Numerical solutions of Hamiltonian PDEs: a multi-symplectic integrator in light-cone coordinates
Abstract
We introduce a novel numerical method to integrate partial differential equations representing the Hamiltonian dynamics of field theories. It is a multi-symplectic integrator that locally conserves the stress-energy tensor with an excellent precision over very long periods. Its major advantage is that it is extremely simple (it is basically a centered box scheme) while remaining locally well defined. We put it to the test in the case of the non-linear wave equation (with quartic potential) in one spatial dimension, and we explain how to implement it in higher dimensions. A formal geometric presentation of the multi-symplectic structure is also given as well as a technical trick allowing to solve the degeneracy problem that potentially accompanies the multi-symplectic structure.
Keywords
Cite
@article{arxiv.1702.06863,
title = {Numerical solutions of Hamiltonian PDEs: a multi-symplectic integrator in light-cone coordinates},
author = {Hugo Ricateau and Leticia F. Cugliandolo},
journal= {arXiv preprint arXiv:1702.06863},
year = {2017}
}