A TIME-PARALLEL MULTIGRID-EXTRAPOLATION METHOD FOR PARABOLIC PARTIAL-DIFFERENTIAL EQUATIONS

We consider the problem of solving unsteady partial differential equations on an MIMD machine. Conventional parallel methods use a data partitioning type approach in which the solution grid at each time-step is divided amongst the available processors. The sequential nature of the time integration is, however, retained. The algorithm presented in this paper makes use of a time-parallel approach, whereby several processors May be employed to solve at several time-steps simultaneously. The time-parallel method enables the inherent parallelism of the extrapolation scheme to be efficiently exploited, allowing a significant increase both in accuracy and in the degree of parallelism. The efficiencies obtained by an implementation on a message-passing multiprocessor demonstrate the suitability of the time-parallel extrapolation method for this type of equation.