Original article

Numerische Mathematik

, Volume 86, Issue 4, pp 733-752

First online:

Overlapping Schwarz methods for Maxwell's equations in three dimensions

  • Andrea ToselliAffiliated withCourant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY 10012, USA, e-mail: toselli@cims.nyu.edu; URL: http://www.math.nyu.edu/~toselli/

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A two-level overlapping Schwarz method is considered for a Nédélec finite element approximation of 3D Maxwell's equations. For a fixed relative overlap, the condition number of the method is bounded, independently of the mesh size of the triangulation and the number of subregions. Our results are obtained with the assumption that the coarse triangulation is quasi-uniform and, for the Dirichlet problem, that the domain is convex. Our work generalizes well–known results for conforming finite elements for second order elliptic scalar equations. Numerical results for one and two-level algorithms are also presented.

Mathematics Subject Classification (1991): 65N22, 65N30, 65N55