The solution of the scalar wave equation in the exterior of a sphere

Leslie Greengard, Thomas Hagstrom, Shidong Jiang

Research output: Contribution to journalArticlepeer-review


We derive new, explicit representations for the solution to the scalar wave equation in the exterior of a sphere, subject to either Dirichlet or Robin boundary conditions. Our formula leads to a stable and high-order numerical scheme that permits the evaluation of the solution at an arbitrary target, without the use of a spatial grid and without numerical dispersion error. In the process, we correct some errors in the analytic literature concerning the asymptotic behavior of the logarithmic derivative of the spherical modified Hankel function. We illustrate the performance of the method with several numerical examples.

Original languageEnglish (US)
Pages (from-to)191-207
Number of pages17
JournalJournal of Computational Physics
StatePublished - Oct 1 2014


  • Numerical stability
  • Scattering
  • Separation of variables
  • Time-domain
  • Wave equation

ASJC Scopus subject areas

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


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