A perfectly matched layer for the time-dependent wave equation in heterogeneous and layered media

Kenneth Duru

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

A mathematical analysis of the perfectly matched layer (PML) for the time-dependent wave equation in heterogeneous and layered media is presented. We prove the stability of the PML for discontinuous media with piecewise constant coefficients, and derive energy estimates for discontinuous media with piecewise smooth coefficients. We consider a computational setup consisting of smaller structured subdomains that are discretized using high order accurate finite difference operators for approximating spatial derivatives. The subdomains are then patched together into a global domain by a weak enforcement of interface conditions using penalties. In order to ensure the stability of the discrete PML, it is necessary to transform the interface conditions to include the auxiliary variables. In the discrete setting, the transformed interface conditions are crucial in deriving discrete energy estimates analogous to the continuous energy estimates, thus proving stability and convergence of the numerical method. Finally, we present numerical experiments demonstrating the stability of the PML in a layered medium and high order accuracy of the proposed interface conditions. © 2013 Elsevier Inc.
Original languageEnglish (US)
Pages (from-to)757-781
Number of pages25
JournalJournal of Computational Physics
Volume257
DOIs
StatePublished - Jan 2014
Externally publishedYes

Fingerprint

Dive into the research topics of 'A perfectly matched layer for the time-dependent wave equation in heterogeneous and layered media'. Together they form a unique fingerprint.

Cite this