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PMLs: A direct approach
Author(s) -
Kausel Eduardo,
Oliveira Barbosa João Manuel
Publication year - 2011
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.3322
Subject(s) - quadrature (astronomy) , position (finance) , finite element method , stiffness , context (archaeology) , mathematics , simple (philosophy) , gaussian , frequency domain , domain (mathematical analysis) , computer science , mathematical analysis , algorithm , structural engineering , engineering , physics , geology , electronic engineering , paleontology , philosophy , finance , epistemology , quantum mechanics , economics
SUMMARY This brief article outlines a new and rather simple method for obtaining the finite element matrices for a perfectly matched layer used for elastic wave propagation in the context of a frequency‐domain formulation. For this purpose, we introduce a fairly mild simplification, which allows applying the stretching functions directly to the mass and stiffness matrices obtained via conventional methods (i.e., elastic elements), a novel strategy that allows circumventing the use of integration via Gaussian quadrature. In essence, the technique proposed herein is equivalent to a direct application of the method of weighted residuals in stretched space, followed by a conversion of the linear dimensions into position‐dependent complex‐values. Most importantly, numerical tests demonstrate that the technique does work as intended, and in fact, splendidly so. Copyright © 2011 John Wiley & Sons, Ltd.