Commun. Comput. Phys., 8 (2010), pp. 1074-1110.


Stable Grid Refinement and Singular Source Discretization for Seismic Wave Simulations

N. Anders Petersson 1*, Bjorn Sjogreen 1

1 Center for Applied Scientific Computing, L-422, Lawrence Livermore National Laboratory, PO Box 808, Livermore, CA 94551.

Received 4 November 2009; Accepted (in revised version) 12 February 2010
Available online 31 May 2010
doi:10.4208/cicp.041109.120210a

Abstract

An energy conserving discretization of the elastic wave equation in second order formulation is developed for a composite grid, consisting of a set of structured rectangular component grids with hanging nodes on the grid refinement interface. Previously developed summation-by-parts properties are generalized to devise a stable second order accurate coupling of the solution across mesh refinement interfaces. The discretization of singular source terms of point force and point moment tensor type are also studied. Based on enforcing discrete moment conditions that mimic properties of the Dirac distribution and its gradient, previous single grid formulas are generalized to work in the vicinity of grid refinement interfaces. These source discretization formulas are shown to give second order accuracy in the solution, with the error being essentially independent of the distance between the source and the grid refinement boundary. Several numerical examples are given to illustrate the properties of the proposed method.

AMS subject classifications: 65M06, 65M12, 74B05, 86A15

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Key words: Elastic wave equation, mesh refinement, stability, summation by parts, singular source term.

*Corresponding author.
Email: andersp@llnl.gov (N. A. Petersson), sjogreen2@llnl.gov (B. Sjogreen)
 

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