Block Preconditioning Strategies for High Order Finite Element Discretization of the Time-Harmonic Maxwell Equations

We study block preconditioning strategies for the solution of large sparse complex coefficients linear systems resulting from the discretization of the time-harmonic Maxwell equations by a high order discontinuous finite element method formulated on unstructured simplicial meshes. The proposed strategies are based on principles from incomplete factorization methods. Moreover, a complex shift is applied to the diagonal entries of the underlying matrices, a technique that has recently been exploited successfully in similar contexts and in particular for the multigrid solution of the scalar Helmholtz equation. Numerical results are presented for 2D and 3D electromagnetic wave propagation problems in homogeneous and heterogeneous media.