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Explicit finite element perfectly matched layer for transient three‐dimensional elastic waves
Author(s) -
Basu Ushnish
Publication year - 2008
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2397
Subject(s) - perfectly matched layer , finite element method , bounded function , transient (computer programming) , domain (mathematical analysis) , computation , displacement (psychology) , overhead (engineering) , computer science , mathematics , mathematical analysis , algorithm , structural engineering , engineering , psychology , psychotherapist , operating system
The use of a perfectly matched layer (PML) model is an efficient approach toward the bounded‐domain modelling of wave propagation on unbounded domains. This paper formulates a three‐dimensional PML for elastic waves by building upon previous work by the author and implements it in a displacement‐based finite element setting. The novel contribution of this paper over the previous work is in making this finite element implementation suitable for explicit time integration, thus making it practicable for use in large‐scale three‐dimensional dynamic analyses. An efficient method of calculating the strain terms in the PML is developed in order to take advantage of the lack of the overhead of solving equations at each time step. The PML formulation is studied and validated first for a semi‐infinite bar and then for the classical soil–structure interaction problems of a square flexible footing on a (i) half‐space, (ii) layer on a half‐space and (iii) layer on a rigid base. Numerical results for these problems demonstrate that the PML models produce highly accurate results with small bounded domains and at low computational cost and that these models are long‐time stable, with critical time step sizes similar to those of corresponding fully elastic models. Copyright © 2008 John Wiley & Sons, Ltd.