Jacobi-Davidson-type algorithms with interior multigrid-scheme for the simulation of electromagnetic resonator structures with gyromagnetic materials

Summary form only given. In some electromagnetic resonators applications, ferrite materials are used for the purpose of frequency tuning. Such gyromagnetic material properties are mathematically described with the complex-valued Polder tensor, which is non-diagonal and non-symmetric. The eigenvalue problem for the resonant fields of such structures can be discretized with the finite integration technique (FIT) (Weiland, T., Int. J. Num. Modelling, vol.9, p.295-319,1996), a technique closely related to that of lowest order Whitney finite elements (WFEM), to yield an algebraic eigenvalue problem. The Jacobi-Davidson (JD) subspace iteration algorithm is used for the calculation of the nonzero eigenpairs with smallest real part of the non-symmetric and complex-valued system matrix. This yields an eigenvalue problem of considerably smaller dimensions. The search space is augmented with the solutions of a correction equation (CE) in each step. A recently developed geometric multigrid (MG) scheme, which relies on the separation of grid incidence and material matrices within the FIT (and certain WFEM) formulations, is found to achieve an improved asymptotical complexity required for large 3D simulations. A resonator test structure with a ferrite material insert is analyzed using the system matrix in a simplified CE.