Laplacian Filters for Integral Equations: Further Developments and Fast\n Algorithms

2022/03/01 by Adrien Merlini, Merlini, Adrien, Clément Henry +7
Engineering · Physics and Astronomy · #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Electrical engineering #Image and Video Processing (eess.IV) #Numerical methods in engineering #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.2203.08603

openalex publication_date 2022/03/01 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

This paper extends the concept of Laplacian filtered quasi-Helmholtz\ndecompositions we have recently introduced, to the basis-free projector-based\nsetting. This extension allows the discrete analyses of electromagnetic\nintegral operators spectra without passing via an explicit Loop-Star\ndecomposition as previously done. We also present a fast scheme for the\nevaluation of the filters in quasi linear complexity in the total number of\nunknowns. Together with the fact that only a logarithmic number of these\nfilters are required for solving the h-refinement breakdown of electric field\nintegral equation, this results in an effective preconditioner that rivals\nCalder 'on strategies in performance without relying on barycentric\nrefinements. Numerical results confirm the theoretically predicted behavior and\nthe effectiveness of the approach.\n

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