Download this article
Download this article For screen
For printing
Recent Issues

Volume 19
Issue 2, 157–302
Issue 1, 1–156

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 5 issues

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 8 issues

Volume 7, 10 issues

Volume 6, 9 issues

Volume 5, 6 issues

Volume 4, 10 issues

Volume 3, 10 issues

Volume 2, 10 issues

Volume 1, 8 issues

The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1559-3959
Author Index
To Appear
 
Other MSP Journals
This article is available for purchase or by subscription. See below.
On perfectly matched layers of nonlocal wave equations in unbounded multiscale media

Yu Du and Jiwei Zhang

Vol. 17 (2022), No. 4, 343–364
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.

PDF Access Denied

We have not been able to recognize your IP address 44.192.20.240 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 45.00:

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