A discrete gradient scheme for preserving QSR-dissipativity

TL;DR

This paper introduces a class of structure-preserving discrete gradient schemes designed to maintain the dissipative properties of nonlinear systems with quadratic supply rates during numerical simulations.

Contribution

The paper proposes a novel discrete gradient scheme that preserves QSR-dissipativity in numerical discretizations of nonlinear systems.

Findings

The scheme effectively maintains dissipative properties in simulations.

Numerical experiments demonstrate improved energy behavior.

The method applies to a specific class of dissipative systems.

Abstract

The notion of dissipative dynamical systems provides a formal description of processes that cannot generate energy internally. For these systems, changes in energy can only occur due to an external energy supply or dissipation effects. Unfortunately, dissipative properties tend to deteriorate in numerical computations, especially in nonlinear systems. Discrete gradient methods can help mitigate this problem. In this paper, we present a class of structure-preserving time discretization schemes based on discrete gradients for a special class of systems that are dissipative with respect to a quadratic supply rate.