A Stable Finite Difference Method for the Elastic Wave Equation on Complex Geometries with Free Surfaces
By D. Appelö, N. Anders Petersson. Communications in Computational Physics, 2007
169 citations recorded by the source corpus.
A stable and explicit second order accurate finite difference method for the elastic wave equation in curvilinear coordinates is presented. The discretization of the spatial operators in the method is shown to be self-adjoint for free-surface, Dirichlet and periodic boundary conditions. The fully discrete version of the method conserves a discrete energy to machine precision.
Subfields: Computational Mechanics, Electrical and Electronic Engineering, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/33fff98e6131b7b0e9fb8e6a5ceb2b73143d405d
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In Computational Mechanics
In Electrical and Electronic Engineering
In Numerical Analysis
Citations in the corpus
- Summation by Parts Operators for Finite Difference Approximations of Second-Derivatives with Variable Coefficients (2012, background): “4 of a narrowdiagonal second-derivative SBP operators alone does not guarantee stability for problems with a combination of mixed (∂(2)/∂x∂y) and non-mixed (∂(2)/∂x(2), ∂(2)/∂y(2)) second-derivatives, such as the compressible Navier-Stokes equations [19] and the elastic wave equation [1].”
- Stable Grid Refinement and Singular Source Discretization for Seismic Wave Simulations (2009, methodology): “The composite grid discretization developed here, together with the generalization of the method to curvilinear grids [2], which enables accurate modeling of free surfaces on realistic (non-planar) topography, makes the finite difference method a very attractive alternative to the recently developed”