Asymptotic-preserving numerical schemes for the semiconductor Boltzmann equation efficient in the high field regime (Q2847747)

The authors are interested in designing asymptotics-preserving schemes for the Boltzmann equation of type NEWLINE\[NEWLINE \partial_tf+v\nabla_xf-\frac{1}{\epsilon}E\cdot\nabla_vf=\frac{1}{\epsilon}Q(f)\;\;t>0,\;x\in\mathbb{R}^{d_x},\;v\in v\in \mathbb{R}^{d_v}, NEWLINE\]NEWLINE where \(\epsilon\) is the ratio between the mean free path and typical length scale. The paper is devoted to the new schemes, as well as the study of their asymptotic properties. The authors consider three cases, the non-degenerate isotropic case, the non-degenerate anisotropic case, and the degenerate case. They present several numerical examples to test the efficiency, accuracy and to illustrate the asymptotic properties of the schemes.