DTIC ADA489360: High Order Quadratures for the pdf

DTIC ADA489360: High Order Quadratures for the

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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

• Creator/s: Defense Technical Information Center
• Date: 4/22/2008
• Year: 2008
• Book Topics/Themes: DTIC Archive, Duan, Ran, YALE UNIV NEW HAVEN CT DEPT OF COMPUTER SCIENCE, *NUMERICAL QUADRATURE, LINEAR SYSTEMS, SCATTERING, PROBLEM SOLVING, HELMHOLTZ EQUATIONS, SPECIAL FUNCTIONS(MATHEMATICS), FORMULAS(MATHEMATICS), ALGORITHMS, EQUATIONS

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