A novel domain decomposition framework for the ground state solution of Bose–Einstein condensates

Abstract

In this study, we present a new type of domain decomposition algorithm to obtain the ground state solution for Bose–Einstein condensates. Using our proposed algorithm, instead of directly solving the nonlinear eigenvalue problem, one only needs to solve a series of linear boundary value problems on a finite element space sequence using the domain decomposition method, and subsequently solve a small-scale nonlinear eigenvalue problem on an enriched space simultaneously. Because solving large-scale nonlinear eigenvalue problem directly is time intensive, our algorithm can obviously improve the efficiency of producing simulation for Bose–Einstein condensates. In addition, any domain decomposition algorithm for linear boundary value problems can be applied to our algorithm framework, which makes the algorithm considerably flexible. Two numerical experiments are presented in the paper to demonstrate the efficiency and scalability of our proposed algorithm.