(Pro-)Seminar in WS 05/06:


Geometric Numerical Integration

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


Assignment of talks:

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

We are available for consultations by appointment (preferably via email).


Prof. Ralf Hiptmair 2005-10-26