Multilevel Preconditioning for Time-Harmonic Eddy-Current Problems Solved With Hierarchical Finite Elements

A multilevel preconditioner is described for high-order finite element analysis of eddy currents using the T-Ω formulation. The preconditioner combines p-type multiplicative Schwartz for the higher order degrees of freedom and auxiliary space preconditioning for the lowest order. Algebraic multigrid is applied to the first-order scalar spaces. The new preconditioner performs four times faster than a standard preconditioner on a test problem with 13.3 million unknowns.