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arXiv · 1204.3701

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

Oscar P. Bruno·Stephane K. Lintner
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Abstract

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 Calder\'on 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.

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Oscar P. Bruno, Stephane K. Lintner. 2012-04-17. Second-Kind integral solvers for TE and TM problems of diffraction by open-arcs. https://doi.org/10.1029/2012rs005035

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