(Pro-)Seminar in WS 05/06:
Lecturer | : | Prof. R. Hiptmair |
Room | : | HG E 1.1 |
Time | : | Mo 15:00 - 16:45 |
Start date | : | 21.11.2005 |
Prep meeting | : | Mon 24.10.2005, 15:00, HG E 1.1 |
Language | : | English |
Contact | : | R.
Hiptmair, hiptmair@sam.math.ethz.ch, T. Dohnal, dohnal@math.ethz.ch |
Prerequisites | : | Familiarity with basic theory of ODEs |
Description:
Geometrical numerical integration aims at devising numerical integration schemes that preserve crucial properties of the target ODE. These properties can be conservation of certain quantities, symplectic structure, reversibilty, etc.
This seminar is based on the famous book by Hairer, Lubich, and Wanner Geometric numerical integration, Springer 2002. Presentations will cover selected chapters of this book (see below).
Some of the Matlab codes
for problems in the book are at: http://www.unige.ch/math/folks/hairer/software.html
Talks and dates:
talk
nr. |
date |
topic |
book
section |
book
pages |
0 |
24.10.2005 | Preparatory meeting | ---------------- |
-------------- |
1 |
21.11.2005 | Runge-Kutta (RK) and Collocation Methods, Slides | II.1, II.2 |
23-29 |
2 |
21.11.2005 | Composition and
Splitting Methods,Slides,MATLAB,LaTeX |
II.4,
II.5 |
39-45 |
3 |
28.11.2005 | Conserv. of 1st Integrals: Examples of 1st Intergals, Quadratic InvariantsSlides,MATLAB | IV.1-
IV.2 (excl. IV.2.3) |
93-99 |
4 |
28.11.2005 | Conserv. of 1st
Integrals: Polynomial Invariants, Slides,
MATLAB |
IV.3 |
101-105 |
5 |
5.12.2005 | Methods on
Manifolds: Projection Methods, Slides |
IV.4 |
105-110 |
6 |
5.12.2005 | Methods on
Manifolds: Num. Methods Based on Local Coordinates, Slides, MATLAB |
IV.5 |
110-115 |
7 |
12.12.2005 | Differential
Equations on Lie Groups (LG), Slides |
IV.6 |
115-118 |
8 |
-------------- |
Methods
Based on
Magnus Series Expansions |
IV.7 |
118-120 |
9 |
12.12.2005 | LG Methods, Slides |
IV.8
(excl. IV.8.3) |
121-125 |
10 |
19.12.2005 | Reversible
Differential Equations and Maps, Symmetric RK Methods, Slides, MATLAB |
V.1,
V.2 |
131-137 |
11 |
19.12.2005 | Symmetric Methods
on Manifolds: Symmetric Projection, Symmetric LG Methods, Slides |
V.4.1,
part of V.4.2 |
149-154,
157-159 |
12 |
9.1.2006 | Energy-Momentum
Methods and Discrete Gradients, |
V.5 |
159-163 |
13 |
9.1.2006 | Hamiltonian
Systems, Symplectic Transformations, Slides |
VI.1,
VI.2 |
168-175 |
14 |
16.1.2006 | First Examples of
Symplectic Integrators, Symplectic RK Methods |
VI.3,
VI.4 |
175-182 |
15 |
16.1.2006 |
Generating
Functions, Slides |
VI.5 |
182-190 |
16 |
23.1.2006 | Variational
Integrators, Slides, MATLAB |
VI.6 |
191-198 |
17 |
23.1.2006 | Volume Preservation |
VII.3 |
248-253 |
18 |
30.1.2006 | Standard and
Reversible Adaptive Step Size Control |
VIII.1,
VIII.2 |
255-261 |
19 |
------------ | Time
Transformations |
VIII.3 |
261-266 |
20 |
30.1.2006 | Highly
Oscillatory DEs : Towards
Longer Time Steps |
XIII.1 |
407-414 |
talk numbers |
student |
consultant |
1, 11 |
Florian Landis |
Ralf Hiptmair |
2, 16 |
Claude Gittelson |
Ralf Hiptmair |
3, 13 |
Marc Sarbach |
Tomas Dohnal |
4, 12 |
Jeannine Roethlin |
Tomas Dohnal |
5, 9 |
Mario Haefeli |
Tomas Dohnal |
6, 14 |
Patrick Meury |
Tomas Dohnal |
7, 10 |
Julian Jordi |
Tomas Dohnal |
17, 18 |
Krishnaswamy Sankaran |
Ralf Hiptmair |
15, 20 |
Thomas Bissig |
Ralf Hiptmair |