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Course, academic year 2024/2025
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Multilevel Methods - NMNV571
Title: Víceúrovňové metody
Guaranteed by: Department of Numerical Mathematics (32-KNM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2023
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Additional information: http://papez.org/multigrid.html
Guarantor: RNDr. Jan Papež, Ph.D.
Teacher(s): RNDr. Jan Papež, Ph.D.
Class: M Mgr. NVM
M Mgr. NVM > Volitelné
Classification: Mathematics > Numerical Analysis
Incompatibility : NNUM113
Interchangeability : NNUM113
Is interchangeable with: NNUM113
Annotation -
Fast iterative and hybrid algorithms. multilevel methods: multigrid, aggregation.
Last update: T_KNM (27.04.2015)
Course completion requirements -

An active participation of students during the lectures is expected. The exam is oral, covering the presented topics.

Last update: Tichý Petr, doc. RNDr., Ph.D. (05.09.2022)
Literature -

W. Hackbusch: Multigrid Methods. Springer Verlag, Berlin-Heidelberg-New York, 1988.

W. Hackbusch, U. Trottenberg (eds.): Multigrid Methods, Lecture Notes in Mathematics, Vol. 96O, Springer Verlag Berlin-Heidelberg-New York, 1982.

W. L. Briggs, V. E. Henson, S. F. McCormick: A Multigrid Tutorial, Society for Industrial and Applied Mathematics (SIAM), 2000.

J. Xu, L. Zikatanov: Algebraic multigrid methods, Acta Numerica 26, 2017.

J. H. Bramble, J. E. Pasciak, J. Xu: Parallel multilevel preconditioners, Math. Comput. 55, 1990.

U. Rüde: Mathematical and computational techniques for multilevel adaptive methods, Society for Industrial and Applied Mathematics (SIAM), 1995.

V. Dolean, P. Jolivet, F. Nataf: An introduction to domain decomposition methods: algorithms, theory, and parallel implementation, Society for Industrial and Applied Mathematics (SIAM), 2015.

Last update: Tichý Petr, doc. RNDr., Ph.D. (05.09.2022)
Requirements to the exam -

The final exam is oral and covers all topics presented in lectures.

Last update: Tichý Petr, doc. RNDr., Ph.D. (05.09.2022)
Syllabus -

1. A brief overview of related topics from previous courses (stationary iterative methods, finite difference and finite element methods)

2a. Geometric multigrid for two levels - derivation, convergence properties

2b. Generalization for more levels, variants (V- a W-cycle, full multigrid)

3. Algebraic multigrid, aggregation

4. Stable splitting, BPX preconditioner

5. GenEO method (overlapping Schwarz method with coarse grid correction)

Lectures can be adapted to respect the interest of students.

Last update: Tichý Petr, doc. RNDr., Ph.D. (05.09.2022)
Entry requirements -

The course is appropriate for master and PhD students. We will elaborate on numerical linear algebra knowledge, finite element method and basic properties of Sobolev spaces.

Last update: Papež Jan, RNDr., Ph.D. (23.08.2023)
 
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