We discuss the approximation of the eigensolutions associated with the Maxwell eigenvalue problem in the framework of least-squares finite elements. We write the Maxwell curl curl equation as a system of two first order equations and design a novel least-squares formulation whose minimum is attained at the solution of the system. The eigensolutions 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 that the method provides optimally convergent results when edge elements are used. It turns out that nodal elements can be successfully employed for the approximation of our problem also in the presence of singular solutions.

Approximation of the Maxwell eigenvalue problem in a least-squares setting

Gastaldi, L
2023-01-01

Abstract

We discuss the approximation of the eigensolutions associated with the Maxwell eigenvalue problem in the framework of least-squares finite elements. We write the Maxwell curl curl equation as a system of two first order equations and design a novel least-squares formulation whose minimum is attained at the solution of the system. The eigensolutions 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 that the method provides optimally convergent results when edge elements are used. It turns out that nodal elements can be successfully employed for the approximation of our problem also in the presence of singular solutions.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11379/589227
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact