Vorträge

Parareal is the most studied Parallel-in-Time method; by introducing parallelism in the time dimension, it allows to relieve communication bottlenecks that appear when parallelism is used only in the spatial dimension.
An expensive part of Parareal is the sequential solve using the coarse operator. So, for performance reasons, it can be interesting to consider the sequential operator not only on a coarser grid in time but also in space.
In this talk, we will discuss an alternative approach to the Generating Function Method (GFM) for computing Parareal bounds and how it can be used to compute linear and superlinear bounds.
We will then extend the analysis to Parareal with spatial-coarsening (coarsening factor 2 in space and time) and discuss the associated challenges. Finally, numerical results for the heat equation will be provided.

Zoomlink:
https://tuhh.zoom.us/j/81920578609?pwd=TjBmYldRdXVDT1VkamZmc1BOajREZz09

We present some recent developments for the numerical simulation of
transport-dominated problems such as compressible fluid flows and
nonlinear dispersive wave equations. We begin with a brief review
of modern entropy-stable semidiscretizations of hyperbolic conservation
laws and use the method of lines to obtain efficient, fully discrete
numerical methods. Next, we introduce means to preserve the entropy
structures also under time discretization. Therefore, we present the
relaxation approach, a recent technique developed as small modifications
of standard time integration schemes such as Runge-Kutta or linear
multistep methods, which is designed to preserve the conservation or
dissipation of important functionals of the solution. This can be an
entropy in the case of compressible fluid flows, the energy of
Hamiltonian problems, or another nonlinear invariant.

We applied the Parallel-In-Time algorithm Parareal to the ocean-circulation model FESOM2 to demonstrate its applicability to complex problems in climate research. The talk is intended to give an overview of the technical challenges that can be expected when attempting to parallelize state-of-the-art simulation software in time. With the convergence results presented the talk concludes with a discussion of whether and how an efficient application of Parareal could be achieved.