Stable and high order accurate difference methods for the elastic wave equation in discontinuous media
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Abstract© 2014 Elsevier Inc. In this paper, we develop a stable and systematic procedure for numerical treatment of elastic waves in discontinuous and layered media. We consider both planar and curved interfaces where media parameters are allowed to be discontinuous. The key feature is the highly accurate and provably stable treatment of interfaces where media discontinuities arise. We discretize in space using high order accurate finite difference schemes that satisfy the summation by parts rule. Conditions at layer interfaces are imposed weakly using penalties. By deriving lower bounds of the penalty strength and constructing discrete energy estimates we prove time stability. We present numerical experiments in two space dimensions to illustrate the usefulness of the proposed method for simulations involving typical interface phenomena in elastic materials. The numerical experiments verify high order accuracy and time stability.
CitationDuru K, Virta K (2014) Stable and high order accurate difference methods for the elastic wave equation in discontinuous media. Journal of Computational Physics 279: 37–62. Available: http://dx.doi.org/10.1016/j.jcp.2014.08.046.
SponsorsThe work of the first author was supported by King Abdullah University of Science and Technology (KAUST) through a joint KAUST Academic Excellence Alliance (AEA) grant with Stanford. The first author also acknowledges the support of Eric M. Dunham during this work.
JournalJournal of Computational Physics