A nested Schur complement solver with mesh-independent convergence for the time domain photonics modeling

Abstract

A nested Schur complement solver is proposed for iterative solution of linear systems arising in exponential and implicit time integration of the Maxwell equations with perfectly matched layer (PML) nonreflecting boundary conditions. These linear systems are the so-called double saddle point systems whose structure is handled by the Schur complement solver in a nested, two-level fashion. The solver is demonstrated to have a mesh-independent convergence at the outer level, whereas the inner level system is of elliptic type and thus can be treated efficiently by a variety of solvers. Keywords: Maxwell equations, perfectly matched layer (PML) nonreflecting boundary conditions, double saddle point systems, Schur complement preconditioners, exponential time integration, shift-and-invert Krylov subspace methods 2010 MSC: 65F08, 65N22, 65L05, 35Q61 Email address: botchev@ya.ru (M.A. Botchev)