Johannes Kepler Symposium für Mathematik

Im Rahmen des Johannes-Kepler-Symposiums für Mathematik wird Dr. Clemens Hofreither, Institute of Computational Mathematics, JKU Linz, am Mon, Nov. 18, 2019 um 17:15 Uhr im S2 416-2 einen öffentlichen Vortrag (mit anschließender Diskussion) zum Thema "Fast algorithms for tensor product discretizations in Isogeometric Analysis and beyond" halten, zu dem die Veranstalter des Symposiums,

O.Univ.-Prof. Dr. Ulrich Langer,
Univ.-Prof. Dr. Gerhard Larcher
A.Univ.-Prof. Dr. Jürgen Maaß, und
die ÖMG (Österreichische Mathematische Gesellschaft)

hiermit herzlich einladen.

Series B - Mathematical Colloquium:

The intention is to present new mathematical results for an audience interested in general mathematics.

Fast algorithms for tensor product discretizations in Isogeometric Analysis and beyond

In this talk, we consider discretizations of partial differential
equations which have an underlying tensor product structure (e.g., are
posed in a square or cube domain) and ask the question: how can we
exploit this underlying structure in order to obtain faster algorithms
for the generation and solution of the discretized problem?

Although this assumption of tensor product structure is quite strong,
there has recently been renewed interest in such algorithms due to the
rise of Isogeometric Analysis. This young competitor to the Finite
Element Method relies strongly on tensor product spline spaces and
allows the treatment of more complicated computational domains while
preserving the underlying tensor product structure of the discretization
space.

We will consider various problems, such as the fast formation of the
isogeometric stiffness matrices, the development of multigrid solvers
which are robust with respect to the spline degree, and the construction
of solvers which mitigate the exponential dependence on the space
dimension, where the tensor product structure can be exploited in order
to achieve significant speedups over classical techniques. In several
situations, methods of low-rank matrix and tensor approximation come
into play.

Although the focus of the talk is on applications in Isogeometric
Analysis, most of the developed techniques are rather general and can be
used for different discretization techniques. As a particularly timely
application, we will see some results for the solution of fractional
diffusion problems in general domains.