Search results for "Numerical-solution"
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Three-dimensional splitting dynamics of giant vortices in Bose-Einstein condensates
2018
We study the splitting dynamics of giant vortices in dilute Bose-Einstein condensates by numerically integrating the three-dimensional Gross-Pitaevskii equation in time. By taking advantage of tetrahedral tiling in the spatial discretization, we decrease the error and increase the reliability of the numerical method. An extensive survey of vortex splitting symmetries is presented for different aspect ratios of the harmonic trapping potential. The symmetries of the splitting patterns observed in the simulated dynamics are found to be in good agreement with predictions obtained by solving the dominant dynamical instabilities from the corresponding Bogoliubov equations. Furthermore, we observe…
Spectral approach to D-bar problems
2017
We present the first numerical approach to D-bar problems having spectral convergence for real analytic, rapidly decreasing potentials. The proposed method starts from a formulation of the problem in terms of an integral equation that is numerically solved with Fourier techniques. The singular integrand is regularized analytically. The resulting integral equation is approximated via a discrete system that is solved with Krylov methods. As an example, the D-bar problem for the Davey-Stewartson II equations is considered. The result is used to test direct numerical solutions of the PDE.© 2017 Wiley Periodicals, Inc.