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Solving electromagnetic eigenvalue problems in polyhedral domains with nodal finite elements. (English) Zbl 1180.78048
This paper deals with the numerical analysis of a class of time-harmonic Maxwell equations in $3D$ polyhedral domains. The main contribution in this study is that the authors propose a constrained formulation which is obtained by adding a constraint on the divergence of the field. In the first part of the paper the authors recall the time-harmonic Maxwell equations, which are expressed as a set of second-order partial differential equations. Next, it is introduced the functional framework and it is developed the continuous variational formulation of the problem. The authors also prove the convergence of the discretized eigenmodes towards the exact eigenmodes. In the last section of the paper there are proposed some numerical examples to illustrate the behavior of the method.

78M10Finite element methods (optics)
35Q60PDEs in connection with optics and electromagnetic theory
65N25Numerical methods for eigenvalue problems (BVP of PDE)
Full Text: DOI
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