Solution of three-dimensional multiple scattering problems by the method of difference potentials

M. Medvinsky, S. Tsynkov*, E. Turkel

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We propose an algorithm based on the Method of Difference Potentials (MDP) for the numerical solution of multiple scattering problems in three space dimensions. The propagation of waves is assumed time-harmonic and governed by the Helmholtz equation. The latter is approximated with 6th order accuracy on a Cartesian grid by means of a compact finite difference scheme. The shape of the scatterers does not have to conform to the discretization grid, yet the MDP enables the approximation with no loss of accuracy. At the artificial outer boundary, which is spherical, the solution is terminated by a 6th order Bayliss–Gunzburger–Turkel (BGT) radiation boundary condition. The method enables efficient solution of a series of similar problems, for example, when the incident field changes while everything else stays the same, or when the type of the scattering changes (e.g., sound-soft vs. sound-hard) while the shape of the scatterer remains the same.

Original languageEnglish
Article number102822
JournalWave Motion
StatePublished - Dec 2021


  • Artificial outer boundary
  • BGT radiation condition
  • Cartesian grid
  • Finite differences
  • Helmholtz equation
  • High-order accuracy
  • Non-conforming boundary
  • Scattering objects
  • Time-harmonic waves
  • Unbounded domain


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