Rapid perturbational calculations for the helmholtz equation in two dimensions

Sang Yeun Shim, Marcos Capistran, Yu Chen

Research output: Contribution to journalArticlepeer-review

Abstract

Existing approaches to the solution of the inverse scattering problems in two and three dimensions rely on linearization of the Helmholtz equation, which requires the knowledge of the Fréchet derivative of the far field with respect to the index of refraction. We present an efficient algorithm for this perturbational calculation in two dimensions. Our method is based on the merging and splitting procedures already established for the solution of the Lippmann-Schwinger equation [2], [3], [4]. For an m-by-m wavelength problem, the algorithm obtains perturbations to scattered waves for m distinct incident waves in O(m3) steps.

Original languageEnglish (US)
Pages (from-to)627-636
Number of pages10
JournalDiscrete and Continuous Dynamical Systems
Volume18
Issue number4
DOIs
StatePublished - Aug 2007

Keywords

  • Fast direct algorithms
  • Merging formulae
  • Scattering matrix

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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