Challenges in the Numerical Solution for Models in Transport Theory

We consider the numerical solution of the linear Boltzmann equation of semiconductor theory in the presence of a weak external field. The numerical algorithm is based on the compressed asymptotic procedure, which provides a general method for the unified treatment of the bulk approximation and the initial layer occurring in conventional perturbation analysis. The numerical experiments are performed in Matlab.

Keywords:

• Linear Boltzmann equation with external field
• Singular perturbation
• Drift‐diffusion approximation
• Compressed asymptotic limit