Speaker
Description
Space-time parallel methods, also known more recently under the name
PinT methods, have received a lot of attention over the past two
decades, driven by the parallel hardware architectures that have now
millions of cores, and acceleration often saturates when one
parallelizes in space only. Research focus has therefore shifted to
trying to parallelize also the time direction. However, for
parallelization, time is very different from space, because evolution
problems satisfy a causality principle: the future is dependent on the
past, and not the other way round. It is therefore not clear a priori
if useful numerical work can be done simultaneously in the near and
far future.
I will first show in my presentation why intuitively there is a
fundamental difference when one parallelizes hyperbolic or parabolic
problems in space-time, and which key properties need to be taken into
account to be successful. I will then give examples of PinT methods
which use the physical properties of the evolution problem to their
advantage to parallelize in space-time. For hyperbolic problems,
effective PinT methods are Domain Decomposition methods of Waveform
Relaxation type, culminating in Unmapped Tent Pitching methods. Very
powerfull techniques are also the ParaDiag methods, and direct
time parallel methods like ParaExp. Several of these methods can also
be very effectively used for parabolic problems, but for such problems
there are also very successful multilevel methods, like Parareal, and
the currently best ones are space-time multigrid methods. These
multilevel methods struggle however when applied to hyperbolic problems.
