High-Order Quadratures for the Solution of Scattering Problems in Two Dimensions

Abstract

We construct an iterative algorithm for the solution of forward scattering problems in two dimensions. The scheme is based on the combination of high-order quadrature formulae, fast application of integral operators in Lippmann-Schwinger equations, and the stabilized biconjugate gradient method (BI-CGSTAB). While the FFT-based fast application of integral operators and the BI-CGSTAB for the solution of linear systems are fairly standard, a large part of this paper is devoted to constructing a class of high-order quadrature formulae applicable to a wide range of singular functions in two and three dimensions; these are used to obtain rapidly convergent discretizations of Lippmann-Schwinger equations. The performance of the algorithm is illustrated with several numerical examples.

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Document Details

Document Type
Technical Report
Publication Date
Apr 22, 2008
Accession Number
ADA489360

Entities

People

  • Ran Duan
  • Vladimir Rokhlin, Jr.

Organizations

  • Yale University

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Complex Numbers
  • Differential Equations
  • Equations
  • Forward Scattering
  • Frequency Domain
  • Helmholtz Equations
  • Integral Equations
  • Integrals
  • Linear Systems
  • Numbers
  • Partial Differential Equations
  • Real Numbers
  • Scattering
  • Standards
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Computational Fluid Dynamics (CFD)
  • Linear Algebra
  • Radio communications and signal processing.