Ing. Jakub Šístek, Ph.D.

Ing. Jakub Šístek, Ph.D.

Ing. Karel Klouda, Ph.D.

Department of Applied Mathematics

The aim of this thesis is to present the blocked algorithm for finding a Cholesky decomposition of a symmetric positive definite matrix and to provide an implementation of the algorithm using the StarPU and OpenMP task-based runtime systems. The implementation is tested using test routines from the LAPACK library and its performance is compared to several available libraries for numerical linear algebra on three different compute nodes. On all three of them, the implementation delivers a competitive performance, especially for larger matrices. In the theoretical part of the thesis, custom proofs of correctness are formulated for both the blocked and the unblocked algorithms for Cholesky decomposition. The rest of the thesis explores matrix storage schemes, the BLAS interface and basic concepts of task-based programming.

Thesis on DSpace

Ing. Jakub Šístek, Ph.D.

Mgr. Petr Šimánek

Department of Applied Mathematics

The result of this work is a model that can quickly and accurately compute residual vorticity magnitude. In this thesis an introduction to vortex identification in flow fields is provided. The Triple decomposition method is presented in detail. This method is excellent at accurately decomposing motion in a fluid into three components -- rotation, strain, and shear. Its downside is that it is time-consuming, since it does not have an analytical representation for 3D flows, which leads to using a grid search. To speed up this method, an attempt is made to predict residual vorticity magnitude using a neural network. Data preparation and the training of a neural network are described.

Thesis on DSpace