Numerical Analysis of DAEs from Coupled Circuit and Semiconductor Simulation

Monica Selva Soto , Caren Tischendorf

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976),

MSC 2000

65M12 Stability and convergence of numerical methods

65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods

Abstract
In this work we are interested in the numerical solution of a coupled model of differential algebraic equations (DAEs) and partial differential equations (PDEs). The DAEs describe the behavior of an electrical circuit that contains semiconductor devices and the partial differential equations constitute drift-diffusion equations modeling the semiconductor devices in the circuit. After space discretization using a finite element method, the coupled system results in a differential-algebraic system with a properly stated leading term. We investigate the structure and the properties of this DAE system. In particular, we develop structural criteria for the DAE index. This is of basic interest since DAE properties like stability, existence and uniqueness of solutions depend strongly on its index.