Partially Penalized Anisotropic Trilinear IFE-PIC Methods for DC Plasma Transport Problems

Implicit and hybrid particle-in-cell methods are widely used for efficient simulation of DC discharge plasma transport. However, their computations require solving anisotropic elliptic equations and face challenges related to mesh geometry, non-axisymmetry, and complex interfaces. Moreover, the accuracy of particle trajectories is critical for plasma etching and erosion studies, where errors near interfaces can significantly impact simulation results. To address these challenges, this paper proposes a three-dimensional anisotropic trilinear partially penalized immersed finite element (ATPPIFE) method, which captures interfaces on Cartesian meshes and effectively reduces discontinuities at interface element faces, ensuring that particle trajectories better align with real-world behavior. Building upon this, we further develop a three-dimensional multicorrection condition anisotropic trilinear immersed finite element (MCC-ATIFE) method, which integrates classical anisotropic trilinear IFE, ATPPIFE, Neumann, and Robin flux jump conditions to enhance computational accuracy and adaptability across different scenarios. Numerical validation and application cases demonstrate the accuracy of these methods and their potential for practical engineering applications.