Geometric exponential integrators

DOI10.1016/j.jcp.2019.01.005zbMath1451.37107arXiv1703.00929OpenAlexW2964160231WikidataQ115571394 ScholiaQ115571394MaRDI QIDQ2214573

Melvin Leok, Xuefeng Shen

Publication date: 9 December 2020

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1703.00929

zbMATH Keywords

Hamiltonian systemssymplectic integratorsgeometric integratorsexponential integratorshighly oscillatory problems

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15)

Related Items (15)

A linearly implicit energy-preserving exponential integrator for the nonlinear Klein-Gordon equation ⋮ A new symmetric linearly implicit exponential integrator preserving polynomial invariants or Lyapunov functions for conservative or dissipative systems ⋮ Efficient energy-preserving exponential integrators for multi-component Hamiltonian systems ⋮ Energy-Preserving Continuous-Stage Exponential Runge--Kutta Integrators for Efficiently Solving Hamiltonian Systems ⋮ A new SOR-type iteration method for solving linear systems ⋮ Two novel conservative exponential relaxation methods for the space-fractional nonlinear Schrödinger equation ⋮ High-order linearly implicit schemes conserving quadratic invariants ⋮ Compact exponential energy-preserving method for the Schrödinger equation in the semiclassical regime ⋮ Mass- and energy-preserving exponential Runge-Kutta methods for the nonlinear Schrödinger equation ⋮ Explicit high-order energy-preserving exponential time differencing method for nonlinear Hamiltonian PDEs ⋮ Exponential integrators based on discrete gradients for linearly damped/driven Poisson systems ⋮ High-order linearly implicit structure-preserving exponential integrators for the nonlinear Schrödinger equation ⋮ Exponential integrator preserving mass boundedness and energy conservation for nonlinear Schrödinger equation ⋮ Adaptive Hamiltonian Variational Integrators and Applications to Symplectic Accelerated Optimization ⋮ A new class of structure-preserving stochastic exponential Runge-Kutta integrators for stochastic differential equations

Uses Software

• Matlab

Cites Work

• Long-term analysis of numerical integrators for oscillatory Hamiltonian systems under minimal non-resonance conditions
• Poisson schemes for Hamiltonian systems on Poisson manifolds
• Exponential Runge-Kutta methods for parabolic problems.
• Exponential integrators
• Simulating Hamiltonian Dynamics
• Discrete mechanics and variational integrators
• Theoretical Numerical Analysis
• Discrete gradient methods for solving ODEs numerically while preserving a first integral
• Spectral Methods in MATLAB
• Numerical long-time energy conservation for the nonlinear Schrödinger equation
• Geometric Numerical Integration

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