A time-parallel multigrid-extrapolation method for parabolic partial differential equations. (English) Zbl 0746.65073
Authors’ summary: 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 amongs the available processors. The sequential natur 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 multi-processor demonstrate the suitability of the time-parallel extrapolation method for this type of equation.
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 multi-processor demonstrate the suitability of the time-parallel extrapolation method for this type of equation.
Reviewer: S.F.McCormick (Denver)
MSC:
65M55 | Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs |
65M20 | Method of lines for initial value and initial-boundary value problems involving PDEs |
65Y05 | Parallel numerical computation |
35K15 | Initial value problems for second-order parabolic equations |