On the Fast Direct Solution of a Preconditioned Electromagnetic Integral Equation
Abstract
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.
Cite
@article{arxiv.2203.13283,
title = {On the Fast Direct Solution of a Preconditioned Electromagnetic Integral Equation},
author = {Davide Consoli and Clément Henry and Alexandre Dély and Lyes Rahmouni and John Erik Ortiz Guzman and Tiffany L. Chhim and Simon B. Adrian and Adrien Merlini and Francesco P. Andriulli},
journal= {arXiv preprint arXiv:2203.13283},
year = {2022}
}