Grid generation and algebraic solvers

This work focuses on some of the most relevant numerical issues in the solution of the Drift-Diffusion model for semiconductor devices. The Drift- Diffusion model consists of an elliptic and two parabolic partial differential equations which are nonlinearly coupled. A reliable numerical approximation of this model unavoidably leads to choose a suitable tessellation of the computational domain as well as specific solvers for linear and nonlinear systems of equations. These are the two main issues tackled in this work, after introducing a classical discretization of the Drift-Diffusion model based on finite elements. Numerical experiments are also provided to investigate the performances both of up-to-date and of advanced numerical procedures.