Seminar Multigrid Methods - Winter 12: Difference between revisions
No edit summary |
No edit summary |
||
| Line 19: | Line 19: | ||
The following paper gives a good introduction into the basic idea of multigrid: | The following paper gives a good introduction into the basic idea of multigrid: | ||
*[http://www.cs.technion.ac.il/people/irad/online-publications/Yav06.pdf|"Why multigrid methods are so efficient" (I. Yavneh, 2006)] | *[http://www.cs.technion.ac.il/people/irad/online-publications/Yav06.pdf |"Why multigrid methods are so efficient" (I. Yavneh, 2006)] | ||
You should be familiar with the numerical terms and concepts used in this paper. | You should be familiar with the numerical terms and concepts used in this paper. | ||
Revision as of 12:01, 19 June 2012
- Term
- Winter 12
- Lecturer
- Prof. Dr. Michael Bader, Benjamin Peherstorfer, Marion Weinzierl
- Time and Place
- t.b.a.
- Audience
- Students from Master Computational Science and Engineering (IN2183) and Informatics (IN2107), and Bachelor Informatics (IN0014)
- Tutorials
- -
- Exam
- -
- Semesterwochenstunden / ECTS Credits
- 2 SWS (2S) / 4 Credits
- TUMonline
Description
Multigrid Methods are (almost incredibly) fast solvers for certain problems in Scientific Computing - mainly systems of equations arising from the discretisation of PDE-based models. For simple model problems, such as the Poisson equation, multigrid solvers can be tuned to solve systems of millions to billions of equations with constant amount of work (some 20 flops in ideal cases) per unknown. However, for realistic scenarios and more complicated model equations, multigrid methods have to be modified to retain their optimal complexity. In addition the efficient implementation of multigrid methods, in particular on massively parallel hardware, is still an area of active research.
The student presentation planned for this seminar will thus explore and introduce to multigrid basics as well as recent research on the numerics and algorithmics of multigrid approaches (see the list of topics below).
Prerequisites
The following paper gives a good introduction into the basic idea of multigrid:
You should be familiar with the numerical terms and concepts used in this paper.
Announcements
- Kick-off session: t.b.a.
Topics
Preliminary list of topics:
- Geometric Multigrid
- Additive and multiplicative multigrid
- Classical AMG
- (Alpha-)Smoothed Aggregation
- (Alpha-)BoxMG
- Adaptive multigrid, MLAT, FAC
- Operator-dependent multigrid methods
- Parallel multigrid
- Smoother: SPAI, ...
- Application: Computational Fluid Dynamics/Navier-Stokes
- Application: Convection-dominated problems, Convection-diffusion equation
- Application: Heat-Equation