Robust finite element modeling of electromagnetic interactions in complex structures via multigrid and multilevel preconditioning

The paper discusses the application of multigrid and multilevel preconditioners for improving the convergence of iterative finite element solvers used for the modeling of electromagnetic wave interactions in structures exhibiting large electrical and/or high geometric and material complexity. The applications considered include both modeling of electromagnetic wave scattering from three-dimensional targets and modeling of reflection and transmission properties of waveguiding structures and related passive components, used in high-frequency/high-speed integrated circuit design. These two classes of problems help contrast the attributes of the multigrid and multilevel processes in the context of improving iterative finite element solution efficiency and accuracy. Furthermore, they suggest possible hybridizations of the two processes, aimed at the robust and accurate solution of complicated electromagnetic problems where improved accuracy requires the utilization of both grid refinement and high-order element interpolation.