Subjects

Your browser does not support JavaScript, or its support is disabled. Some features may not be available.

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
Teaching methods:	full-time
Additional information:	http://papez.org/multigrid.html

Guarantor:	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

Opinion survey results Examination dates SS schedule Noticeboard

Annotation -

Last update: T_KNM (27.04.2015)

Fast iterative and hybrid algorithms. multilevel methods: multigrid, aggregation.

Course completion requirements -

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

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

Literature -

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

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.

Requirements to the exam -

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

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

Syllabus -

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

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.

Entry requirements -

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

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.