Solving Numerically the Static Maxwell Equations in an Axisymmetric Singular Geometry

Abstract

We propose a new numerical method to compute the singular solution of the Maxwell equations in axisymmetric domains, as for example in non convex polygonal domains. As geometrical singularities are mainly related to the space dependent part of the model, we focus on the static field computation. We then introduce a new approach, that consists in decomposing the domain into two or more subdomains, and to derive an ad hoc variational formulation in each subdomain. The interface conditions are then imposed with a method deduced from a Nitsche method coupled with a specific “exchange” approach. An advantage of this domain decomposition method is that it does not require neither overlapping nor iteration process. Another advantage is that no particular mesh refinement is needed near the geometrical singularities. Numerical examples will be shown.

Keywords:

• Maxwell equations
• singular geometries
• Laplace operator
• Nitsche method
• domain decomposition

AMS Subject Classification:

• 65P25
• 77C10