DeepAI
Log In Sign Up

Symplectic GARK methods for Hamiltonian systems

03/06/2021
by   Michael Günther, et al.
0

Generalized Additive Runge-Kutta schemes have shown to be a suitable tool for solving ordinary differential equations with additively partitioned right-hand sides. This work generalizes these GARK schemes to symplectic GARK schemes for additively partitioned Hamiltonian systems. In a general setting, we derive conditions for symplecticeness, as well as symmetry and time-reversibility. We show how symplectic and symmetric schemes can be constructed based on schemes which are only symplectic. Special attention is given to the special case of partitioned schemes for Hamiltonians split into multiple potential and kinetic energies. Finally we show how symplectic GARK schemes can use efficiently different time scales and evaluation costs for different potentials by using different order for these parts.

READ FULL TEXT

page 1

page 2

page 3

page 4

08/26/2019

Partitioned Exponential Methods for Coupled Multiphysics Systems

Multiphysics problems involving two or more coupled physical phenomena a...
12/02/2019

Efficient implementation of partitioned stiff exponential Runge-Kutta methods

Multiphysics systems are driven by multiple processes acting simultaneou...
09/03/2019

High-order partitioned spectral deferred correction solvers for multiphysics problems

We present an arbitrarily high-order, conditionally stable, partitioned ...
01/07/2020

Inter/extrapolation-based multirate schemes – a dynamic-iteration perspective

Multirate behavior of ordinary differential equations (ODEs) and differe...
12/02/2019

A general symplectic integrator for canonical Hamiltonian systems

The focus of this paper is to recommend a novel symplectic scheme for ca...
07/14/2022

Learning port-Hamiltonian systems – algorithms

In this article we study the possibilities of recovering the structure o...
07/15/2020

On the benchmarking of partitioned real-time systems

Avionic software is the subject of critical real time, determinism and s...