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
• 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
• 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