Waveform Relaxation Methods for Initial Boundary Value Problems

Abstract

We comment on the use of waveform relaxation techniques for solving parabolic initial boundary value problems. It is illustrated that the Jacobi, Gauss-Seidel and SOR methods do not lead to satisfactory, rapidly convergent algorithms. A linear multigrid acceleration is presented, and illustrated by a numerical example. An analysis of the continuous-time and discrete-time variants is given. The method is extended to nonlinear problems and related to a multigrid method on a space-time grid.

In VLSI-simulation this type of approach, called waveform relaxation method, seems to result in considerable savings in computing time. It would not be surprising if an efficient implementation of the idea appeared also to applications outside circuit equations.

—U. Miekkala and O. Nevanlinna, in [84, 1987].