Projects

Ziel des Projekts ist es, die Zeitreihen von
Erdbeobachtungs(EO)-Daten mit innovativen Methoden des „Deep Learnings“
zu analysieren, um effiziente Algorithmen zur Bewältigung der großen
Datenmengen zu entwickeln. Der Wert dieser EO-Produkte wird durch
fortgeschrittene Interpolationstechniken und Assimilation in
geophysikalische Modelle, die es in der angewandten Mathematik gibt,
weiter erhöht.

The Message Passing Interface\cite{mpi-standard} (MPI) is the de facto
standard for distributed programming on all modern compute clusters and
supercomputers. It features a large number of communication patterns with
virtually no overhead. Our work on bringing MPI functionality to Common
Lisp resulted in vast improvements to the message passing library CL-MPI
and the development of severaly new approaches to distributed computing.
 

We optimized and parallelized a framework which compiles stencil operations defined by abstract operators into code, which performs the corresponding stencil update. Therefore, we are now able to formulate solvers for a large number of application problems (flow simulation, image analysis, ...) in an abstract way, and then solve efficiently on structured meshes.

The fundamental problems in the numerical approximation of multiphase systems, or more generally speaking, in the treatment of flows with capillary free boundaries are the representation of the free surface, evaluating the curvature, handling of discontinuities, most importantly the pressure jump, and time discretization strategies for the decoupling of flow computation and geometry. While for the first three items there exists a vast literature and many techniques developed over the last two decades, the last problem of how to efficiently treat the time discretization has been widely ignored. The majority of the existing approaches just decouple the flow field from the geometry by a simple segregated approach, i.e. evaluating the geometric quantities from the previous time step. These strategy leads to a) a severe capillary CFL condition and b) is of first order in time at most. Existing semi-implicit discretizations exist that overcome problem a), but are still first order only and rather dissipative in certain situations. Thus this project aims at developing, implementing, and analysing time discretizations of higher order that are unconditionally stable and minimally dissipative, thus allowing for rather large time steps. To solve the arising systems, which will necessarily comprise a coupling between flow field and geometry, efficient solution techniques will be developed.