Fast high-order FEM solutions of dielectric wave guiding structures

Dielectric wave guiding structures are solved in terms of high-order hierarchal vector bases that provide maximum mutual orthogonality in both the approximation space and in the range space of the curl operator. This new finite element formulation results in well-conditioned matrices and makes the iterative solution of the system equation robust. Numerical examples show that p-refinement yields much higher rates of convergence than h-refinement when the resultant matrix is solved using the multilevel preconditioned conjugate gradient (MPCG) algorithm.