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Journal of Computational Physics, ISSN 0021-9991, 03/2017, Volume 332, pp. 83 - 98
Spectral methods are a popular choice for constructing numerical approximations for smooth problems, as they can achieve geometric rates of convergence and... 
Spectral-collocation methods | Variational integrators | Lagrangian mechanics | Geometric numerical integration | MECHANICS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MATHEMATICAL | SYMPLECTIC INTEGRATORS
Journal Article
The Astrophysical Journal, ISSN 2041-8213, 08/2015, Volume 809, Issue 1, p. L9
2015 ApJ 809 L9 Symplectic integrators are widely used for long-term integration of conservative astrophysical problems due to their ability to preserve the... 
PLANETS | GRAVITATIONAL RADIATION | ASTROPHYSICS, COSMOLOGY AND ASTRONOMY | ASTROPHYSICS | SATELLITES | ALGORITHMS | HARMONIC OSCILLATORS | VARIATIONAL METHODS
Journal Article
Journal Article
Quarterly Journal of the Royal Meteorological Society, ISSN 0035-9009, 04/2019, Volume 145, Issue 720, pp. 1070 - 1088
We develop a variational integrator for the shallow‐water equations on a rotating sphere. The variational integrator is built around a discretization of the... 
variational integrator on sphere | rotating shallow‐water equations | structure‐preserving discretization | DISCRETIZATION | ENERGY | POTENTIAL ENSTROPHY | NUMERICAL-INTEGRATION | rotating shallow-water equations | structure-preserving discretization | METEOROLOGY & ATMOSPHERIC SCIENCES | SCHEMES | Hydrodynamics | Equations | Framework
Journal Article
International Journal for Numerical Methods in Engineering, ISSN 0029-5981, 04/2018, Volume 114, Issue 3, pp. 215 - 231
Journal Article
ACM Transactions on Mathematical Software (TOMS), ISSN 0098-3500, 11/2012, Volume 39, Issue 1, pp. 1 - 28
Journal Article
IMA Journal of Numerical Analysis, ISSN 0272-4979, 10/2011, Volume 31, Issue 4, pp. 1497 - 1532
We derive a variational characterization of the exact discrete Hamiltonian, which is a Type II generating function for the exact flow of a Hamiltonian system,... 
geometric mechanics | Hamiltonian mechanics | symplectic integrators | geometric numerical integration | variational integrators | MATHEMATICS, APPLIED | MECHANICS | PDES | SYSTEMS | GEOMETRY | SCHEMES | Hamilton-Jacobi equation | Mathematical analysis | Integrators | Mathematical models | Runge-Kutta method | Transformations | Variational principles | Galerkin methods
Journal Article
Applied Numerical Mathematics, ISSN 0168-9274, 09/2013, Volume 71, pp. 14 - 23
We extend the notion of variational integrator for classical Euler–Lagrange equations to the fractional ones. As in the classical case, we prove that the... 
Variational integrator | Noetherʼs theorem | Fractional calculus | Euler–Lagrange equations | Euler-Lagrange equations | Noether's theorem | SCHEME | MATHEMATICS, APPLIED | MECHANICS | NOETHERS THEOREM | FORMULATION
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 01/2014, Volume 257, pp. 1040 - 1061
Journal Article
BIT Numerical Mathematics, ISSN 0006-3835, 12/2018, Volume 58, Issue 4, pp. 1009 - 1048
Journal Article
IMA Journal of Numerical Analysis, ISSN 0272-4979, 4/2009, Volume 29, Issue 2, pp. 421 - 443
This paper presents a continuous and discrete Lagrangian theory for stochastic Hamiltonian systems on manifolds, akin to the Ornstein-Uhlenbeck theory of... 
Ornstein-Uhlenbeck process | Variational integrators | Stochastic Hamiltonian systems | MATHEMATICS, APPLIED | MECHANICS | RIGID-BODY | MOTION | DIRAC STRUCTURES | EQUATIONS | stochastic Hamiltonian systems | SYSTEMS | variational integrators | Mathematics - Probability
Journal Article
IMA Journal of Numerical Analysis, ISSN 0272-4979, 01/2018, Volume 38, Issue 1, pp. 377 - 398
Abstract Discrete Hamiltonian variational integrators are derived from type II and type III generating functions for symplectic maps, and in this article, we... 
Hamiltonian mechanics | Symplectic integrators | Variational integrators | Geometric mechanics | Geometric numerical integration | MATHEMATICS, APPLIED | symplectic integrators | MECHANICS | geometric numerical integration | geometric mechanics | variational integrators
Journal Article
International Journal for Numerical Methods in Engineering, ISSN 0029-5981, 03/2017, Volume 109, Issue 11, pp. 1549 - 1581
Summary This article presents a family of variational integrators from a continuous time point of view. A general procedure for deriving symplectic integration... 
numerical integration methods | symplectic integrators | multibody dynamics | discontinuous Galerkin methods | variational integrators | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | FINITE-ELEMENTS | ENGINEERING, MULTIDISCIPLINARY | DYNAMICS | Concretes | Numerical analysis | Pendulums | Runge-Kutta method | Integrators | Regularization | Cartesian coordinates
Journal Article
Journal Article
Journal of Nonlinear Science, ISSN 0938-8974, 10/2017, Volume 27, Issue 5, pp. 1399 - 1434
Journal Article
Physica D: Nonlinear Phenomena, ISSN 0167-2789, 08/2015, Volume 310, pp. 37 - 71
Journal Article