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Efficient Simulation of Wave Propagation with Implicit Finite Difference Schemes

Published online by Cambridge University Press:  28 May 2015

Wensheng Zhang ,
Li Tong  and
Eric T. Chung
Wensheng Zhang*
Affiliation:
LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing P. O. Box 2719, 100190 China
Li Tong*
Affiliation:
LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing P. O. Box 2719, 100190 China
Eric T. Chung*
Affiliation:
Department of Mathematics, The Chinese University of Hong Kong, Hong Kong
*
Corresponding author.Email address:zws@lsec.cc.ac.cn
Corresponding author.Email address:tongli@lsec.cc.ac.cn
Corresponding author.Email address:tschung@math.cuhk.edu.hk
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Abstract

Finite difference method is an important methodology in the approximation of waves. In this paper, we will study two implicit finite difference schemes for the simulation of waves. They are the weighted alternating direction implicit (ADI) scheme and the locally one-dimensional (LOD) scheme. The approximation errors, stability conditions, and dispersion relations for both schemes are investigated. Our analysis shows that the LOD implicit scheme has less dispersion error than that of the ADI scheme. Moreover, the unconditional stability for both schemes with arbitrary spatial accuracy is established for the first time. In order to improve computational efficiency, numerical algorithms based on message passing interface (MPI) are implemented. Numerical examples of wave propagation in a three-layer model and a standard complex model are presented. Our analysis and comparisons show that both ADI and LOD schemes are able to efficiently and accurately simulate wave propagation in complex media.

Keywords

35L0565M06765Y05Acoustic wave equationimplicit schemesADILODstability conditiondispersion curveMPI parallel computations

Information

Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 5 , Issue 2 , May 2012 , pp. 205 - 228
Copyright
Copyright © Global Science Press Limited 2012

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