A structure preserving hybrid finite volume scheme for semi-conductor models with magnetic field on general meshes

Abstract

We are interested in the discretisation of a drift-diffusion system in the framework of hybrid finite volume (HFV) methods on general polygonal/polyhedral meshes. The system under study is composed of two anisotropic and nonlinear convection-diffusion equations coupled with a Poisson equation and describes in particular semi-conductor devices immersed in a magnetic field. We introduce a new scheme based on an entropy-dissipation relation and prove that the scheme admits solutions with values in admissible sets -especially, the computed densities remain positive. Moreover, we show that the discrete solutions to the scheme converge exponentially fast in time towards the associated discrete thermal equilibrium. Several numerical tests confirm our theoretical results.

Numerical analysis of a finite volume scheme for charge transport in perovskite solar cells

“…The design of numerical schemes for drift-diffusion models is also an mature but still very active field of research (see for instance [9,11,25,28,29,34,35,36,40]). In order to ensure the quality of the numerical simulation and the stability of the numerical method, efforts have been made towards the design of structure preserving schemes [6,12,24,31,34]. Their aim is to preserve physical features of the original model such as the decay of free-energy or non-negativity of solutions.…”