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Modular Algorithms for Transient Semiconductor Device Simulation

#### By: William Coughran and Joseph W. Jerome

An outer iteration, based upon linearization, is introduced at
discrete time steps for the one-dimensional semiconductor device model.
The iteration depends upon solving the semidiscrete device equations
approximately, specifically, in such a way that the residual is of the order
of the time step in an appropriate norm.
It is shown that this maintains the order of the backward Euler method.
A monitoring of the constants, including time-step
requirements for solvability of the semidiscrete systems, as well as
boundedness, smoothness and invertibility for the maps defining
the Newton approximations, is carried out.
An invariant-region principle provides an important theoretical basis,
and a novel proof is provided.
An essential component of the theory, providing the interface
with the sequel to this paper, is that the Newton iterations are small
in number, typically one or two, and may be realized as approximate
Newton iterations.
Continuation is employed as the time-stepping bridge

This paper appeared in:
Lectures in Applied Mathematics 25 (R. E. Bank,
editor), American Mathematical Society, Providence (1990), 107--149.

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