Kolloquiumsvortrag, Dr. Peter Zaspel, Universität Heidelberg / am 09.12.2016

09.12.2016 von 14:15 bis 15:45

Institut für Informatik, Ludewig-Meyn-Straße 2, 24118 Kiel, Raum: Übungsraum 2/K

Titel: H-matrices on many-core hardware with applications in parametric PDEs


Hierarchical matrices approximate specific types of dense matrices,
e.g., from discretized integral equations, kernel-based approximation
and Gaussian process regression, leading to log-linear time complexity
in dense matrix-vector products. To be able to solve large-scale
applications, H-matrix algorithms have to be parallelized. A special
kind of parallel hardware are many-core processors, e.g. graphics
processing units (GPUs). The parallelization of H-matrices on many-core
processors is difficult due to the complex nature of the underlying
algorithms that need to be mapped to rather simple parallel operations.

We are interested to use these many-core processors for the full
H-matrix construction and application process. A motivation for this
interest lies in the well-known claim that future standard processors
will evolve towards many-core hardware, anyway. In order to be prepared
for this development, we want to discuss many-core parallel formulations
of classical H-matrix algorithms and adaptive cross approximations.

In the presentation, the use of H-matrices is motivated by the model
application of kernel-based approximation for the solution of parametric
PDEs, e.g. PDEs with stochastic coefficients. The main part of the talk
will be dedicated to the challenges of H-matrix parallelizations on
many-core hardware with the specific model hardware of GPUs. We propose
a set of parallelization strategies which overcome most of these
challenges. Benchmarks of our implementation are used to explain the
effect of different parallel formulations of the algorithms.

Prof. Steffen Börm

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