$\mathcal{H}$-matrix approximability of inverses of FEM matrices for the time-harmonic Maxwell equations

Abstract

The inverse of the stiffness matrix of the time-harmonic Maxwell equation with perfectly conducting boundary conditions is approximated in the blockwise low-rank format of $\mathcal{H}$-matrices. We prove that root exponential convergence in the block rank can be achieved if the block structure conforms to a standard admissibility criterion.