Nested multigrid finite element method for rapid simulation of microwave devices

The vector-scalar potential formulation of the weak statement of the electrodynamic boundary value problem is combined with a multigrid scheme to develop a robust preconditioning technique for the fast finite element solution of electromagnetic devices. It is shown that for the multigrid process to converge the resolution on the coarsest grid needs to be of the order of three to four elements per minimum wavelength. Numerical experiments from the application of the new preconditioned iterative finite element solver to the analysis of microwave passive structures are used to validate its accuracy and demonstrate its superior numerical convergence and efficient memory usage