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Laplacian Filtered Loop-Star Decompositions and Quasi-Helmholtz Laplacian Filters: Definitions, Analysis, and Efficient Algorithms by Merlini, Adrien; Henry, Clément; Consoli, Davide; Rahmouni, Lyes; Dély, Alexandre; Andriulli, Francesco P. is a scholarly article available to read on EtoBox.

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

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 Laplacian 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.

Author

Merlini, Adrien; Henry, Clément; Consoli, Davide; Rahmouni, Lyes; Dély, Alexandre; Andriulli, Francesco P.

Published

2022

Language

EN