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Multiscale iterative solvers
Multiscale Iterative Solvers
Last Updated: 2026-02-05 15:09:57
Abstract
Introduction into theoretical and implementational aspects of fast multilevel iterativesolvers for discretized (elliptic) boundary value problems. The course addressesmultigrid methods, wavelet based schemes, operator preconditioning, and domaindecomposition methods. Practical exercises rely on MATLAB.
Content
Main topics to be covered in the course: * Variational theory of Schwarz methods (multigrid and domain decomposition) * Multigrid theory based on smoothing and approximation properties * Multiiscale bases and preconditioners * Multigrid for non-selfadjoint problems and singularly perturbed problems * Multigrid for problems in H(div) and H(curl) * Multiigrid methods for Stokes equations * Non-overlapping domain decomposition methods * Algebraic multigrid
Resources
Lecture Notes
No
Literature
J. Xu: An introduction to multilevel methods, in Wavelets, Multilevel Methods and Elliptic PDEs, Clarendon Press, 1997 J. Xu: Iterative methods by space decomposition and subspace correction, SIAM Review 34, 1992 J. Bramble: Multigrid methods, Longman, 1993 W. Hackbusch: Multi--grid Methods and Applications, Springer, 1985 U. Trottenberg,C.W. Oosterlee, and A. Schueller: Multigrid, Academic Press 2000 B. Smith and P. Bjorstad and W. Gropp: Domain decomposition, Cambridge University Press, 1996 W. Dahmen: Wavelet and Multiscale Methods for Operator Equations, Acta Numerica 1997
General Information
- Language
- English
Examination
- Type
- session examination
- Mode
- oral 20 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Multiscale Iterative Solvers |
|
3 h weekly |
| exercise | Multiscale Iterative Solvers |
|
1 h weekly |