Timestep Acceleration Of Waveform Relaxation

Dynamic iteration methods for treating linear systems of differential equations are considered. It is shown that the discretized Picard-Lindelof (waveform relaxation) iteration can be accelerated by solving the defect equations with a larger timestep, or by using a recursive procedure based on a succession of increasing timesteps. A discussion of convergence is presented, including analysis of a discrete smoothing property maintained by symmetric multistep methods. Numerical experiments with a linear wave equation indicate that the method can speed convergence