Accelerating Dynamic Iteration Methods With Application To Parallel Semiconductor Device Simulation

. In this paper we apply a Galerkin method to solving the system of second-kind Volterra integral equations that characterize waveform relaxation, or dynamic iteration, methods for solving linear time-varying initial-value problems. It is shown that the Galerkin approximations can be computed iteratively using Krylovsubspace algorithms. The resulting iterative methods are combined with an operator Newton method and applied to solving the nonlinear differential-algebraic system generated by spatial discretization of the time-dependent semiconductor device equations. Experimental results are included to demonstrate that waveform Krylov-subspace methods converge significantly faster than classical waveform relaxation, and are better able to exploit the parallelism available in loosely coupled parallel machines than parallel versions of standard point-wise iterative schemes. Key words. Krylov-subspace methods, dynamic iteration, Galerkin method, waveform relaxation. AMS subject classific..