GPU-accelerated solutions of the nonlinear Schrödinger equation for simulating 2D spinor BECs

Abstract

As a first approximation beyond linearity, the nonlinear Schrödinger equation reliably describes a broad class of physical systems. Though numerical solutions of this model are well-established, these methods can be computationally complex, especially when system-specific details are incorporated. In this paper, we demonstrate how numerical computations that exploit the features of a graphics processing unit (GPU) result in 40-70× reduction in the time for solutions (depending on hardware details). As a specific case study, we investigate the Gross-Pitaevskii equation, a specific version of the nonlinear Schrödinger model, as it describes a trapped, interacting two-component Bose-Einstein condensate subject to spatially dependent interspin coupling, resulting in an analog to a spin-Hall system. This computational method allows us to probe high-resolution spatial features -revealing an interaction dependent phase transition -all in a reasonable amount of time with readily available hardware.

GPU-accelerated time integration of Gross-Pitaevskii equation with discrete exterior calculus

“…The independent nature of a time integration step of an individual grid vertex, makes the method ideal for the massively parallel computing model [21]. In [22], [23], [24], and [25], general-purpose GPU computing (GPGPU) [26] has been utilized for solving the non-linear Schrödinger equation with promising results. Though this has only been done using Cartesian spatial discretization and in many cases by utilizing a ready-made linear algebra library.…”