Seminar Multigrid Methods - Winter 12

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

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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:

• "Why multigrid methods are so efficient" (I. Yavneh, 2006)

We would expect all participants to be familiar with the numerical terms and concepts used in this paper before the seminar starts.

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, ...

• Analysis of multigrid methods, Local Fourier Analysis

• Application: Computational Fluid Dynamics/Navier-Stokes

• Application: Convection-dominated problems, Convection-diffusion equation

• Application: Heat-Equation