A stabilized multilevel vector finite-element solver for time-harmonic electromagnetic waves

An enhanced finite-element method (FEM) for the vector wave equation is presented. For improved speed and stability ranging from microwave frequencies down to the static limit, we propose a multilevel solver that uses a tree-gauged formulation on the coarsest mesh and a partially gauged scheme for the iterative cycle. Moreover, we have generalized the concept of hanging nodes to higher order H(curl)-conforming tetrahedral elements. The combination of hierarchical basis functions and the hanging variables framework yields great flexibility in placing degrees of freedom and provides a very attractive alternative to remeshing in an hp-adaptive context.