Parallel Time Integration with Multigrid

We consider optimal-scaling multigrid solvers for the linear systems that arise from the discretization of problems with evolutionary behavior. Typically, solution algorithms for evolution equations are based on a time-marching approach, solving sequentially for one time step after the other. Parall...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:SIAM journal on scientific computing Ročník 36; číslo 6; s. C635 - C661
Hlavní autoři: Falgout, R. D., Friedhoff, S., Kolev, Tz. V., MacLachlan, S. P., Schroder, J. B.
Médium: Journal Article
Jazyk:angličtina
Vydáno: 01.01.2014
Témata:
Algorithms
Discretization
Evolutionary
Mathematical analysis
Mathematical models
Processors
Reduction
Time marching
ISSN:1064-8275, 1095-7197
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Popis
Shrnutí:We consider optimal-scaling multigrid solvers for the linear systems that arise from the discretization of problems with evolutionary behavior. Typically, solution algorithms for evolution equations are based on a time-marching approach, solving sequentially for one time step after the other. Parallelism in these traditional time-integration techniques is limited to spatial parallelism. However, current trends in computer architectures are leading toward systems with more, but not faster, processors. Therefore, faster compute speeds must come from greater parallelism. One approach to achieving parallelism in time is with multigrid, but extending classical multigrid methods for elliptic operators to this setting is not straightforward. In this paper, we present a nonintrusive, optimal-scaling time-parallel method based on multigrid reduction (MGR). We demonstrate optimality of our multigrid-reduction-in-time algorithm (MGRIT) for solving diffusion equations in two and three space dimensions in numerical experiments. Furthermore, through both parallel performance models and actual parallel numerical results, we show that we can achieve significant speedup in comparison to sequential time marching on modern architectures.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:1064-8275
1095-7197
DOI:10.1137/130944230