Compact high order schemes with gradient-direction derivatives for absorbing boundary conditions

Dan Gordon, Rachel Gordon, Eli Turkel

Research output: Contribution to journalArticlepeer-review


We consider several compact high order absorbing boundary conditions (ABCs) for the Helmholtz equation in three dimensions. A technique called "the gradient method" (GM) for ABCs is also introduced and combined with the high order ABCs. GM is based on the principle of using directional derivatives in the direction of the wavefront propagation. The new ABCs are used together with the recently introduced compact sixth order finite difference scheme for variable wave numbers. Experiments on problems with known analytic solutions produced very accurate results, demonstrating the efficacy of the high order schemes, particularly when combined with GM. The new ABCs are then applied to the SEG/EAGE Salt model, showing the advantages of the new schemes.

Original languageEnglish
Pages (from-to)295-315
Number of pages21
JournalJournal of Computational Physics
StatePublished - 5 Sep 2015

Bibliographical note

Publisher Copyright:
© 2015 Elsevier Inc..


  • Absorbing boundary conditions
  • Compact schemes
  • Geophysics
  • Gradient method
  • Helmholtz equation
  • High order accuracy
  • Wavefront direction

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy (all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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