TY - GEN
T1 - Discrete computational mechanics for stiff phenomena
AU - Michels, Dominik L.
AU - Mueller, J. Paul T.
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: 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.
PY - 2016/11/28
Y1 - 2016/11/28
N2 - 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.
AB - 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.
KW - Differential equations
KW - Discrete computational mechanics
KW - Efficient time integration
KW - Exponential integrators
KW - Fast simulation
KW - Hamiltonian mechanics
KW - High-fidelity simulation
KW - Lagrange formalism
KW - Legendre transformation
KW - Real-time physics
KW - Real-time simulation
KW - Stiff differential equations
KW - Structure preservation
KW - Symmetry
KW - Symplecticity
KW - Variational integrators
KW - Variational principles
UR - http://www.scopus.com/inward/record.url?scp=85007236764&partnerID=8YFLogxK
U2 - 10.1145/2988458.2988464
DO - 10.1145/2988458.2988464
M3 - Conference contribution
AN - SCOPUS:85007236764
T3 - SA 2016 - SIGGRAPH ASIA 2016 Courses
BT - SA 2016 - SIGGRAPH ASIA 2016 Courses
PB - Association for Computing Machinery (ACM)
T2 - 2016 SIGGRAPH ASIA Courses, SA 2016
Y2 - 5 December 2016 through 8 December 2016
ER -