Perfectly matched layers for the Boltzmann equation: Stability and sensitivity analysis

Abstract

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.