Multi-Conformal-Symplectic Pdes And Discretizations

Keywords

Conformal symplectic; Multi-symplectic PDE; Structure-preserving algorithm

Abstract

Past work on integration methods that preserve a conformal symplectic structure focuses on Hamiltonian systems with weak linear damping. In this work, systems of PDEs that have conformal symplectic structure in time and space are considered, meaning conformal symplecticity is fully generalized for PDEs. Using multiple examples, it is shown that PDEs with this particular structure have interesting applications. What it means to preserve a multi-conformal-symplectic conservation law numerically is explained, along with presentation of two numerical methods that preserve such properties. Then, the advantages of the methods are briefly explored through applications to linear equations, consideration of momentum and energy dissipation, and backward error analysis. Numerical simulations for two PDEs illustrate the properties of the methods, as well as the advantages over other standard methods.

Publication Date

10-15-2017

Publication Title

Journal of Computational and Applied Mathematics

Volume

323

Number of Pages

1-15

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.cam.2017.04.008

Socpus ID

85018642569 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85018642569

This document is currently not available here.

Share

COinS