Gauss-Seidel-type methods for energy states of a multi-component Bose-Einstein condensate
Journal of Computational Physics
Local spectral time splitting method for first- and second-order partial differential equations
Journal of Computational Physics
Simulating the deformation of vesicle membranes under elastic bending energy in three dimensions
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A mode elimination technique to improve convergence of iteration methods for finding solitary waves
Journal of Computational Physics
Two-grid discretization schemes for nonlinear Schrödinger equations
Journal of Computational and Applied Mathematics
Journal of Computational Physics
A minimisation approach for computing the ground state of Gross-Pitaevskii systems
Journal of Computational Physics
Numerical Simulations on Stationary States for Rotating Two-Component Bose-Einstein Condensates
Journal of Scientific Computing
An adaptive multigrid scheme for Bose-Einstein condensates in a periodic potential
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Applied Numerical Mathematics
Journal of Computational Physics
Journal of Computational Physics
Simulation of coherent structures in nonlinear Schrödinger-type equations
Journal of Computational Physics
Journal of Computational and Applied Mathematics
On the computation of ground state and dynamics of Schrödinger-Poisson-Slater system
Journal of Computational Physics
A New Sobolev Gradient Method for Direct Minimization of the Gross-Pitaevskii Energy with Rotation
SIAM Journal on Scientific Computing
Mathematics and Computers in Simulation
Journal of Computational Physics
Journal of Computational Physics
Operator splitting ADI schemes for pseudo-time coupled nonlinear solvation simulations
Journal of Computational Physics
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In this paper, we present a continuous normalized gradient flow (CNGF) and prove its energy diminishing property, which provides a mathematical justification of the imaginary time method used in the physics literature to compute the ground state solution of Bose--Einstein condensates (BEC). We also investigate the energy diminishing property for the discretization of the CNGF. Two numerical methods are proposed for such discretizations: one is the backward Euler centered finite difference (BEFD) method, the other is an explicit time-splitting sine-spectral (TSSP) method. Energy diminishing for BEFD and TSSP for the linear case and monotonicity for BEFD for both linear and nonlinear cases are proven. Comparison between the two methods and existing methods, e.g., Crank--Nicolson finite difference (CNFD) or forward Euler finite difference (FEFD), shows that BEFD and TSSP are much better in terms of preserving the energy diminishing property of the CNGF. Numerical results in one, two, and three dimensions with magnetic trap confinement potential, as well as a potential of a stirrer corresponding to a far-blue detuned Gaussian laser beam, are reported to demonstrate the effectiveness of BEFD and TSSP methods. Furthermore we observe that the CNGF and its BEFD discretization can also be applied directly to compute the first excited state solution in BEC when the initial data is chosen as an odd function.