On some Operator Filtering Strategies Based on Suitably Modified Green's Functions

Recent contributions showed the benefits of operator filtering for both preconditioning and fast solution strategies. While previous contributions leveraged laplacian-based filters, in this work we introduce and study a different approach leveraging the truncation of appropriately chosen spectral re...

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Bibliographic Details
Main Authors Masciocchi, Matteo E, Citraro, Ermanno, Dély, Alexandre, Rahmouni, Lyes, Merlini, Adrien, Andriulli, Francesco P
Format Journal Article
LanguageEnglish
Published 18.07.2023
Subjects
Computer Science - Numerical Analysis
Mathematics - Mathematical Physics
Mathematics - Numerical Analysis
Physics - Computational Physics
Physics - Mathematical Physics
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Summary:Recent contributions showed the benefits of operator filtering for both preconditioning and fast solution strategies. While previous contributions leveraged laplacian-based filters, in this work we introduce and study a different approach leveraging the truncation of appropriately chosen spectral representations of operators' kernels. In this contribution, the technique is applied to the operators of the 2D TE- and TM-electric field integral equations (EFIE). We explore two different spectral representations for the 2D Green's function that lead to two distinct types of filtering of the EFIE operators. Numerical results corroborate the effectiveness of the newly proposed approaches, also in the Calder\'on preconditioned EFIE
DOI:10.48550/arxiv.2307.09276