Second order conformal symplectic schemes for damped Hamiltonian systems

DOI10.1007/s10915-015-0062-zzbMath1377.65165OpenAlexW2280533987MaRDI QIDQ2398483

Dwayne Floyd, Brian E. Moore, Ashish Bhatt

Publication date: 16 August 2017

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-015-0062-z

zbMATH Keywords

algorithmstabilityHamiltonian systemsfinite differencenumerical experimentStörmer-Verlet methodimplicit midpoint methodlinear dampingconformal symplecticstructure-preserving methoddissipation preservation

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15)

Related Items (20)

A Dissipation-Preserving Integrator for Damped Oscillatory Hamiltonian Systems ⋮ Reduced-order modeling for Ablowitz-Ladik equation ⋮ Conformal structure‐preserving schemes for damped‐driven stochastic nonlinear Schrödinger equation with multiplicative noise ⋮ Conformal structure‐preserving method for two‐dimensional damped nonlinear fractional Schrödinger equation ⋮ Friction-adaptive descent: a family of dynamics-based optimization methods ⋮ Structure-preserving combined high-order compact schemes for multiple order spatial derivatives differential equations ⋮ Dissipation-preserving spectral element method for damped seismic wave equations ⋮ Structure-preserving integrators for dissipative systems based on reversible– irreversible splitting ⋮ Exponential integrators preserving local conservation laws of PDEs with time-dependent damping/driving forces ⋮ Modelling damped acoustic waves by a dissipation-preserving conformal symplectic method ⋮ A Conformal Energy-Conserved Method for Maxwell’s Equations with Perfectly Matched Layers ⋮ Geometric-integration tools for the simulation of musical sounds ⋮ Structure-preserving Exponential Runge--Kutta Methods ⋮ Exponential integrators based on discrete gradients for linearly damped/driven Poisson systems ⋮ Projected exponential Runge-Kutta methods for preserving dissipative properties of perturbed constrained Hamiltonian systems ⋮ Asymptotic analysis of a structure-preserving integrator for damped Hamiltonian systems ⋮ On dissipative symplectic integration with applications to gradient-based optimization ⋮ Stochastic conformal schemes for damped stochastic Klein-Gordon equation with additive noise ⋮ Conformal symplectic and relativistic optimization ⋮ Structure-preserving deep learning

Cites Work

• Unnamed Item
• Unnamed Item
• Multi-symplectic Birkhoffian structure for PDEs with dissipation terms
• Geometric integration of Hamiltonian systems perturbed by Rayleigh damping
• Conformal multi-symplectic integration methods for forced-damped semi-linear wave equations
• Finite dimensional exponential attractors for semilinear wave equations with damping
• Multisymplectic box schemes and the Korteweg-de Vries equation.
• Finite difference schemes for \(\frac{\partial u}{\partial t}=(\frac{\partial}{\partial x})^\alpha\frac{\delta G}{\delta u}\) that inherit energy conservation or dissipation property
• Conformal conservation laws and geometric integration for damped Hamiltonian PDEs
• What kinds of dynamics are there? Lie pseudogroups, dynamical systems and geometric integration
• Splitting methods
• Structure-preserving algorithms for Birkhoffian systems
• Structure-preserving algorithms for Birkhoffian systems
• On the formulation of high-frequency dissipative time-stepping algorithms for nonlinear dynamics. I: Low-order methods for two model problems and nonlinear elastodynamics
• Dissipative or conservative finite-difference schemes for complex-valued nonlinear partial differential equations
• On the formulation of high-frequency dissipative time-stepping algorithms for nonlinear dynamics. II: Second-order methods.
• Conformal Hamiltonian systems

This page was built for publication: Second order conformal symplectic schemes for damped Hamiltonian systems