Journal ArticleDOI
Multi-Symplectic Runge—Kutta Collocation Methods for Hamiltonian Wave Equations
Reads0
Chats0
About:
This article is published in Journal of Computational Physics.The article was published on 2000-01-20. It has received 275 citations till now. The article focuses on the topics: Symplectic integrator & Symplectic manifold.read more
Citations
More filters
Journal ArticleDOI
Discrete mechanics and variational integrators
Jerrold E. Marsden,Matthew West +1 more
TL;DR: In this paper, a review of integration algorithms for finite dimensional mechanical systems that are based on discrete variational principles is presented, including the Verlet, SHAKE, RATTLE, Newmark, and the symplectic partitioned Runge-Kutta schemes.
Journal ArticleDOI
Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity
TL;DR: In this article, the authors proposed a new theoretical framework for generalizing ODE numerical integrators to Hamiltonian PDEs in R 2 : time plus one space dimension, where the structure of the PDE is decomposed into distinct components representing space and time independently, and the integrators can be constructed by concatenating uni-directional ODE symplectic integrators.
Journal ArticleDOI
Numerical methods for Hamiltonian PDEs
TL;DR: A survey of variational, symplectic and multi-symplectic discretization methods for Hamiltonian partial differential equations can be found in this paper, where the derivation of methods as well as some of their fundamental geometric properties are discussed.
Journal ArticleDOI
A 3-D discrete-element method for dry granular flows of ellipsoidal particles
TL;DR: In this article, the authors used 3D discrete element method (DEM) to simulate dry granular flows of non-spherical particles, which are represented by clusters of spheres for contact detection and for contact-force calculation.
Journal ArticleDOI
A compact split-step finite difference method for solving the nonlinear Schrödinger equations with constant and variable coefficients
Mehdi Dehghan,Ameneh Taleei +1 more
TL;DR: This method improves the accuracy of split-step finite difference method by introducing a compact scheme for discretization of space variable while this improvement does not reduce the stability range and does not increase the computational cost.
References
More filters
Book
A practical guide to pseudospectral methods
TL;DR: In this article, the authors introduce spectral methods via orthogonal functions and finite differences, and compare computational cost of spectral methods with FD and PS methods in polar and spherical geometries.
Journal ArticleDOI
Multisymplectic Geometry, Variational Integrators, and Nonlinear PDEs
TL;DR: In this article, the existence of the fundamental geometric structures as well as their preservation along solutions can be obtained directly from the variational principle in continuous and discrete mechanics and field theories using multisymplectic geometry.
Journal ArticleDOI
Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity
TL;DR: In this article, the authors proposed a new theoretical framework for generalizing ODE numerical integrators to Hamiltonian PDEs in R 2 : time plus one space dimension, where the structure of the PDE is decomposed into distinct components representing space and time independently, and the integrators can be constructed by concatenating uni-directional ODE symplectic integrators.
Journal ArticleDOI
On the numerical integration of ordinary differential equations by symmetric composition methods
TL;DR: Free Lie algebra theory gives simple formulae for the number of determining equations for a method to have a particular order, and a new, more accurate way of applying the methods thus obtained to compositions of an arbitrary first-order integrator is described and tested.
Journal ArticleDOI
Multi-symplectic structures and wave propagation
TL;DR: In this article, a generalized Hamiltonian structure is proposed for dispersive wave propagation problems, which generalizes classical Hamiltonian structures by assigning a distinct symplectic operator for each unbounded space direction and time of a Hamiltonian evolution equation on one or more space dimensions.