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Numerical studies of time-independent and time-dependent scattering by several elliptical cylinders

Authors
Journal
Journal of Computational and Applied Mathematics
0377-0427
Publisher
Elsevier
Publication Date
Volume
204
Issue
2
Identifiers
DOI: 10.1016/j.cam.2006.01.041
Keywords
  • Elliptic Cylinders
  • Multiple Scattering
  • Elliptic Coordinates
  • Scalar Scattering Problems
  • Two-Dimensional Systems
Disciplines
  • Mathematics

Abstract

Abstract A numerical solution to the problem of time-dependent scattering by an array of elliptical cylinders with parallel axes is presented. The solution is an exact one, based on the separation-of-variables technique in the elliptical coordinate system, the addition theorem for Mathieu functions, and numerical integration. Time-independent solutions are described by a system of linear equations of infinite order which are truncated for numerical computations. Time-dependent solutions are obtained by numerical integration involving a large number of these solutions. First results of a software package generating these solutions are presented: wave propagation around three impenetrable elliptical scatterers. As far as we know, this method described has never been used for time-dependent multiple scattering.

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