A novel, structure-preserving, second-order-in-time relaxation scheme for Schrödinger-Poisson systems

DOI10.1016/j.jcp.2023.112307arXiv2103.04903OpenAlexW4381548669MaRDI QIDQ6173338

Stephen Metcalfe, Irene Kyza, Theodoros Katsaounis, Agissilaos G. Athanassoulis

Publication date: 21 July 2023

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

Full work available at URL: https://arxiv.org/abs/2103.04903

zbMATH Keywords

finite element methodSchrödinger-Poisson systemenergy preserving schemerelaxation scheme in time

Mathematics Subject Classification ID

Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Partial differential equations of mathematical physics and other areas of application (35Qxx) General mathematical topics and methods in quantum theory (81Qxx)

Cites Work

• Unnamed Item
• Unnamed Item
• On the computation of ground state and dynamics of Schrödinger-Poisson-Slater system
• A compact split-step finite difference method for solving the nonlinear Schrödinger equations with constant and variable coefficients
• Solving highly-oscillatory NLS with SAM: numerical efficiency and long-time behavior
• A Fourier spectral-discontinuous Galerkin method for time-dependent 3-D Schrödinger-Poisson equations with discontinuous potentials
• Conservation of phase space properties using exponential integrators on the cubic Schrödinger equation
• Finite-difference solutions of a non-linear Schrödinger equation
• On fully discrete Galerkin methods of second-order temporal accuracy for the nonlinear Schrödinger equation
• Discrete Schrödinger-Poisson systems preserving energy and mass
• Derivation of the Schrödinger-Poisson equation from the quantum \(N\)-body problem
• A numerical scheme based on radial basis function finite difference (RBF-FD) technique for solving the high-dimensional nonlinear Schrödinger equations using an explicit time discretization: Runge-Kutta method
• Numerical solution of the Gross--Pitaevskii equation for Bose--Einstein condensation
• Numerical simulation of nonlinear Schrödinger systems: A new conservative scheme
• DMLPG method for numerical simulation of soliton collisions in multi-dimensional coupled damped nonlinear Schrödinger system which arises from Bose-Einstein condensates
• Structure-preserving Gauss methods for the nonlinear Schrödinger equation
• From optics to dark matter: a review on nonlinear Schrödinger-Poisson systems
• Efficiency of exponential time differencing schemes for nonlinear Schrödinger equations
• Fast calculation of energy and mass preserving solutions of Schrödinger-Poisson systems on unbounded domains
• Effective one particle quantum dynamics of electrons: a numerical study of the Schrödinger-Poisson-X\(_\alpha\) model
• On the convergence of a linear two-step finite element method for the nonlinear Schrödinger equation
• On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations
• The Gaussian Beam Methods for Schrödinger-Poisson Equations
• deal.II—A general-purpose object-oriented finite element library
• The three-dimensional wigner-poisson problem: Existence, uniqueness and approximation
• An analytical approach to the Schrödinger-Newton equations
• A Space-Time Finite Element Method for the Nonlinear Schrödinger Equation: The Continuous Galerkin Method
• Global existence, uniqueness and asymptotic behaviour of solutions of the Wigner–Poisson and Schrödinger‐Poisson systems
• L² Solutions to the Schrödinger–Poisson System: Existence, Uniqueness, Time Behaviour, and Smoothing Effects
• A space-time finite element method for the nonlinear Schrödinger equation: the discontinuous Galerkin method
• Numerical Approximation of Blow-Up of Radially Symmetric Solutions of the Nonlinear Schrödinger Equation
• A Relaxation Scheme for the Nonlinear Schrödinger Equation
• The limit from the Schrödinger‐Poisson to the Vlasov‐Poisson equations with general data in one dimension
• Convergence Analysis of High-Order Time-Splitting Pseudospectral Methods for Nonlinear Schrödinger Equations
• Energy-preserving methods for nonlinear Schrödinger equations
• Error estimation of the Besse Relaxation Scheme for a semilinear heat equation
• High Order Exponential Integrators for Nonlinear Schrödinger Equations with Application to Rotating Bose--Einstein Condensates
• Convergence of a Strang splitting finite element discretization for the Schrödinger–Poisson equation
• Optimal Error Estimates of Compact Finite Difference Discretizations for the Schrödinger-Poisson System
• ON AN OPEN TRANSIENT SCHRÖDINGER–POISSON SYSTEM
• Error Estimates for Galerkin Approximations to the Periodic Schrödinger‐Poisson System
• A Posteriori Error Analysis for Evolution Nonlinear Schrödinger Equations up to the Critical Exponent
• A variational approach to the Schrödinger-Poisson system: asymptotic behaviour, breathers, and stability

This page was built for publication: A novel, structure-preserving, second-order-in-time relaxation scheme for Schrödinger-Poisson systems