# 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.