Timestep Acceleration of Waveform Relaxation
Benedict Leimkuhler · SIAM Journal on Numerical Analysis · 1998
Dynamic iteration methods for treating certain classes of linear systems of differential equations are considered. It is shown that the discretized Picard--Lindelöf (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 applied to linear wave equations. Numerical experiments indicate that the method can speed convergence.