SBP-SAT finite difference discretization of acoustic wave equations on staggered block-wise uniform grids
KAUST DepartmentExtreme Computing Research Center
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Applied Mathematics and Computational Science Program
KAUST Grant NumberCCF-CAF/URF/1-2596
Preprint Posting Date2018-02-16
Online Publication Date2018-09-06
Print Publication Date2019-03
Permanent link to this recordhttp://hdl.handle.net/10754/627203
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AbstractWe consider the numerical simulation of the acoustic wave equations arising from seismic applications, for which staggered grid finite difference methods are popular choices due to their simplicity and efficiency. We relax the uniform grid restriction on finite difference methods and allow the grids to be block-wise uniform with nonconforming interfaces. In doing so, variations in the wave speeds of the subterranean media can be accounted for more efficiently. Staggered grid finite difference operators satisfying the summation-by-parts (SBP) property are devised to approximate the spatial derivatives appearing in the acoustic wave equation. These operators are applied within each block independently. The coupling between blocks is achieved through simultaneous approximation terms (SATs), which impose the interface condition weakly, i.e., by penalty. Ratio of the grid spacing of neighboring blocks is allowed to be rational number, for which specially designed interpolation formulas are presented. These interpolation formulas constitute key pieces of the simultaneous approximation terms. The overall discretization is shown to be energy-conserving and examined on test cases of both theoretical and practical interests, delivering accurate and stable simulation results.
CitationGao L, Del Rey Fernández DC, Carpenter M, Keyes D (2019) SBP–SAT finite difference discretization of acoustic wave equations on staggered block-wise uniform grids. Journal of Computational and Applied Mathematics 348: 421–444. Available: http://dx.doi.org/10.1016/j.cam.2018.08.040.
SponsorsGao and Mark Carpenter gratefully acknowledge the support of KAUST’s Office of Sponsored Research under CCF-CAF/URF/1-2596.