Asynchronous Variational Integrators

By Adrian J. Lew, Jerrold E. Marsden, Magdalena Ortiz, Matthew West. 2003

299 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/5078ee5fffe28a986ff91b6c580ac2eaac576014

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Citations in the corpus

Variational integrators for constrained dynamical systems (2008, background): “One possibility to deal with a large spectrum of frequencies in a problem is to use asynchronous variational integration [50].”
Variational time integrators (2004, methodology): “These cases do not present any essential difficulties and can be found Reference [19].”
Numerical methods for Hamiltonian PDEs (2006, background): “One can also start with the Lagrangian formulation and derive algorithms based on a discrete variational principle leading to variational integrators and this approach is reviewed in Marsden & West [102].”
Geometric integrators for ODEs (2006, methodology): “The Newmark method, well known in computational engineering, is variational [73], a fact that allowed the determination of the (nonstandard) symplectic form it preserves; singular Lagrangians can be treated; it suggests a natural treatment of holonomic (position) and nonholonomic (velocity) constrai”
Nonintrusive and Structure Preserving Multiscale Integration of Stiff ODEs, SDEs, and Hamiltonian Systems with Hidden Slow Dynamics via Flow Averaging (2009, background): “Asynchronous variational integrators [77] provide a way to derive conservative symplectic integrators for PDEs where the solution advances nonuniformly in time; however, stiff potentials require a fine time step discretization over the whole time evolution.”
Momentum maps and measure-valued solutions (peakons, filaments, and sheets) for the EPDiff equation (2003, methodology): “It would be interesting to pursue this aspect further and also incorporate discrete exterior calculus and variational multisymplectic integration methods (see Desbrun, Hirani, Leok and Marsden [2003] as well as Marsden, Patrick and Shkoller [1998] and Lew, Marsden, Ortiz and West [2003] ).”
Structure-preserving model reduction for mechanical systems (2003, methodology): “[13]; see also[20] for an asynchronous generalization to the PDE context and with applications to nonlinear elastodynamic simulations.”
Optimal transportation meshfree approximation schemes for fluid and plastic flows (2010, background): “Exact local conservation of momenta and energy can be achieved by means of asynchronous variational integrators [45].”
On geometric discretization of elasticity (2008, background): “Putting continuum mechanics, and in particular, nonlinear elasticity, in the proper geometric framework [28] is not just a matter of mathematical authenticity; it has been observed recently that geometry can lead to nontrivial developments [41; 26].”