A variational approach to solve the axisymmetric Maxwell equations in a non convex geometry
We propose a new numerical method to solve the axisymmetric static Maxwell equations in singular domains, as for example non convex polygonal domains. We focus on the computation of the static magnetic field, and show that the key point to solve this problem is related to the solution of a Laplace-like operator in a singular domain. We then introduce a new approach, that consists in decomposing the domain into 2 subdomains, and to derive an ad hoc variational formulation, in which the interface conditions are imposed with a method deduced from a Nitsche approach. Numerical examples to illustrate our method will be shown.
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