A compact three-dimensional fourth-order scheme for elasticity using the first-order formulation

Rachel Gordon; Eli Turkel; Dan Gordon

doi:10.1002/nme.6794

A compact three-dimensional fourth-order scheme for elasticity using the first-order formulation

Rachel Gordon, Eli Turkel, Dan Gordon

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

Abstract

We develop a compact fourth-order scheme for the three-dimensional elastic wave equation in frequency space, using the first-order velocity-stress formulation. The scheme is implemented numerically for homogeneous media on a staggered grid, and both the acoustic and elastic cases are considered. We use a one-directional point source of impact, for which Pilant developed a closed solution. Numerical results for the acoustic and the elastic cases compare favorably with the analytic solutions and show a very significant improvement over the second-order scheme.

Original language	English
Pages (from-to)	6341-6360
Number of pages	20
Journal	International Journal for Numerical Methods in Engineering
Volume	122
Issue number	21
DOIs	https://doi.org/10.1002/nme.6794
State	Published - 15 Nov 2021

Bibliographical note

Publisher Copyright:
© 2021 John Wiley & Sons, Ltd.

Keywords

compact schemes
elastic wave equation
first-order formulation
fourth-order accuracy
frequency space
staggered grid

ASJC Scopus subject areas

Numerical Analysis
General Engineering
Applied Mathematics

Access to Document

10.1002/nme.6794

Cite this

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abstract = "We develop a compact fourth-order scheme for the three-dimensional elastic wave equation in frequency space, using the first-order velocity-stress formulation. The scheme is implemented numerically for homogeneous media on a staggered grid, and both the acoustic and elastic cases are considered. We use a one-directional point source of impact, for which Pilant developed a closed solution. Numerical results for the acoustic and the elastic cases compare favorably with the analytic solutions and show a very significant improvement over the second-order scheme.",

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