A fast implicit solver for semiconductor models in one space dimension
Abstract
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.
Cite
@article{arxiv.1906.04174,
title = {A fast implicit solver for semiconductor models in one space dimension},
author = {M. Paul Laiu and Zheng Chen and Cory D. Hauck},
journal= {arXiv preprint arXiv:1906.04174},
year = {2020}
}