Research References: Discretisation
Discrete Mechanics and Field Theory, Variational and Multisymplectic Integrators
- Jerrold E. Marsden, George W. Patrick and Steve Shkoller:
Multisymplectic Geometry, Variational Integrators, and Nonlinear PDEs (1998)
Communications in Mathematical Physics, Vol. 199, p. 351-395, doi:10.1007/s002200050505, arXiv:math/9807080
- Jerrold E. Marsden and Matthew West: Discrete Mechanics and Variational Integrators (2001)
Acta Numerica 2001, p. 357-514, doi: 10.1017/S096249290100006X
- Mathieu Desbrun, Anil N. Hirani, Melvin Leok and Jerrold E. Marsden: Discrete Exterior Calculus (2005)
arXiv:math/0508341
- Ari Stern, Yiying Tong, Mathieu Desbrun and Jerrold E. Marsden:
Geometric Computational Electrodynamics (2007)
arXiv:0707.4470
- Evan S. Gawlik, Patrick Mullen, Dmitry Pavlov, Jerrold E. Marsden and Mathieu Desbrun:
Geometric, Variational Discretization of Continuum Theories (2011)
Physica D: Nonlinear Phenomena, Vol. 240, p. 1724–1760,
doi: 10.1016/j.physd.2011.07.011,
arXiv:1010.4851
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Dmitry Pavlov, Patrick Mullen, Yiying Tong, Eva Kanso, Jerrold E. Marsden, Mathieu Desbrun:
Structure-Preserving Discretization of Incompressible Fluids (2011)
Physica D, Vol. 240, p. 443–458,
doi: 10.1016/j.physd.2010.10.012,
arXiv:0912.3989
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Tomasz M. Tyranowski, Mathieu Desbrun:
Variational Partitioned Runge-Kutta Methods for Lagrangians Linear in Velocities (2014)
arXiv:1401.7904
- Anil N. Hirani: Discrete Exterior Calculus (PhD Thesis, 2003)
Caltech Thesis
- Melvin Leok: Foundations of Computational Geometric Mechanics (PhD Thesis, 2004)
Caltech Thesis
- Matthew West: Variational Integrators (PhD Thesis, 2004)
Caltech Thesis
- Ari Stern: Geometric Discretization of Lagrangian Mechanics and Field Theories (PhD Thesis, 2009)
Caltech Thesis
- Dmitry Pavlov: Structure-Preserving Discretization of Incompressible Fluids (PhD Thesis, 2009)
Caltech Thesis
- Patrick G. Mullen: Eulerian Geometric Discretizations of Manifolds and Dynamics (PhD Thesis, 2012)
Caltech Thesis