Numerical Simulation Of The Ground State Of A Bose-Einstein Condensate With Impurities

In this paper,the normalized gradient flow and the preconditioned conjugate gradient method(PCG)are developed to compute ground states of the BEC-impurity model,thus new physical phenomenon are found based on the application of them.The key points of the paper include two aspects: on one hand,since the impurities only localised in a small domain which contains several vortices of the BECs,two imbedded meshes and the DST discrete technique are applied to discrete the wave functions of the BEC and impurities,respectively.As a result,the computational cost is greatly reduced.On the other hand,the preconditioned conjugate gradient method is designed to further improve the efficiency of computing ground states of the BEC-impurity system.A large number of numerical results are given to test the feasibility of the two numerical methods,compare their efficiency,and demonstrate a series of properies of ground states and corresponding physical phenomenon.