Arbitrarily high-order structure-preserving schemes for the Gross-Pitaevskii equation with angular momentum rotation

In this paper, we design a novel class of arbitrarily high-order structure-preserving numerical schemes for the time-dependent Gross-Pitaevskii equation with angular momentum rotation. Based on the idea of the scalar auxiliary variable approach which is proposed in the recent papers [J. Comput. Phys., 353 (2018) 407-416 and SIAM Rev., 61(2019) 474-506] for developing energy stable schemes for gradient flow systems, we firstly reformulate the Gross-Pitaevskii equation into an equivalent system with a modified energy conservation law. The reformulated system is then discretized by the Gauss collocation method in time and the standard Fourier pseudo-spectral method in space, respectively. We show that the proposed schemes can preserve the discrete mass and modified energy exactly. Numerical results are addressed to verify the efficiency and high-order accuracy of the proposed schemes. (C) 2020 Elsevier B.V. All rights reserved.

Automated summary

In this paper, a novel class of high-order structure-preserving numerical schemes for the time-dependent Gross-Pitaevskii equation with angular momentum rotation is designed. The schemes are shown to accurately preserve discrete mass and modified energy, and numerical results confirm their efficiency and high-order accuracy.