PMLs: A direct approach

• Published in: International journal for numerical methods in engineering Vol. 90; no. 3; pp. 343 - 352
• Main Authors: Kausel, Eduardo, de Oliveira Barbosa, João Manuel
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 20.04.2012; Wiley
• Subjects: Exact sciences and technology; finite elements; Fundamental areas of phenomenology (including applications); Mathematics; Methods of scientific computing (including symbolic computation, algebraic computation); Numerical analysis. Scientific computation; perfectly matched layer; Physics; Sciences and techniques of general use; Solid mechanics; solids; Structural and continuum mechanics; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); vibrations; Simplification; Vibration; solids; Gauss method; Frequency domain method; Elastic wave; Conversion; Gauss formula; Modeling; Direct method; Finite element method; Impedance matching; Weighted residual method; Elastodynamics; Stretching; finite elements; perfectly matched layer; vibrations
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.3322

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.