Seminar in Numerical Analysis: Peter Zaspel (Universität Heidelberg / HITS)
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.
Veranstaltung übernehmen als iCal