Parallel Numerical Solution of the Time-Harmonic Maxwell Equations

We develop a parallel implementation of a scalable numerical solution to linear systems arising from finite element discretization of the mixed formulation of the time-harmonic Maxwell equations. We apply this method to complicated domains. Our approach is based on a recently proposed diagonal preconditioner, an algebraic multigrid method and a new auxiliary space preconditioning technique. Numerical experiments demonstrate the scalability of our implementation.