Variational time integrators
By Adrian J. Lew, Jerrold E. Marsden, Magdalena Ortiz, Matthew West. 2004
300 citations recorded by the source corpus.
Subfields: Computational Mechanics, Control and Systems Engineering, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/973f4709999c165e6f596c8aa90fbfbca383b08a
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computational Mechanics
- Jerrold E. Marsden
- Magdalena Ortiz
- Thomas J. Bridges
- Marino Arroyo
- Adrian J. Lew
- Sigrid Leyendecker
- B. Li
- F. Habbal
In Control and Systems Engineering
- Magdalena Ortiz
- Jerrold E. Marsden
- Sigrid Leyendecker
- Marino Arroyo
- Romeo Ortega
- J. Alexander Fax
- Sina Ober-Blöbaum
In Numerical Analysis
- Jerrold E. Marsden
- Magdalena Ortiz
- Thomas J. Bridges
- Sigrid Leyendecker
- Sebastian Reich
- Adrian J. Lew
- B. Li
- F. Habbal
Citations in the corpus
- Discontinuous Galerkin methods for non‐linear elasticity (2006, background): “This has proved to be advantageous for the algorithmic analysis and mesh adaption in the context of non-linear problems [35], and for the computation of configurational forces [36], such as the J -integral in fracture mechanics.”
- Geometric integrators for ODEs (2006, unknown): “−b”
- Variational integrators for constrained dynamical systems (2008, methodology): “In [51], this method enables the long term integration of the motion of a long thin helicopter blade for different sets of material parameters ranging from very stiff almost rigid motion to rather soft material behavior.”
- Modelling fluid deformable surfaces with an emphasis on biological interfaces (2018, methodology): “Time-integrators based on the discretization of a variational principle are usually referred to as variational time-integrators, and have been widely employed, for instance, for the discretization of Hamilton’s principle in conservative systems including molecular dynamics (Frenkel & Smit 2001) and ”
- Nonintrusive and Structure Preserving Multiscale Integration of Stiff ODEs, SDEs, and Hamiltonian Systems with Hidden Slow Dynamics via Flow Averaging (2009, unknown): “(2.4) FLAVOR can then be defined by Θδ := Φ 0 δ−τ ◦ Φ 1 τ (2.5) Theorem 1.3 establishes the accuracy of this integrator under Conditions 1.5 and 1.6 provided that τ √ δ and τ2 δ τ√ .”
- 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].”
- Optimal transportation meshfree approximation schemes for fluid and plastic flows (2010, methodology): “[41, 42]) to establish the conservation properties of the OTM method.”