On the Fast Direct Solution of a Preconditioned Electromagnetic Integral Equation

This work presents a fast direct solver strategy for electromagnetic integral equations in the high-frequency regime. The new scheme relies on a suitably preconditioned combined field formulation and results in a single skeleton form plus identity equation. This is obtained after a regularization of...

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Bibliographic Details
Published inarXiv.org
Main Authors Consoli, Davide, Clément, Henry, Dély, Alexandre, Rahmouni, Lyes, Ortiz Guzman, John Erik, Chhim, Tiffany L, Adrian, Simon B, Merlini, Adrien, Andriulli, Francesco P
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 04.04.2022
Subjects
Integral equations
Matrix algebra
Operators (mathematics)
Regularization
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Summary:This work presents a fast direct solver strategy for electromagnetic integral equations in the high-frequency regime. The new scheme relies on a suitably preconditioned combined field formulation and results in a single skeleton form plus identity equation. This is obtained after a regularization of the elliptic spectrum through the extraction of a suitably chosen equivalent circulant problem. The inverse of the system matrix is then obtained by leveraging the Woodbury matrix identity, the low-rank representation of the extracted part of the operator, and fast circulant algebra yielding a scheme with a favorable complexity and suitable for the solution of multiple right-hand sides. Theoretical considerations are accompanied by numerical results both of which are confirming and showing the practical relevance of the newly developed scheme.
ISSN:2331-8422