Some applications of semi-discrete variational integrators to classical field theories

TL;DR

This paper introduces a semi-discrete variational integrator framework for classical field theories, emphasizing geometric preservation and numerical integration advantages.

Contribution

It develops a semi-discrete variational mechanics approach specifically tailored for classical field theories, enhancing geometric structure preservation in numerical methods.

Findings

Preserves geometric properties in numerical simulations

Provides a new semi-discrete variational integrator framework

Applicable to classical field theory simulations

Abstract

We develop a semi-discrete version of discrete variational mechanics with applications to numerical integration of classical field theories. The geometric preservation properties are studied.