High-order solutions of three-dimensional rough-surface scattering problems at high frequencies. I: The scalar case

F. Reitich, C. Turc

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We present a new high-order numerical method for the solution of high-frequency scattering problems from rough surfaces in three dimensions. The method is based on the asymptotic solution of appropriate integral equations in the high-frequency regime, in a manner that bypasses the need to resolve the fields on the scale of the wavelength of radiation. Indeed, inspired by prior work in two dimensions, we seek a solution of the integral equation in the form of a slow modulation of the incoming radiation, and we choose a series expansion in inverse powers of the wavenumber to represent the unknown slowly varying envelope. As we show, this framework can be made to yield an efficiently computable recursion for the terms in the series to any arbitrary order. The resulting algorithms generally provide a very significant improvement over classical (e.g. Kirchhoff) approximations in both accuracy and applicability and they can, in fact, effectively produce results with full double-precision accuracy for configurations of practical interest and up to the resonance regime.

Original languageEnglish (US)
Pages (from-to)1-16
Number of pages16
JournalWaves in Random and Complex Media
Volume15
Issue number1
DOIs
StatePublished - Feb 2005
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Engineering
  • General Physics and Astronomy

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