FEM modeling of axisymmetric cavities with divergence-free constraint equation and hierarchical basis functions

Development and implementation of efficient divergence-free constraint equation in the FEM modeling of axisymmetric cavities using hierarchical higher order vector/scalar basis functions is presented. In the FEM modeling of the Maxwell eigenvalue problem, non-physical modes with zero eigenvalues are present. Occurrence of such eigenmodes is eliminated by constraining the electric field solution to be divergence-free in a weak sense. Two different FEM implementations are considered. Discrete constraint equation is developed for both the implementations. Coupling of the constraint equation with Lanczos/Arnoldi method results in a solution free of non-physical zero eigenvalues. Convergence in solution is demonstrated for basis functions of orders up to p = 2, while the proposed technique can be extended to basis functions of arbitrary order.