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dc.contributor.authorMichels, Dominik L.
dc.contributor.authorMueller, J. Paul T.
dc.date.accessioned2017-10-03T12:49:25Z
dc.date.available2017-10-03T12:49:25Z
dc.date.issued2016-11-28
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.
dc.identifier.doi10.1145/2988458.2988464
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.
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.
dc.publisherACM Press
dc.relation.urlhttp://dl.acm.org/citation.cfm?doid=2988458.2988464
dc.subjectDifferential equations
dc.subjectDiscrete computational mechanics
dc.subjectEfficient time integration
dc.subjectExponential integrators
dc.subjectFast simulation
dc.subjectHamiltonian mechanics
dc.subjectHigh-fidelity simulation
dc.subjectLagrange formalism
dc.subjectLegendre transformation
dc.subjectReal-time physics
dc.subjectReal-time simulation
dc.subjectStiff differential equations
dc.subjectStructure preservation
dc.subjectSymmetry
dc.subjectSymplecticity
dc.subjectVariational integrators
dc.subjectVariational principles
dc.titleDiscrete computational mechanics for stiff phenomena
dc.typeConference Paper
dc.contributor.departmentKAUST
dc.identifier.journalSIGGRAPH ASIA 2016 Courses on - SA '16
dc.conference.date2016-12-05 to 2016-12-08
dc.conference.name2016 SIGGRAPH ASIA Courses, SA 2016
dc.conference.locationMacau, CHN
dc.contributor.institutionStanford University
kaust.personMichels, Dominik L.
kaust.personMueller, J. Paul T.


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