Year: 2012
Numerical Mathematics: Theory, Methods and Applications, Vol. 5 (2012), Iss. 2 : pp. 205–228
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2011.m1026
Numerical Mathematics: Theory, Methods and Applications, Vol. 5 (2012), Iss. 2 : pp. 205–228
Published online: 2012-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Acoustic wave equation implicit schemes ADI LOD stability condition dispersion curve MPI parallel computations.
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