Ground-state solution of Bose--Einstein condensate by directly minimizing the energy functional
Journal of Computational Physics
Numerical solution of the Gross--Pitaevskii equation for Bose--Einstein condensation
Journal of Computational Physics
Numerical methods for the generalized Zakharov system
Journal of Computational Physics
An efficient and stable numerical method for the Maxwell-Dirac system
Journal of Computational Physics
Numerical simulation of a generalized Zakharov system
Journal of Computational Physics
Gauss-Seidel-type methods for energy states of a multi-component Bose-Einstein condensate
Journal of Computational Physics
A time-splitting spectral scheme for the Maxwell-Dirac system
Journal of Computational Physics
A Time-Splitting Spectral Method for the Generalized Zakharov System in Multi-Dimensions
Journal of Scientific Computing
Journal of Computational Physics
Journal of Computational Physics
A semiclassical transport model for two-dimensional thin quantum barriers
Journal of Computational Physics
A perfectly matched layer approach to the nonlinear Schrödinger wave equations
Journal of Computational Physics
Two-grid discretization schemes for nonlinear Schrödinger equations
Journal of Computational and Applied Mathematics
Numerical computations for long-wave short-wave interaction equations in semi-classical limit
Journal of Computational Physics
Journal of Computational Physics
Numerical solution to coupled nonlinear Schrödinger equations on unbounded domains
Mathematics and Computers in Simulation
Journal of Computational and Applied Mathematics
On the computation of ground state and dynamics of Schrödinger-Poisson-Slater system
Journal of Computational Physics
Journal of Computational Physics
A convergent 2D finite-difference scheme for the Dirac-Poisson system and the simulation of graphene
Journal of Computational Physics
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In this paper we study the performance of time-splitting spectral approximations for general nonlinear Schrödinger equations (NLS) in the semiclassical regimes, where the Planck constant $\varepsilon$ is small. The time-splitting spectral approximation under study is explicit, unconditionally stable and conserves the position density in L^1. Moreover it is time-transverse invariant and time-reversible when the corresponding NLS is. Extensive numerical tests are presented for weak/strong focusing/defocusing nonlinearities, for the Gross--Pitaevskii equation, and for current-relaxed quantum hydrodynamics. The tests are geared towards the understanding of admissible meshing strategies for obtaining "correct" physical observables in the semiclassical regimes. Furthermore, comparisons between the solutions of the NLS and its hydrodynamic semiclassical limit are presented.