Martin Gander, Mathematics, University of Geneva Title. Time Parallel Time Integration:  When and how one can predict the far and near future simultaneously

Abstract. I will start my presentation by explaining the causality principle for
initial value problems, which seems to indicate that one can not
predict the far and near future simultaneously. Historically,
nevertheless, many researchers have tried to develop methods to do so,
and I will explain that for certain type of problems this seems more
promising than for others, and this in spite of the causality
principle.  I will then show the four main classes of such time
parallel methods, and one specific method in each: multiple shooting
type methods for initial value problems leading to Parareal, waveform
relaxation methods based on domain decomposition leading to Schwarz
waveform relaxation, multigrid methods leading to a highly scalable
space-time multigrid (STMG) method, and also direct space-time
parallel methods including ParaExp and ParaDiag.