Abstract We present an adaptive multilevel Monte Carlo algorithm for solving the stochastic drift–diffusion–Poisson system with non-zero recombination rate. The a-posteriori error is estimated to enable goal-oriented adaptive mesh refinement for the spatial dimensions, while the a-priori error is estimated to guarantee linear convergence of the H 1 error. In the adaptive mesh refinement, efficient estimation of the error indicator gives rise to better error control. For the stochastic dimensions, we use the multilevel Monte Carlo method to solve this system of stochastic partial differential equations. Finally, the advantage of the technique developed here compared to uniform mesh refinement is discussed using a realistic numerical example.

中文翻译：

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随机漂移-扩散-泊松系统的自适应多级蒙特卡罗算法

摘要 我们提出了一种自适应多级蒙特卡罗算法，用于求解具有非零复合率的随机漂移-扩散-泊松系统。估计后验误差以实现空间维度的面向目标的自适应网格细化，而估计先验误差以保证 H 1 误差的线性收敛。在自适应网格细化中，误差指标的有效估计产生了更好的误差控制。对于随机维度，我们使用多级蒙特卡罗方法来求解这个随机偏微分方程组。最后，使用实际数值示例讨论了与均匀网格细化相比，此处开发的技术的优势。