Multigrid Waveform Relaxation on Spatial Finite Element Meshes: The Discrete-Time Case

The e ciency of numerically solving time-dependent partial di erential equations on parallel computers can be greatly improved by computing the solution on many time-levels simultaneously. The theoretical properties of one such method, namely the discrete-time multigrid waveform relaxation method, are investigated for systems of ordinary di erential equations obtained by spatial nite element discretisation of linear parabolic initial boundary value problems. The results are compared to the corresponding continuous-time results. The theory is illustrated for a one-dimensional and a two-dimensional model problem and checked against results obtained by numerical experiments.