattering phenomena via microlocal analysis, Novel Phenomena in Steklov Type Problems, G8303649209

OpenAlex ID: W7212292764

Cites: 2

Cited by: 1

Related to: 10