${\cal H}$-Matrix-Based Operator Preconditioning for Full Maxwell at Low Frequencies

A robust formulation for the computation of combined resistive, capacitive and inductive effects in time-harmonic low frequency applications has been introduced in . The Galerkin discretization with conforming finite elements leads to a sparse system matrix. Large jumps in the material coefficients may cause severe ill-conditioning of the matrix. In this paper, we investigate how
operator preconditioning
can be used to construct an efficient real-valued symmetric positive definite preconditioner for the iterative solution. This enables the use of a large number of unknowns for the simulation of intricate industrial devices. The approach can be treated with almost linear complexity by making use of
hierarchical matrices
.