A Krylov-Subspace-Based Exponential Time Integration Scheme for Discontinuous Galerkin Time-Domain Methods

Abstract

Discontinuous Galerkin time-domain (DGTD) methods using explicit time integration schemes often suffer from unreasonably small time-step size when applied to simulations involving electrically small structures. In this paper, an exponential time integration (ETI) scheme based on Krylov subspace is proposed for DGTD. The proposed scheme is unconditionally stable and exhibits good accuracy for large time-step sizes. When compared with classic ETI schemes, in the proposed scheme, the dense matrix exponentials are absorbed in matrix–vector products, hence the prohibitive memory costs are avoided. Moreover, a preconditioner combining the shift-and-invert technique and restricted additive Schwarz method is also developed to accelerate the proposed scheme.