Perfectly matched layer for computing the dynamics of nonlinear Schrödinger equations by pseudospectral methods. Application to rotating Bose-Einstein condensates

Abstract

In this paper, we first propose a general strategy to implement the Perfectly Matched Layer (PML) approach in the most standard numerical schemes used for simulating the dynamics of nonlinear Schrödinger equations. The methods are based on the time-splitting Bao et al. (2003)[15] or relaxation Besse (2004)[24] schemes in time, and FFT-based pseudospectral discretization method in space. A thorough numerical study is developed for linear and nonlinear problems to understand how the PML approach behaves (absorbing function and tuning parameters) for a given scheme. The extension to the rotating Gross-Pitaevskii equation is then proposed by using the rotating Lagrangian coordinates transformation method Antonelli et al. (2012), Bao et al. (2013), García-Ripoll et al. (2001)[13,16,38], some numerical simulations illustrating the strength of the proposed approach.