论文标题
一种用于半导体模型的结构，该结构具有一般网格上的磁场的半导体模型
A structure preserving hybrid finite volume scheme for semi-conductor models with magnetic field on general meshes
论文作者
论文摘要
我们对一般多边形/多面体网格的混合有限体积（HFV）方法的漂移扩散系统的离散感兴趣。所研究的系统由两个各向异性和非线性对流扩散方程组成，其非对称张量与泊松方程相结合，并在浸入磁场中的特定半导体设备中描述。我们介绍了一种基于熵散文关系的新方案，并证明该方案在可接受的集合中允许具有值的解决方案 - 尤其是，计算的密度仍然是阳性的。此外，我们表明，该方案的离散解决方案在及时呈指数速度趋于指数趋于相关的离散热平衡。几个数值测试证实了我们的理论结果。据我们所知，该方案是第一个能够离散各向异性漂移扩散系统的方案，同时保持密度的界限。
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 with nonsymmetric tensors, coupled with a Poisson equation and describes in particular semiconductor 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. Up to our knowledge, this scheme is the first one able to discretise anisotropic drift-diffusion systems while preserving the bounds on the densities.
