Parallel Matrix Computations - NMNV532
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The goal of this course is to introduce parallel processing of basic computational cores that can be
encountered in mathematical modeling as well as in scientific computing in general. These cores
include, for example, basic operations with dense and sparse matrices and preconditioning of
Krylov space methods. The course includes also elementary introduction into multigrid and domain
decomposition methods.
Last update: T_KNM (07.04.2015)
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The main goal of the course is to understand basic ideas related to computational tools on contemporary and inevitably parallel computer architectures. The focus is to discuss what should a computational mathematician consider to get basic computational schemes efficient in parallel computational environment. The goal is also to learn basic practical experience with parallel matrix computations on unix-like systems using Python.
Last update: Tůma Miroslav, prof. Ing., CSc. (22.02.2018)
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Needed to get credits:
• students will independently prepare a parallel program based on theoretical examples discussed during lectures. The lectures can be also online having a distant form.
Last update: Tůma Miroslav, prof. Ing., CSc. (02.09.2026)
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M. Tůma: Parallel matrix computations, 2018, http:://www.karlin.mff.cuni.cz/~mirektuma/ps/pp.pdf
Other resources: A.Grama, G. Karypis, V. Kumar, A. Gupta. Introduction to Parallel Computing, 2nd edition, Addison Wesley, 2003.
J. Dongarra, I.S. Duff, D. Sorensen, H. A. van der Vorst. Solving Linear Systems on Vector and Shared Memory Computers, SIAM, 1991.
A. Toselli, O. Widlund. Domain Decomposition Methods - Algorithms and Theory. Springer Series in Computational Mathematics, Vol. 34, 2005
M. Heath, E. Ng, B. W. Peyton, Parallel Algorithms for Sparse Linear Systems, SIAM Review 33(1991), 420-460.
B. Smith, P. Bjorstad, W. Gropp. Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations, Cambridge University Press 2004
W.L. Briggs, van Emden Henson, S.F. Cormick. A Multigrid Tutorial, SIAM, 2000.
Y. Saad, Iterative Methods for Sparse Linear Systems, 2nd edition, SIAM, Philadelphia, 2003. Last update: Kučera Václav, doc. RNDr., Ph.D. (15.01.2019)
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Lectures and tutorials in a lecture hall. A possible variant it to use an online distant lectures and tutorials. Last update: Tůma Miroslav, prof. Ing., CSc. (28.04.2020)
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Examination according to the syllabus.
• students will be asked one thematically general question • students will have enough time to prepare their answer • examinor can pose subquestion related to the main question • all of this can be replaced by an online distant examination Last update: Tůma Miroslav, prof. Ing., CSc. (28.04.2020)
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1. Computational models for parallel architectures.
2. Basic parallel operations with dense and sparse matrices.
3. Preconditioning and preconditioned Krylov space methods.
4. Domain decomposition and multigrid methods.
5. Parallelization of direct methods for sparse matrices. Last update: T_KNM (07.04.2015)
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As a preliminary we assume to have basic knowledge of linear algebra as, for example, from the course NMAG101. Some graph theory knowledge is an advantage but not necessity. Last update: Tůma Miroslav, prof. Ing., CSc. (16.05.2018)
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