Solving electromagnetic eigenvalue problems in polyhedral domains with nodal finite elements

摘要

A few years ago, Costabel and Dauge proposed a variational setting, which allows one to solve numerically the time-harmonic Maxwell equations in 3D polyhedral geometries, with the help of a continuous approximation of the electromagnetic field. In order to remove spurious eigenmodes, their method required a parameterization of the variational formulation. In order to avoid this difficulty, we use a mixed variational setting instead of the parameterization, which allows us to handle the divergence-free constraint on the field in a straightforward manner. The numerical analysis of the method is carried out, and numerical examples are provided to show the efficiency of our approach. Mathematics Subject Classification (2000) 35Q60 (PDEs, Eqs of EM theory and optics) - 65N25 (Numerical analysis, eigenvalue problems) - 78M10 (Optics & EM theory, finite element methods)