Extended krylov subspace methods for transient wavefield problems

We present an extended Krylov subspace method to solve multiscale transient electromagnetic wavefield problems. A basis of an extended Krylov subspace is generated by iterating with the system matrix and its inverse. We show that such a basis can be computed very efficiently via three-term recurrence and CG-type updating formulas by exploiting specific symmetry properties of the system matrix, which are related to energy conservation and reciprocity. Multiscale transmission line and full electromagnetic wavefield problems are considered, and numerical experiments illustrate the performance of the method.