论文标题
分析半导体模型的新隐式求解器
Analysis of a new implicit solver for a semiconductor model
论文作者
论文摘要
我们介绍并分析了一种新的迭代求解器，以进行简化的Boltzmann-Poisson系统的隐式离散化。该算法建立在最近的工作基础上，该工作纳入了Vlasov-Poisson方程的清扫算法，作为Boltzmann-Poisson方程的嵌套内部迭代迭代求解器的一部分。新方法消除了筑巢的需求，每次迭代只需要一次运输。它作为离散系统的新的定点配方出现，我们被证明对给定的电势是依赖的。我们还得出了一个加速器，以提高漂移扩散状态中系统的收敛速率。我们从数值上比较了有和没有加速度的新求解器的效率，并与最近开发的嵌套迭代求解器进行比较。
We present and analyze a new iterative solver for implicit discretizations of a simplified Boltzmann-Poisson system. The algorithm builds on recent work that incorporated a sweeping algorithm for the Vlasov-Poisson equations as part of nested inner-outer iterative solvers for the Boltzmann-Poisson equations. The new method eliminates the need for nesting and requires only one transport sweep per iteration. It arises as a new fixed-point formulation of the discretized system which we prove to be contractive for a given electric potential. We also derive an accelerator to improve the convergence rate for systems in the drift-diffusion regime. We numerically compare the efficiency of the new solver, with and without acceleration, with a recently developed nested iterative solver.
