Overlapping Schwarz Preconditioning for High Order Edge Finite Elements: Application to the Time-Harmonic Maxwell's Equations

Marcella Bonazzoli (1) , Victorita Dolean (1, 2) , Frédéric Hecht (3) , Francesca Rapetti (1)

1 LJAD - Laboratoire Jean Alexandre Dieudonné
2 Department of Mathematics and Statistics [Univ Strathclyde]
3 LJLL - Laboratoire Jacques-Louis Lions

Developing high-speed microwave field measurement systems for wireless, medical or engineering industries is a challenging task. These systems generally rely on high frequency (from 1 to 60GHz) electromagnetic wave propagation in waveguides. High order discretizations of PDEs are well suited for wave propagation since they can provide a highly accurate solution with very low dispersion and dissipation errors. However, the resulting algebraic linear systems can be ill conditioned, so that preconditioning becomes mandatory. In this work, suitable domain decomposition preconditioners for the solution of linear systems resulting from high order edge element discretizations of the time-harmonic Maxwell's equations are described, and validated numerically on 2d and 3d waveguide configurations. The implementation issue of high order edge elements is also discussed in detail.

Mots clés: High order finite elements; edge elements; Schwarz preconditioners; time-harmonic Maxwell's equations

Domaines: Analyse numérique [math.NA]

Marcella Bonazzoli, Victorita Dolean, Frédéric Hecht, Francesca Rapetti. Overlapping Schwarz Preconditioning for High Order Edge Finite Elements: Application to the Time-Harmonic Maxwell's Equations. 2016. ⟨hal-01298938v1⟩