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    Discrete computational mechanics for stiff phenomena

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    Type
    Conference Paper
    Authors
    Michels, Dominik L.
    Mueller, J. Paul T.
    KAUST Department
    KAUST
    Date
    2016-11-28
    Permanent link to this record
    http://hdl.handle.net/10754/625555
    
    Metadata
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    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.
    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.
    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.
    Publisher
    Association for Computing Machinery (ACM)
    Journal
    SIGGRAPH ASIA 2016 Courses on - SA '16
    Conference/Event name
    2016 SIGGRAPH ASIA Courses, SA 2016
    DOI
    10.1145/2988458.2988464
    Additional Links
    http://dl.acm.org/citation.cfm?doid=2988458.2988464
    ae974a485f413a2113503eed53cd6c53
    10.1145/2988458.2988464
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