Mixed Finite Element Discretization of Continuity Equations Arising in Semiconductor Device Simulation

Summary

In the wake of decoupling and linearization semiconductor device simulation based on van Roosbroecks’s equations requires the solution of convection—diffusion equations. It is well known that due to the occurrence of local regions of strong convection standard discretizations do not behave properly. As an alternative among others, mixed methods have been suggested having their roots in the dual variational formulation of the convection—diffusion problem. Their efficient implementation has to make use of Lagrangian multipliers. In a novel approach we already introduce the multiplier prior to discretizing, through a process called hybridization. In the sequel we use the resulting variational problem to develop a new discretization scheme. Next, we outline how to implement a standard mixed scheme and investigate some of its aspects. Finally, the behaviour of the mixed method is illustrated by a series of numerical experiments.

The first author was supported by FORTWIHR, Bavarian Consortium for High Performance Scientific Computing