Convergence analysis of a partial differential algebraic system from coupling a semiconductor model to a circuit model

Convergence analysis of a partial differential algebraic system from coupling a semiconductor model to a circuit model: "Publication year: 2010
Source: Applied Numerical Mathematics, In Press, Accepted Manuscript, Available online 12 November 2010
Michael, Matthes , Caren, Tischendorf
We are interested in circuit simulation including distributed semiconductor models. The circuit itself is modeled by the modified nodal analysis. The stationary drift diffusion equations are used to describe the semiconductors. The complete system is then a partial differential-algebraic system. We discretize it first in space with finite elements and the Scharfetter-Gummel discretization. The resulting semi-discrete system can be analyzed as a differential-algebraic equation with properly stated leading term. We present topological index one criteria. They coincide with previous results for the non-discretized partial differential-algebraic equation. For the time discretization we use standard BDF methods (implicit Gear formulas). Finally we..."