Laplacian Filtered Loop-Star Decompositions and Quasi-Helmholtz Filters: Definitions, Analysis, and Efficient Algorithms

Quasi-Helmholtz decompositions are fundamental tools in integral equation modeling of electromagnetic problems because of their ability of rescaling solenoidal and non-solenoidal components of solutions, operator matrices, and radiated fields. These tools are however incapable, per se , of modifying...

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Bibliographic Details
Published inIEEE transactions on antennas and propagation Vol. 71; no. 12; p. 1
Main Authors Merlini, Adrien, Henry, Clement, Consoli, Davide, Rahmouni, Lyes, Dely, Alexandre, Andriulli, Francesco P.
Format Journal Article
LanguageEnglish
Published New York IEEE 01.12.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Institute of Electrical and Electronics Engineers
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Summary:Quasi-Helmholtz decompositions are fundamental tools in integral equation modeling of electromagnetic problems because of their ability of rescaling solenoidal and non-solenoidal components of solutions, operator matrices, and radiated fields. These tools are however incapable, per se , of modifying the refinement-dependent spectral behavior of the different operators and often need to be combined with other preconditioning strategies. This paper introduces the new concept of filtered quasi-Helmholtz decompositions proposing them in two incarnations: the filtered Loop-Star functions and the quasi-Helmholtz filters. Because they are capable of manipulating large parts of the operators' spectra, new families of preconditioners and fast solvers can be derived from these new tools. A first application to the case of the frequency and h -refinement preconditioning of the electric field integral equation is presented together with numerical results showing the practical effectiveness of the newly proposed decompositions.
ISSN:0018-926X
1558-2221
DOI:10.1109/TAP.2023.3283043