NLSEmagic: Nonlinear Schrödinger equation multi-dimensional Matlab-based GPU-accelerated integrators using compact high-order schemes

Caplan, Ronald M.

doi:10.1016/j.cpc.2012.12.010

Cited by 24 publications

(23 citation statements)

References 32 publications

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“…The previous GPE equations can be solved numerically without difficulty using readily available sequential Fortran codes [50] or OpenMP-parallelized C codes [51] which implement Crank-Nicolson methods, but other numerical approaches are also available [52][53][54][55][56][57]. However, for analytical insights into the dynamics of the condensate, such numerical calculations are usually accompanied by variational or hydrodynamical approaches [2].…”

Section: Variational Treatment Of the Gross-pitaevskii Equationmentioning

confidence: 99%

Faraday waves in collisionally inhomogeneous Bose-Einstein condensates

et al. 2014

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We study the emergence of Faraday waves in cigar-shaped collisionally inhomogeneous BoseEinstein condensates subject to periodic modulation of the radial confinement. Considering a Gaussian-shaped radially inhomogeneous scattering length, we show through extensive numerical simulations and detailed variational treatment that the spatial period of the emerging Faraday waves increases as the inhomogeneity of the scattering length gets weaker, and that it saturates once the width of the radial inhomogeneity reaches the radial width of the condensate. In the regime of strongly inhomogeneous scattering lengths, the radial profile of the condensate is akin to that of a hollow cylinder, while in the weakly inhomogeneous case the condensate is cigar-shaped and has a Thomas-Fermi radial density profile. Finally, we show that when the frequency of the modulation is close to the radial frequency of the trap, the condensate exhibits resonant waves which are accompanied by a clear excitation of collective modes, while for frequencies close to twice that of the radial frequency of the trap, the observed Faraday waves set in forcefully and quickly destabilize condensates with weakly inhomogeneous two-body interactions.

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Section: Variational Treatment Of the Gross-pitaevskii Equationmentioning

confidence: 99%

Faraday waves in collisionally inhomogeneous Bose-Einstein condensates

et al. 2014

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“…While there are numerous numerical methods that can be used to simulate solutions to the NLSE, we perform the simulations using the code package NLSEmagic 1 [16] which uses the fourth-order-in-time Runge-Kutta method with either a secondorder central difference (RK4+CD) or a two-step high-order compact fourth-order central-differencing-in-space (RK4+2SHOC) scheme [18] (all simulations in this paper are performed using the RK4+2SHOC scheme).…”

Section: Numerical Resultsmentioning

confidence: 99%

A Modulus-Squared Dirichlet Boundary Condition for Time-Dependent Complex Partial Differential Equations and Its Application to the Nonlinear Schrödinger Equation

Caplan¹,

Carretero-González²

2014

SIAM J. Sci. Comput.

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Abstract. An easy to implement modulus-squared Dirichlet (MSD) boundary condition is formulated for numerical simulations of time-dependent complex partial differential equations in multidimensional settings. The MSD boundary condition approximates a constant modulus-squared value of the solution at the boundaries and is defined as 1. Introduction. When utilizing numerical methods to approximate the solutions to time-dependent partial differential equations (PDEs), proper handling of boundary conditions can be quite challenging. Sometimes, an otherwise stable numerical scheme will become unstable depending on how the boundary conditions are computed [42]. In addition, high-order schemes can degrade in accuracy to lower order when using boundary conditions which are not compatible with the high-order accuracy [26]. Proper handling of boundary conditions in higher-order schemes, especially in high-order compact schemes, can be even more of a challenge [19,20].Often, researchers will forgo a complicated boundary condition implementation and instead use tried-and-true boundary condition techniques which are very simple yet provide acceptable results. One of the most common is the use of Dirichlet boundary conditions when simulating solutions which decay towards zero at infinity, and where most of the dynamics (or "action") is expected to remain in the central regions of the computational grid. Another simple method in such cases is to use periodic boundary conditions.Infinite-domain problems involving PDEs whose function values are complex cannot, in general, make use of numerical Dirichlet or periodic boundary conditions because of the oscillation of the real and imaginary parts of the function due to the intrinsic frequency of the system. (In cases when both the real and imaginary parts of the solution converge to a constant at infinity, such boundary conditions can be

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“…The image was divided into 32 × 32 (1024 domains) domain matrix in the block. 20 Hence, the conventional OSEM was modified in order to perform the iteration at each individual area without an overlap. The matrix number of the reconstructed image was 96 × 96 with a 30 × 30 cm field of view (FOV).…”

Section: Methodsmentioning

confidence: 99%