Second-Kind integral solvers for TE and TM problems of diffraction by open-arcs

We present a novel approach for the numerical solution of problems of diffraction by open arcs in two dimensional space. Our methodology relies on composition of {\em weighted versions} of the classical integral operators associated with the Dirichlet and Neumann problems (TE and TM polarizations, r...

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Bibliographic Details
Published in:arXiv.org 2012-04
Main Authors: Bruno, Oscar P, Lintner, Stephane K
Format: Article
Language:English
Subjects:
Diffraction
Dirichlet problem
Formulations
Integrals
Linear algebra
Operators (mathematics)
Solvers
Online Access:Get full text
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Summary:We present a novel approach for the numerical solution of problems of diffraction by open arcs in two dimensional space. Our methodology relies on composition of {\em weighted versions} of the classical integral operators associated with the Dirichlet and Neumann problems (TE and TM polarizations, respectively) together with a generalization to the open-arc case of the well known closed-surface Calderón formulae. When used in conjunction with spectrally accurate discretization rules and Krylov-subspace linear algebra solvers such as GMRES, the new second-kind TE and TM formulations for open arcs produce results of high accuracy in small numbers of iterations and short computing times---for low and high frequencies alike.
ISSN:2331-8422
DOI:10.48550/arxiv.1204.3701