Results 11 to 20 of about 50,984 (262)

Discrete Variational Optimal Control [PDF]

Journal of Nonlinear Science, 2012
This paper develops numerical methods for optimal control of mechanical systems in the Lagrangian setting. It extends the theory of discrete mechanics to enable the solutions of optimal control problems through the discretization of variational ...
A. Iserles, A. Weinstein, A.I. Bobenko, A.M. Bloch, A.M. Bloch, D. Iglesias, David Martín de Diego, E. Hairer, E. Martínez, F. Bullo, F. Jiménez, Fernando Jiménez, I. Hussein, J. Cortés, J.C. Marrero, J.E. Marsden, J.E. Marsden, J.E. Marsden, J.E. Marsden, J.E. Marsden, M. Kobilarov, M. Kobilarov, M. Kobilarov, Marin Kobilarov, N. Bou-Rabee, R. Abraham, S. Ferraro, S. Ober-Blöbaum, T. Lee   +28 more
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Geometric, Variational Discretization of Continuum Theories [PDF]

Physica D: Nonlinear Phenomena, 2010
This study derives geometric, variational discretizations of continuum theories arising in fluid dynamics, magnetohydrodynamics (MHD), and the dynamics of complex fluids.
Desbrun, Mathieu, Gawlik, Evan S., Marsden, Jerrold E., Mullen, Patrick, Pavlov, Dmitry   +4 more
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Variational Discrete Action Theory [PDF]

Physical Review Letters, 2021
Here we propose the Variational Discrete Action Theory (VDAT) to study the ground state properties of quantum many-body Hamiltonians. VDAT is a variational theory based on the sequential product density matrix (SPD) ansatz, characterized by an integer $\mathcal{N}$, which monotonically approaches the exact solution with increasing $\mathcal{N}$.
Zhengqian Cheng, Chris A. Marianetti
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Discrete Hamiltonian variational integrators [PDF]

IMA Journal of Numerical Analysis, 2011
23 ...
Leok, Melvin, Zhang, Jingjing
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Variational convergence of discrete elasticae [PDF]

IMA Journal of Numerical Analysis, 2020
AbstractWe discuss a discretization of the Euler–Bernoulli bending energy and of Euler elasticae under clamped boundary conditions by polygonal lines. We show Hausdorff convergence of the set of almost minimizers of the discrete bending energy to the set of smooth Euler elasticae under mesh refinement in (i) the $W^{1,\infty }$-topology for piecewise ...
Scholtes, Sebastian, Schumacher, Henrik, Wardetzky, Max   +2 more
openaire   +3 more sources

Stochastic discrete Hamiltonian variational integrators [PDF]

BIT Numerical Mathematics, 2018
Variational integrators are derived for structure-preserving simulation of stochastic Hamiltonian systems with a certain type of multiplicative noise arising in geometric mechanics. The derivation is based on a stochastic discrete Hamiltonian which approximates a type-II stochastic generating function for the stochastic flow of the Hamiltonian system ...
Darryl D. Holm, Tomasz M. Tyranowski
openaire   +7 more sources

Discrete-time fractional variational problems [PDF]

Signal Processing, 2011
We introduce a discrete-time fractional calculus of variations on the time scale $h\mathbb{Z}$, $h > 0$. First and second order necessary optimality conditions are established. Examples illustrating the use of the new Euler-Lagrange and Legendre type conditions are given.
Bastos, N.R.O., Ferreira, R.A.C., Torres, D.F.M.   +2 more
openaire   +5 more sources

Nonstandard Finite Difference Variational Integrators for Multisymplectic PDEs

Journal of Applied Mathematics, 2012
We use the idea of nonstandard finite difference methods to derive the discrete variational integrators for multisymplectic PDEs. We obtain a nonstandard finite difference variational integrator for linear wave equation with a triangle discretization and
Cuicui Liao, Xiaohua Ding
doaj   +1 more source

An Approximation Method for Variational Inequality with Uncertain Variables

Advances in Mathematical Physics, 2023
In this paper, a Stieltjes integral approximation method for uncertain variational inequality problem (UVIP) is studied. Firstly, uncertain variables are introduced on the basis of variational inequality.
Cunlin Li, Hongyu Zhang, Rui Yuan, Yee Hooi Min, Tzu-Chien Yin   +4 more
doaj   +1 more source

Numerical analysis of a relaxed variational model of hysteresis in two-phase solids [PDF]

, 2001
This paper presents the numerical analysis for a variational formulation of rate-independent phase transformations in elastic solids due to Mielke et al.
Ball, Ball, Bildhauer, Carstensen, Carstensen, Carstensen, Carstensen, Fonseca, Goodman, Kohn, Le Dret, Seregin   +11 more
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