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Numerical analysis of DAEs from coupled circuit and semiconductor simulation. (English) Zbl 1073.65094
The paper is devoted to the problem of numerical solving a system of differential-algebraic equatins (DAEs) and partial differential equations (PDEs) that present an electrical circuit containing semiconductor devices. The desired functions are node potentials, currents through inductors, currents through voltage sources that are functions of time and are connected by ordinary DAE, as well as semiconductor’s electrostatic potential, densities of electrons and holes that depend on time and one space variable. The last three objects are connected by PDEs consisting of the Poisson equation and continuity equations (drift-diffusion equations). The DAEs and PDEs systems are connected by boundary conditions of the potential. The Poisson equation can be replaced by the equivalent energy conservation equation.
The investigated numerical method is the semi-discretization of the PDEs on the spatial variable. The resulting system is an ordinary DAE with properly stated leading term. The main results of the paper are three theorems that present structural criteria of the circuits which provides to the differentiation index of system of value 1 or 2.

MSC:
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
65L80 Numerical methods for differential-algebraic equations
35Q60 PDEs in connection with optics and electromagnetic theory
82D37 Statistical mechanics of semiconductors
34A09 Implicit ordinary differential equations, differential-algebraic equations
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
Software:
WIAS-TeSCA
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References:
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