Abstract This paper develops a two-dimensional implicit particle-in-cell model, which considers algorithms without and with magnetic field, based on the anisotropic immersed-finite-element method. The direct implicit particle-in-cell (DIPIC) algorithm is utilized to track the movement of electrons and ions, while the anisotropic immersed-finite-element method is developed to compute the electric field. Compared with the previous works, the immersed-finite-element direct implicit particle-in-cell (IFE-DIPIC) method developed in this article can use larger temporal and spatial step sizes to simulate the plasma problems and can handle the complex interface problems on a Cartesian mesh independent of the interface. Hence, the IFE-DIPIC method can significantly improve the computational efficiency, especially for the large-scale and long-time evolution plasma problems with complex interface. Numerical experiments are provided to demonstrate the proposed method and show the applicability in the simulations of plasma sheath problems.

中文翻译：

---

基于各向异性浸入有限元法的隐式胞内粒子模型

摘要 本文基于各向异性浸入有限元方法，开发了一种二维隐式细胞内粒子模型，该模型考虑了无磁场和有磁场的算法。直接隐式细胞内粒子 (DIPIC) 算法用于跟踪电子和离子的运动，同时开发各向异性浸入有限元方法来计算电场。与之前的工作相比，本文开发的浸入式有限元直接隐式粒子内粒子（IFE-DIPIC）方法可以使用更大的时空步长来模拟等离子体问题，并且可以处理复杂的界面问题。独立于界面的笛卡尔网格。因此，IFE-DIPIC 方法可以显着提高计算效率，特别是对于复杂界面的大规模和长时间演化的等离子体问题。提供了数值实验来证明所提出的方法并表明其在等离子体鞘层问题的模拟中的适用性。