Finite element methods with stable hybrid explicit-implicit time-integration schemes

Abstract

Finite element methods with stable hybrid explicit-implicit time-integration schemes are reviewed. In particular, constructions that reduce to the well-known finite-difference time-domain (FDTD) scheme on structured grids of cubes are considered. Unstructured tetrahedrons with implicit time-stepping are used in the vicinity of curved and complex boundaries. The tetrahedrons are connected to the FDTD cells either directly or by means of a layer of pyramids. The hybrid methods show second order convergence (when the field solution is regular) with respect to cell size, preserve the null-space of the curl-operator, do not suffer from spectral contamination, and provide stable-time stepping up to the Courant condition of the FDTD scheme without artificial damping.