Towards a combined perfectly matching layer and infinite element formulation for unbounded elastic wave problems

Pettigrew, Joseph S. and Mulholland, Anthony J. and Tant, Katherine M. M. (2021) Towards a combined perfectly matching layer and infinite element formulation for unbounded elastic wave problems. Mathematics and Mechanics of Solids, 27 (5). pp. 1-19. ISSN 1081-2865 (https://doi.org/10.1177/10812865211040855 Article ...)

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Abstract

This paper presents a framework for implementing a novel Perfectly Matching Layer and Infinite Element (PML+IE) combination boundary condition for unbounded elastic wave problems in the time domain. To achieve this, traditional hexahedral finite elements are used to model wave propagation in the inner domain and infinite element test functions are implemented in the exterior domain. Two alternative implementations of the PML formulation are studied: the case with constant stretching in all three dimensions and the case with spatially dependent stretching along a single direction. The absorbing ability of the PML+IE formulation is demonstrated by the favourable comparison with the reflection coefficient for a plane wave incident on the boundary achieved using a finite element only approach where stress free boundary conditions are implemented at the domain edge. Values for the PML stretching function parameters are selected based on the minimisation of the reflected wave amplitude and it is shown that the same reduction in reflection amplitude can be achieved using the PML+IE approach with approximately half of the number of elements required in the finite element only approach.

ORCID iDs

Pettigrew, Joseph S. ORCID logoORCID: https://orcid.org/0000-0002-1512-8555, Mulholland, Anthony J. and Tant, Katherine M. M. ORCID logoORCID: https://orcid.org/0000-0003-4345-7054;
  • Item type:Article
    ID code:77332
    Dates:
    Date
    Event
    15 September 2021
    Published
    15 September 2021
    Published Online
    2 August 2021
    Accepted
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:10 Aug 2021 09:07
    Last modified:11 Nov 2024 13:10
    URI:https://strathprints.strath.ac.uk/id/eprint/77332
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