Discrete computational mechanics for stiff phenomena

Dominik L. Michels, J. Paul T. Mueller

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations

Abstract

Many natural phenomena which occur in the realm of visual computing and computational physics, like the dynamics of cloth, fibers, fluids, and solids as well as collision scenarios are described by stiff Hamiltonian equations of motion, i.e. differential equations whose solution spectra simultaneously contain extremely high and low frequencies. This usually impedes the development of physically accurate and at the same time efficient integration algorithms. We present a straightforward computationally oriented introduction to advanced concepts from classical mechanics. We provide an easy to understand step-by-step introduction from variational principles over the Euler-Lagrange formalism and the Legendre transformation to Hamiltonian mechanics. Based on such solid theoretical foundations, we study the underlying geometric structure of Hamiltonian systems as well as their discrete counterparts in order to develop sophisticated structure preserving integration algorithms to efficiently perform high fidelity simulations.
Original languageEnglish (US)
Title of host publicationSIGGRAPH ASIA 2016 Courses on - SA '16
PublisherAssociation for Computing Machinery (ACM)
ISBN (Print)9781450345385
DOIs
StatePublished - Nov 28 2016

Cite this