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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Published in | arXiv.org |
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Main Authors | , , , , , , , , |
Format | Paper |
Language | English |
Published |
Ithaca
Cornell University Library, arXiv.org
04.04.2022
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Subjects | |
Online Access | Get full text |
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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. |
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ISSN: | 2331-8422 |