Linear Reduction and Homotopy Control for Steady
Drift-Diffusion Systems in Narrow Convex Domains
By: Joseph W. Jerome
This article develops and applies results, originally introduced in
earlier work, for the existence of homotopy curves, terminating
at a desired solution.
We describe the principal hypotheses and results in section two;
right inverse approximation is at the core of the theory.
We apply this theory in section three
to the basic drift-diffusion equations.
The carrier densities are not
assumed to satisfy Boltzmann statistics and the Einstein relations are
not assumed. By proving the existence of the homotopy curve, we validate
the underlying
computational
framework of a predictor/corrector scheme, where the corrector utilizes an
approximate Newton method.
The analysis depends on the assumption of
domains of narrow width. However, no assumption is made regarding the
domain diameter.
The article appears in arXiv:2412.01918 [math.NA],
and is subject to the following license:
https://creativecomments.org/licenses/by/4.0
It can be viewed directly in the following format: