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A hybrid discontinuous Galerkin method for computing the ground state solution of Bose-Einstein condensates. (English) Zbl 1250.81040

Summary: A numerical method for computing the ground state solution of Bose-Einstein condensates modeled by the Gross-Pitaevskii equation is presented. In this method, the three-dimensional computational domain is divided into hexahedral elements in which the solution is approximated by a sum of basis functions. Both polynomial and plane wave bases are considered for this purpose, and Lagrange multipliers are introduced to weakly enforce the interelement continuity of the solution. The ground state is computed by an iterative procedure for minimizing the energy. The performance results obtained for several numerical experiments demonstrate that the proposed method is more computationally efficient than similar solution approaches based on the standard higher-order finite element method.

MSC:

81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35Q55 NLS equations (nonlinear Schrödinger equations)
82B26 Phase transitions (general) in equilibrium statistical mechanics
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