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Approximation of the Maxwell eigenvalue problem in a Least-Squares setting

Year: 2023

Type: preprint

Abstract: We discuss the approximation of the eigensolutions associated with the Maxwell eigenvalues problem in the framework of least-squares finite elements. We write the Maxwell curl curl equation as a system of two first order equation and design a novel least-squares formulation whose minimum is attained at the solution of the system. The eigensolution are then approximated by considering the eigenmodes of the underlying solution operator. We study the convergence of the finite element approximation and we show several numerical tests confirming the good behavior of the method. It turns out that nodal elements can be successfully employed for the approximation of our problem also in presence of singular solutions.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2305.08996

Authors: Bertrand, Fleurianne, Boffi, Daniele, Gastaldi, Lucia

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Ministero dell’Istruzione, dell’Università e della Ricerca, Gruppo Nazionale per il Calcolo Scientifico

OpenAlex ID: W4376988533

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