Seminar Multigrid Methods - Summer 13

Term

Summer 13

Lecturer

Benjamin Peherstorfer, Marion Weinzierl

Time and Place

Preliminary meeting: Tuesday, Jan 22, 9:00, room FMI 02.09.014

Audience

Students from Master Computational Science and Engineering (IN2183), Informatics (IN2107), and Bachelor Informatics (IN0014)

Tutorials

-

Exam

-

Semesterwochenstunden / ECTS Credits

2 SWS (2S) / 4 Credits

TUMonline

Seminar page of last semester

---

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

• The seminar will be completely in English, so the students also have to give their talks and to write their papers in English.

• Preliminary meeting: Tuesday, Jan 22, 9:00, room FMI 02.09.014
• Kick-off with final assignment of topics: tba

• Presentations will take place: tba

Possible Topics (not fixed yet)

• Multigrid Basics:
  • Hierarchical Transformation Multigrid
  • Semidefinit Systems
  • Adaptive Multigrid, MLAT, FAC
  • Multigrid for Non-linear Problems

• Smoothers:
  • Smoothers for Multigrid Methods
  • Smoothing Analysis

• Algebraic Multigrid:
  • BoxMG
  • Classical AMG
  • Smoothed Aggregation

• Parallel Multigrid
  • Overview of Parallel Multigrid
  • Parallel Smoothers
  • Parallel AMG

Literature

• Trottenberg, Oosterlee, Schüller: "Multigrid"

• Briggs, Henson, McCormick: "A Multigrid Tutorial", 2nd edition

• Publications in Journals etc.

Requirements

For successful completion of the seminar course you have to fulfil the following tasks:

• solid understanding of your topic
• writing of a paper (about 8 pages)
• presentation (30 min + discussion)
• participation in the presentations of all other participants
• deadlines: tba

The paper template is available here. Usage of Latex is required.