(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