Generalized Finite-Difference Time-Domain method with absorbing boundary conditions for solving the nonlinear Schrodinger equation on a GPU

Explicit absorbing boundary conditions (ABCs) are presented for the recently developed Generalized Finite-Difference Time-Domain (G-FDTD) method for solving the nonlinear Schrodinger equation so that the method can be used for unbounded domains when the analytical solution along the boundary is unknown. The ABC scheme results from the Box-like discretization of Engquist-Majda one-way wave equations. Using the energy-weighted wave-number parameter selection method, the ABCs are made to be adaptive. By simulating the impact of solitons onto the computational boundary, the reflection coefficient is numerically shown to be function of the incoming soliton's wave number and other simulation parameters. Furthermore, a parallelized algorithm is developed for implementing the G-FDTD method with ABCs. The algorithm, when implemented on a GPU, is shown to give a 200-times speedup for large simulations as compared with a CPU. Examples are given to show the applicability of the algorithm. (C) 2018 Elsevier B.V. All rights reserved.