On the Fast Direct Solution of a Preconditioned Electromagnetic Integral Equation

Davide Consoli (1) , Clément Henry (2, 3) , Alexandre Dély (1) , Lyes Rahmouni (1) , John Erik Ortiz Guzman (4) , Tiffany L. Chhim (1) , Simon B. Adrian (5) , Adrien Merlini (2, 3) , Francesco P. Andriulli (1)

1 Polito - Politecnico di Torino = Polytechnic of Turin
2 IMT Atlantique - MO - Département Micro-Ondes
3 Lab-STICC_PIM - Equipe PIM
4 Universidad de Nariño
5 Universität Rostock

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.

Mots clés: Integral equations; preconditioning; fast direct solvers

Domaines: Physique Numérique [physics.comp-ph]; Electromagnétisme

Davide Consoli, Clément Henry, Alexandre Dély, Lyes Rahmouni, John Erik Ortiz Guzman, et al.. On the Fast Direct Solution of a Preconditioned Electromagnetic Integral Equation. International Conference on Electromagnetics in Advanced Applications (ICEAA 2022), Sep 2022, Le Cap, South Africa. ⟨10.1109/ICEAA49419.2022.9899870⟩. ⟨hal-03762873⟩