Proceedings chapter
Open access

50 Years of Time Parallel Time Integration

Published inMultiple Shooting and Time Domain Decomposition Methods, Editors Carraro, Thomas ; Geiger, Michael ; Körkel, Stefan & Rannacher, Rolf, p. 69-113
Presented at MuS-TDD, Heidelberg, May 6-8, 2013
PublisherCham : Springer
  • Contributions in Mathematical and Computational Sciences; 9
Publication date2015

Time parallel time integration methods have received renewed interest over the last decade because of the advent of massively parallel computers, which is mainly due to the clock speed limit reached on today's processors. When solving time dependent partial differential equations, the time direction is usually not used for parallelization. But when parallelization is space saturates, the time direction offers itself as a further direction for parallelization. The time direction is however special, and for evolution problems there is a causality principale : the solution later in time is affected (it is even determined) by the solution earlier in time, but not the other way round. Algorithm strying to use the time direction for parallelization must therefore be special, and take this very different property of the time dimension into account. We show in this chapter how time domain decomposition methods were invented, and give an overview of the existing techniques. Time parallel methods can be classified into four different groups: methods based on multiple shooting, methods based on domain decomposition and waveform relaxation, space-time multigrid methods and direct time parallel methods. We show for each of these techniques the main inventions over time by choosing specific publications and explaining the core ideas of the authors. This chapter is for people who want to quickly gain an overview of the exciting and rapidly developing are of research of time parallel methods.

Citation (ISO format)
GANDER, Martin Jakob. 50 Years of Time Parallel Time Integration. In: Multiple Shooting and Time Domain Decomposition Methods. Heidelberg. Cham : Springer, 2015. p. 69–113. (Contributions in Mathematical and Computational Sciences) doi: 10.1007/978-3-319-23321-5_3
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