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

Rachel Gordon, Eli Turkel, Dan Gordon

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)6341-6360
Number of pages20
JournalInternational Journal for Numerical Methods in Engineering
Issue number21
StatePublished - 15 Nov 2021

Bibliographical note

Funding Information:
The authors wish to thank the reviewers for their detailed and helpful comments.

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


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

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering (all)
  • Applied Mathematics


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