Volume 11, Issue 5
A Well-Posed and Discretely Stable Perfectly Matched Layer for Elastic Wave Equations in Second Order Formulation

Kenneth Duru & Gunilla Kreiss

Commun. Comput. Phys., 11 (2012), pp. 1643-1672.

Published online: 2012-11

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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.

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@Article{CiCP-11-1643, author = {}, title = {A Well-Posed and Discretely Stable Perfectly Matched Layer for Elastic Wave Equations in Second Order Formulation}, journal = {Communications in Computational Physics}, year = {2012}, volume = {11}, number = {5}, pages = {1643--1672}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.120210.240511a}, url = {http://global-sci.org/intro/article_detail/cicp/7428.html} }
TY - JOUR T1 - A Well-Posed and Discretely Stable Perfectly Matched Layer for Elastic Wave Equations in Second Order Formulation JO - Communications in Computational Physics VL - 5 SP - 1643 EP - 1672 PY - 2012 DA - 2012/11 SN - 11 DO - http://dor.org/10.4208/cicp.120210.240511a UR - https://global-sci.org/intro/article_detail/cicp/7428.html KW - AB -

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.

Kenneth Duru & Gunilla Kreiss. (2020). A Well-Posed and Discretely Stable Perfectly Matched Layer for Elastic Wave Equations in Second Order Formulation. Communications in Computational Physics. 11 (5). 1643-1672. doi:10.4208/cicp.120210.240511a
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