50 Years of Time Parallel Time Integration

50 Years of Time Parallel Time Integration

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 in 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
principle: the solution later in time is affected (it is even
determined) by the solution earlier in time, but not the other way
round. Algorithms trying to use the time direction for parallelization
must therefore be special, and take this very different property of
the time dimension into account.

I will show in this talk 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. I will show for each of these techniques the main
inventions over time by choosing specific publications and explaining
the core ideas of the authors. This talk is for people who want to
quickly gain an overview of the exciting and rapidly developing area
of research of time parallel methods.