An improved semi-Lagrangian time splitting spectral method for the semi-classical Schrödinger equation with vector potentials using NUFFT
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Publication:338533
DOI10.1016/j.apnum.2016.08.015zbMath1416.65380OpenAlexW2520347720MaRDI QIDQ338533
Yong Zhang, Zhennan Zhou, Zheng Ma
Publication date: 7 November 2016
Published in: Applied Numerical Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.apnum.2016.08.015
vector potentialnonuniform FFTsemi-classical Schrödinger equationsemi-Lagrangian time splitting method
Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Numerical methods for discrete and fast Fourier transforms (65T50) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)
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Cites Work
- Unnamed Item
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- The Gaussian wave packet transform: efficient computation of the semi-classical limit of the Schrödinger equation. II: Multidimensional case
- Numerical approximation of the Schrödinger equation with the electromagnetic field by the Hagedorn wave packets
- Splitting and composition methods for explicit time dependence in separable dynamical systems
- Computing the ground state and dynamics of the nonlinear Schrödinger equation with nonlocal interactions via the nonuniform FFT
- Superpositions and higher order Gaussian beams
- Gaussian beam methods for the Schrödinger equation in the semi-classical regime: Lagrangian and Eulerian formulations
- A new method of computation of wave fields using Gaussian beams
- Schrödinger operators with magnetic fields. I: General interactions
- Raising and lowering operators for semiclassical wave packets
- Multi-phase computations of the semiclassical limit of the Schrödinger equation and related problems: Whitham vs Wigner
- On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime
- A semi-Lagrangian time splitting method for the Schrödinger equation with vector potentials
- Gaussian beam formulations and interface conditions for the one-dimensional linear Schrödinger equation
- The Gaussian wave packet transform: efficient computation of the semi-classical limit of the Schrödinger equation. I: Formulation and the one dimensional case
- A level set method for the computation of multivalued solutions to quasi-linear hyperbolic PDEs and Hamilton-Jacobi equations
- Fast Gaussian wavepacket transforms and Gaussian beams for the Schrödinger equation
- Fast and Accurate Evaluation of Nonlocal Coulomb and Dipole-Dipole Interactions via the Nonuniform FFT
- Mathematical and computational methods for semiclassical Schrödinger equations
- Computing Semiclassical Quantum Dynamics with Hagedorn Wavepackets
- A Spectral Method of Characteristics for Hyperbolic Problems
- Fast Fourier Transforms for Nonequispaced Data
- Numerical Study of Time-Splitting Spectral Discretizations of Nonlinear Schrödinger Equations in the Semiclassical Regimes
- Computational high frequency wave propagation
- Accelerating the Nonuniform Fast Fourier Transform
- Error estimates for Gaussian beam superpositions
- Semi-Eulerian and High Order Gaussian Beam Methods for the Schrödinger Equation in the Semiclassical Regime
- Accurate and Efficient Numerical Methods for Computing Ground States and Dynamics of Dipolar Bose-Einstein Condensates via the Nonuniform FFT
