We study the stability and sensitivity of an absorbing layer for the Boltzmann equation by examining the Bhatnagar-Gross-Krook (BGK) approximation and using the perfectly matched layer (PML) technique. To ensure stability, we discard some parameters in the model and calculate the total sensitivity indices of the remaining parameters using the ANOVA expansion of multivariate functions. We conduct extensive numerical experiments on two test cases to study stability and compute the total sensitivity indices, which allow us to identify the essential parameters of the model.

翻译：我们通过研究Bhatnagar-Gross-Krook（BGK）近似并运用完美匹配层（PML）技术，探讨玻尔兹曼方程吸收层的稳定性与敏感性。为确保稳定性，我们舍弃模型中的部分参数，并利用多变量函数的ANOVA展开计算剩余参数的总敏感性指数。我们在两个测试案例上开展了大量的数值实验，以研究稳定性并计算总敏感性指数，从而识别模型中的关键参数。