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.

中文翻译：

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一种新的半导体模型隐式求解器的分析

我们提出并分析了一种新的迭代求解器，用于简化 Boltzmann-Poisson 系统的隐式离散化。该算法建立在最近的工作之上，该工作将 Vlasov-Poisson 方程的扫描算法作为 Boltzmann-Poisson 方程的嵌套内外迭代求解器的一部分。新方法消除了嵌套的需要，每次迭代只需要一次传输扫描。它是离散系统的一个新的定点公式，我们证明它对于给定的电势是收缩的。我们还推导出了一个加速器来提高漂移扩散机制中系统的收敛速度。我们在数值上比较了新求解器（有加速和无加速）与最近开发的嵌套迭代求解器的效率。