Discrete computational mechanics for stiff phenomena

Handle URI:
http://hdl.handle.net/10754/625555
Title:
Discrete computational mechanics for stiff phenomena
Authors:
Michels, Dominik L.; Mueller, J. Paul T.
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.
KAUST Department:
KAUST
Citation:
Michels DL, Mueller JPT (2016) Discrete computational mechanics for stiff phenomena. SIGGRAPH ASIA 2016 Courses on - SA ’16. Available: http://dx.doi.org/10.1145/2988458.2988464.
Publisher:
ACM Press
Journal:
SIGGRAPH ASIA 2016 Courses on - SA '16
Conference/Event name:
2016 SIGGRAPH ASIA Courses, SA 2016
Issue Date:
28-Nov-2016
DOI:
10.1145/2988458.2988464
Type:
Conference Paper
Sponsors:
The authors are grateful to Stefan Feess for preparing the simulation of the righting response of the turtle and its rendering. The reviewers' valuable comments that improved the manuscript are gratefully acknowledged. This work has been partially supported by the King Abdullah University of Science and Technology (KAUST baseline grants), the German Academic Exchange Service (Deutscher Akademischer Austauschdienst e.V.) funded by the government of the Federal Republic of Germany and the European Union, and the German National Merit Foundation (Studienstiftung des deutschen Volkes e.V.) funded by federal, state, and local authorities of the Federal Republic of Germany.
Additional Links:
http://dl.acm.org/citation.cfm?doid=2988458.2988464
Appears in Collections:
Conference Papers

Full metadata record

DC FieldValue Language
dc.contributor.authorMichels, Dominik L.en
dc.contributor.authorMueller, J. Paul T.en
dc.date.accessioned2017-10-03T12:49:25Z-
dc.date.available2017-10-03T12:49:25Z-
dc.date.issued2016-11-28en
dc.identifier.citationMichels DL, Mueller JPT (2016) Discrete computational mechanics for stiff phenomena. SIGGRAPH ASIA 2016 Courses on - SA ’16. Available: http://dx.doi.org/10.1145/2988458.2988464.en
dc.identifier.doi10.1145/2988458.2988464en
dc.identifier.urihttp://hdl.handle.net/10754/625555-
dc.description.abstractMany 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.en
dc.description.sponsorshipThe authors are grateful to Stefan Feess for preparing the simulation of the righting response of the turtle and its rendering. The reviewers' valuable comments that improved the manuscript are gratefully acknowledged. This work has been partially supported by the King Abdullah University of Science and Technology (KAUST baseline grants), the German Academic Exchange Service (Deutscher Akademischer Austauschdienst e.V.) funded by the government of the Federal Republic of Germany and the European Union, and the German National Merit Foundation (Studienstiftung des deutschen Volkes e.V.) funded by federal, state, and local authorities of the Federal Republic of Germany.en
dc.publisherACM Pressen
dc.relation.urlhttp://dl.acm.org/citation.cfm?doid=2988458.2988464en
dc.subjectDifferential equationsen
dc.subjectDiscrete computational mechanicsen
dc.subjectEfficient time integrationen
dc.subjectExponential integratorsen
dc.subjectFast simulationen
dc.subjectHamiltonian mechanicsen
dc.subjectHigh-fidelity simulationen
dc.subjectLagrange formalismen
dc.subjectLegendre transformationen
dc.subjectReal-time physicsen
dc.subjectReal-time simulationen
dc.subjectStiff differential equationsen
dc.subjectStructure preservationen
dc.subjectSymmetryen
dc.subjectSymplecticityen
dc.subjectVariational integratorsen
dc.subjectVariational principlesen
dc.titleDiscrete computational mechanics for stiff phenomenaen
dc.typeConference Paperen
dc.contributor.departmentKAUSTen
dc.identifier.journalSIGGRAPH ASIA 2016 Courses on - SA '16en
dc.conference.date2016-12-05 to 2016-12-08en
dc.conference.name2016 SIGGRAPH ASIA Courses, SA 2016en
dc.conference.locationMacau, CHNen
dc.contributor.institutionStanford Universityen
kaust.authorMichels, Dominik L.en
kaust.authorMueller, J. Paul T.en
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