Stable Grid Refinement and Singular Source Discretization for Seismic Wave Simulations

@article{Petersson2009StableGR,
  title={Stable Grid Refinement and Singular Source Discretization for Seismic Wave Simulations},
  author={N. Anders Petersson and Bj{\"o}rn Sj{\"o}green},
  journal={Communications in Computational Physics},
  year={2009}
}
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… 
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References

SHOWING 1-10 OF 41 REFERENCES
An Embedded Boundary Method for the Wave Equation with Discontinuous Coefficients
TLDR
It is proved that the one-dimensional restriction of the method is stable without damping for arbitrary locations of the interface relative to the grid, and pointwise second order accuracy is confirmed.
A Domain Decomposition Method for the Acoustic Wave Equation with Discontinuous Coefficients and Grid Change
A domain decomposition technique is proposed for the computation of the acoustic wave equation in which the bulk modulus and density fields are allowed to be discontinuous at the interfaces. Inside
Arbitrary high-order finite volume schemes for seismic wave propagation on unstructured meshes in 2D and 3D
SUMMARY We present a new numerical method to solve the heterogeneous anelastic seismic wave equations with arbitrary high order of accuracy in space and time on unstructured triangular and
Cartesian grid method for unsteady compressible flow in irregular regions
TLDR
An adaptive Cartesian grid method for modeling time-dependent inviscid compressible flow in irregular regions using an unsplit second-order Godunov algorithm followed by a corrector applied to cells at the boundary.
An energy absorbing far-field boundary condition for the elastic wave equation
We present an energy absorbing non-reflecting boundary condition of Clayton-Engquist type for the elastic wave equation together with a discretization which is stable for any ratio of compressional
Stable and accurate wave-propagation in discontinuous media
Simulating seismic wave propagation in 3D elastic media using staggered-grid finite differences
TLDR
This article provides an overview of the application of the staggered-grid finite-difference technique to model wave propagation problems in 3D elastic media and introduces a memory optimization procedure that allows large-scale 3D finite-Difference problems to be computed on a conventional, single-processor desktop workstation.
An arbitrary high-order discontinuous Galerkin method for elastic waves on unstructured meshes — II. The three-dimensional isotropic case
TLDR
The development of the highly accurate ADER–DG approach for tetrahedral meshes provides a numerical technique to approach 3-D wave propagation problems in complex geometry with unforeseen accuracy.
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