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A Well-Posed and Discretely Stable Perfectly Matched Layer for Elastic Wave Equations in Second Order Formulation

Published online by Cambridge University Press:  20 August 2015

Kenneth Duru  and
Gunilla Kreiss
Kenneth Duru*
Affiliation:
Division of Scientific Computing, Department of Information Technology, Uppsala University, Box 337, SE-751 05 Uppsala, Sweden
Gunilla Kreiss*
Affiliation:
Division of Scientific Computing, Department of Information Technology, Uppsala University, Box 337, SE-751 05 Uppsala, Sweden
*
Corresponding author.Email:kenneth.duru@it.uu.se
Email:gunilla.kreiss@it.uu.se
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Abstract

We present a well-posed and discretely stable perfectly matched layer for the anisotropic (and isotropic) elastic wave equations without first re-writing the governing equations as a first order system. The new model is derived by the complex coordinate stretching technique. Using standard perturbation methods we show that complex frequency shift together with a chosen real scaling factor ensures the decay of eigen-modes for all relevant frequencies. To buttress the stability properties and the robustness of the proposed model, numerical experiments are presented for anisotropic elastic wave equations. The model is approximated with a stable node-centered finite difference scheme that is second order accurate both in time and space.

Keywords

35B3535L0535L1537C75Perfectly matched layerwell-posednessstabilityhyperbolicityelastic waves
Type
Research Article
Information
Communications in Computational Physics , Volume 11 , Issue 5 , May 2012 , pp. 1643 - 1672
Copyright
Copyright © Global Science Press Limited 2012

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