A fast implicit solver for semiconductor models in one space dimension

JOURNAL OF COMPUTATIONAL PHYSICS

卷:417

Article

Laiu, M. Paul¹  Chen, Zheng²  Hauck, Cory D.¹ 

[1] Oak Ridge Natl Lab, Comp Sci & Math Div, Computat & Appl Math Grp, Oak Ridge, TN 37831 USA

[2] Univ Massachusetts, Dept Math, 285 Old Westport Rd, Dartmouth, MA 02747 USA

关键词: Semiconductor Boltzmann equation;    Boltzmann-Poisson systems;    Drift-diffusion limit;    Domain decomposition;    Synthetic acceleration;    Preconditioner;   

DOI  :  10.1016/j.jcp.2020.109567

来源: Elsevier

【 摘 要 】

Several different approaches are proposed for solving fully implicit discretizations of a simplified Boltzmann-Poisson system with a linear relaxation-type collision kernel. This system models the evolution of free electrons in semiconductor devices under a low-density assumption. At each implicit time step, the discretized system is formulated as a fixed-point problem, which can then be solved with a variety of methods. A key algorithmic component in all the approaches considered here is a recently developed sweeping algorithm for Vlasov-Poisson systems. A synthetic acceleration scheme has been implemented to accelerate the convergence of iterative solvers by using the solution to a drift-diffusion equation as a preconditioner. The performance of four iterative solvers and their accelerated variants has been compared on problems modeling semiconductor devices with various electron mean-free-path. Published by Elsevier Inc.

【 授权许可】

Free