Iterative solvers for hierarchal vector finite element analysis of microwave problems

The finite element analysis of microwave devices reduces to the solution of a large, sparse matrix equation. Several iterative solution methods were tested on the matrices arising when high-order, hierarchical edge elements are used. The best algorithm tested was the conjugate gradient method, with a preconditioner based on symmetric successive overrelaxation. The number of iterations needed was found to increase only slowly with element order for the first three orders, despite the corresponding large increase in the matrix dimension. In all cases there was a rapid deterioration in performance when the element size exceeded about a tenth of a wavelength.