Multiscale Analysis and Computation for a Stationary Schrödinger--Poisson System in Heterogeneous Nanostructures
Lei Zhang, Liqun Cao, Jianlan Luo · Multiscale Modeling and Simulation · 2014
This paper discusses the multiscale analysis and computation of a stationary Schrödinger--Poisson system with rapidly oscillating discontinuous coefficients arising from the modeling of a heterogeneous nanostructure with a periodic microstructure. The multiscale asymptotic expansions of the solutions for the above nonlinear equations are presented, and the convergence result with an explicit rate is derived. The efficient numerical method based on the multiscale asymptotic expansions is advanced. Numerical simulations are then carried out to validate the above theoretical results. The physical model used to describe the low-dimensional nanometer-sized systems will be introduced in an appendix.