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Course, academic year 2023/2024
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Parallel Matrix Computations - NMNV532
Title: Paralelní maticové výpočty
Guaranteed by: Department of Numerical Mathematics (32-KNM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2022
Semester: summer
E-Credits: 5
Hours per week, examination: summer s.:2/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: English
Teaching methods: full-time
Teaching methods: full-time
Guarantor: prof. Ing. Miroslav Tůma, CSc.
Class: M Mgr. MMIB > Povinně volitelné
M Mgr. MOD
M Mgr. MOD > Povinně volitelné
M Mgr. NVM
M Mgr. NVM > Povinně volitelné
Classification: Mathematics > Numerical Analysis
Annotation -
Last update: T_KNM (07.04.2015)
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.
Aim of the course -
Last update: prof. Ing. Miroslav Tůma, CSc. (22.02.2018)

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.

Course completion requirements -
Last update: prof. Ing. Miroslav Tůma, CSc. (28.04.2020)

Needed to get credits:

• students will independently prepare a parallel program based on theoretical examples discussed during lectures. The lectures can be also in the online distant form.

Literature -
Last update: doc. RNDr. Václav Kučera, Ph.D. (15.01.2019)

M. Tůma: Parallel matrix computations, 2018, http:://

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.

Teaching methods -
Last update: prof. Ing. Miroslav Tůma, CSc. (28.04.2020)

Lectures and tutorials in a lecture hall. A possible variant it to use an online distant lectures and tutorials.

Requirements to the exam -
Last update: prof. Ing. Miroslav Tůma, CSc. (28.04.2020)

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

Syllabus -
Last update: T_KNM (07.04.2015)

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.

Entry requirements -
Last update: prof. Ing. Miroslav Tůma, CSc. (16.05.2018)

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.

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