A minimizing-movements approach to GENERIC systems

TL;DR

This paper introduces a variational time discretization scheme tailored for GENERIC systems, ensuring stability and convergence, with demonstrated implementation on the damped harmonic oscillator and supporting numerical results.

Contribution

A novel variational discretization scheme for GENERIC systems that guarantees stability and convergence, specifically applied to the damped harmonic oscillator.

Findings

Scheme is stable and convergent for GENERIC systems

Successfully implemented for the damped harmonic oscillator

Numerical experiments confirm the method's effectiveness

Abstract

We present a new time discretization scheme adapted to the structure of GENERIC systems. The scheme is variational in nature and is based on a conditional incremental minimization. The GENERIC structure of the scheme provides stability and convergence of the scheme. We prove that the scheme can be rigorously implemented in the case of the damped harmonic oscillator. Numerical evidence is collected, illustrating the performance of the method.