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ARTICLE

A symmetric discretization of the perfectly matched layer for the 2D Helmholtz equation

HYUNSEO PARK1 ,  HYEONJUN SONG2 ,  YOONSEO PARK3 ,  CHANGSOO SHIN2
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1 Department of Mechanical and Aerospace Engineering, Seoul National University, South Korea,
2 Department of Energy Systems Engineering, Seoul National University, South Korea,
3 Computational Science and Technology Program, Seoul National University, South Korea,
JSE 2017, 26(6), 541–560;
Submitted: 8 April 2017 | Accepted: 18 September 2017 | Published: 1 December 2017
© 2017 by the Authors. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
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Abstract

Park, H., Song, H., Park, Y. and Shin, C., 2017. Journal of Seismic Exploration, 26: 541- 560. A symmetric discretization of the Perfectly Matched Layer (PML) for the 2D Helmholtz equation is introduced. The PML is an efficient method to suppress spurious reflections at the boundaries of the computational domain, so that the Sommerfeld radiation condition in unbounded medium is effectively achieved. The PML can be formulated in the symmetric form, which has not been used with dispersion-minimizing finite difference methods in the exploration geophysics community. We suggest a simple symmetrization of the discretized matrix that can be used with a dispersion-minimizing method. The symmetric discretization of the PML enables us to utilize the LDLT (LDL) decomposition with the Bunch-Kaufman pivoting, which considerably reduces not only the number of arithmetic operations but also storage requirement for numerical factorization of a sparse matrix, compared to the LU decomposition. Some numerical experiments are shown to demonstrate the efficiency of the suggested scheme.

Keywords
acoustic wave
Helmholtz equation
symmetric matrix
finite difference
absorbing boundary
numerical dispersion minimization.
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Journal of Seismic Exploration, Print ISSN: 0963-0651, Published by AccScience Publishing
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