On perfectly matched layers of nonlocal wave equations in unbounded multiscale media

Du, Yu; Zhang, Jiwei

doi:10.2140/jomms.2022.17.343

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On perfectly matched layers of nonlocal wave equations in unbounded multiscale media

Yu Du and Jiwei Zhang

Vol. 17 (2022), No. 4, 343–364

DOI: 10.2140/jomms.2022.17.343

Abstract

A nonlocal perfectly matched layer (PML) is formulated for the nonlocal wave equation in the whole real axis, and numerical discretization is designed for solving the reduced PML problem on a bounded domain. The nonlocal PML poses challenges not faced in PDEs. For example, there is no derivative in nonlocal models, which makes it impossible to replace derivatives with complex ones. Here we provide a way of constructing the PML for nonlocal models, which decays the waves exponentially impinging in the layer and makes reflections at the truncated boundary very tiny. To numerically solve the nonlocal PML problem, we design the asymptotically compatible (AC) scheme for a spatially nonlocal operator by combining Talbot’s contour and a Verlet-type scheme for time evolution. The accuracy and effectiveness of our approach are illustrated by various numerical examples.

Keywords

nonlocal wave equation, asymptotically compatible (AC) scheme, perfectly matched layer (PML), artificial/absorbing boundary condition (ABC), multiscale media

Milestones

Received: 7 November 2021

Revised: 16 March 2022

Accepted: 21 March 2022

Published: 18 February 2023

Authors

Yu Du
Department of Mathematics Xiangtan University Yuhu District, Xiangtan, Hunan China

Jiwei Zhang
School of Mathematics and Statistics Wuhan University Wuhan, Hubei China

Vol. 17, No. 4, 2022

Yu Du and Jiwei Zhang

Abstract

Keywords

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Authors