4.6 Article

Exponential Integrators Based on Discrete Gradients for Linearly Damped/Driven Poisson Systems

Journal

JOURNAL OF SCIENTIFIC COMPUTING
Volume 87, Issue 2, Pages -

Publisher

SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-021-01468-1

Keywords

Damped; driven Poisson system; Exponential integrator; Discrete gradient; Energy-preserving integrator; Structure-preserving integrator; 65L12; 65P10

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Exponential integrators based on discrete gradient methods are applied to non-canonical Hamiltonian systems with added linear forcing/damping terms, showing the ability to exactly preserve changes in dynamics in special circumstances. These methods are also symmetric, second order, and linearly stable, demonstrating advantages in accuracy and efficiency over other standard methods when applied to specific systems.
Exponential integrators based on discrete gradient methods are applied to non-canonical Hamiltonian systems with added linear forcing/damping terms, which may be time-dependent. Changes in the dynamics, such as conservation of energy or Casimirs, which result from inclusion of the linear forcing/damping terms, are not exactly preserved by standard discrete gradient methods. However, those changes are shown to be exactly preserved by the exponential integrators in special circumstances. The methods are also symmetric, second order, and linearly stable. To demonstrate advantages in both accuracy and efficiency over other standard methods, the exponential integrators are applied to a three dimensional Lotka-Volterra system and a damped/driven Ablowitz-Ladik system.

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