Galerkin methods for Boltzmann–Poisson transport with reflection conditions on rough boundaries
Galerkin methods for Boltzmann–Poisson transport with reflection conditions on rough boundaries
复制标题
粗糙边界反射条件下玻尔兹曼-泊松输运的 Galerkin 方法
DOI：
10.1016/j.jcp.2018.02.041
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发表时间：
2018
影响因子：
4.1
通讯作者：
Gamba, Irene M.
中科院分区：
文献类型：
--
作者：
Morales Escalante, José A.;Gamba, Irene M.
在本文中，我们认为在纳米尺度的半导体器件建模中的电子输运的上下文中，与玻尔兹曼-泊松系统，包括漫反射，除了镜面反射的反射边界条件（BC）的数学和数值建模，以及它们在不连续Galerkin（DG）计划的实现。我们研究这些BC上的设备的物理边界，并开发一个数值近似模型的绝缘边界条件，或等效地，逐点零通量的数学条件的电子输运方程。在具有动量依赖镜面概率p（k→）的更一般的混合反射的情况下，这样的条件在微观水平上、在边界处逐点地平衡入射和反射动量通量。我们比较计算预测的物理观测值的数值实现这些不同的反射条件在我们的DG计划BP模型，并观察到扩散条件的影响在整个域的位置空间的动力学矩。
We consider in this paper the mathematical and numerical modeling of reflective boundary conditions (BC) associated to Boltzmann–Poisson systems, including diffusive reflection in addition to specularity, in the context of electron transport in semiconductor device modeling at nano scales, and their implementation in Discontinuous Galerkin (DG) schemes. We study these BC on the physical boundaries of the device and develop a numerical approximation to model an insulating boundary condition, or equivalently, a pointwise zero flux mathematical condition for the electron transport equation. Such condition balances the incident and reflective momentum flux at the microscopic level, pointwise at the boundary, in the case of a more general mixed reflection with momentum dependant specularity probability p (k→). We compare the computational prediction of physical observables given by the numerical implementation of these different reflection conditions in our DG scheme for BP models, and observe that the diffusive condition influences the kinetic moments over the whole domain in position space.