Geometric Numerical Integration of Simple Dynamical Systems

Schmitt, P. R. and Steinmann, P. (2007) Geometric Numerical Integration of Simple Dynamical Systems. In: 2nd Workshop of the DFG's International Research Training Group on Visualization of Large and Unstructured Data Sets - Applications in Geospatial Planning, Modeling, and Engineering, VLUDS 2007, Kaiserslautern; Germany, 9-11 Sept 2007, ISBN 9783885794417

Abstract

Understanding the behavior of a dynamical system is usually accomplished by visualization of its phase space portraits. Finite element simulations of dynamical systems yield a very high dimensionality of phase space, i.e. twice the number of nodal degrees of freedom. Therefore insight into phase space structure can only be gained by reduction of the model's dimensionality. The phase space of Hamiltonian systems is of particular interest because of its inherent geometric features namely being the co-tangent bundle of the configuration space of the problem and therefore having a natural symplectic structure. In this contribution a class of geometry preserving integrators based on Lie-groups and -algebras is presented which preserve these geometric features exactly. Examples of calculations for a simple dynamical system are detailed.

• Item Type: Conference Proceedings
• Additional Information: Lecture Notes in Informatics (LNI), Proceedings - Series of the Gesellschaft fur Informatik (GI) 2008, pages 115-124.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Steinmann, Professor Paul
• Authors: Schmitt, P. R., and Steinmann, P.
• College/School: College of Science and Engineering > School of Engineering > Infrastructure and Environment
• Journal Name: Lecture Notes in Informatics (LNI), Proceedings - Series of the Gesellschaft fur Informatik (GI)
• ISSN: 1617-5468
• ISBN: 9783885794417

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