On Krylov Subspace Implementation of ParaExp for Linear Switched Systems

A direct time-parallel time domain simulation algorithm based on ParaExp with Krylov subspace implementation for the large-scale linear switched systems (LSSs) is studied in this paper. It is built upon the superposition principle that the LSSs can be decoupled into independent subsystems consisting of homogeneous and inhomogeneous subproblems. The states of these independent subsystems are approximated by the residual-based shift-and-invert (SAI) Krylov subspace methods, and this time-parallel algorithm can thus be regarded as a parallel Krylov subspace approximation algorithm for LSSs. We demonstrate the efficiency of the proposed algorithm with numerical experiments.