Application of Hermite Interpolation Finite Element Method in Two-dimensional Ion Flow Field Calculation

At present, the description of the high-voltage direct current ion flow field is mainly calculated based on the finite element method. The traditional finite element method uses linear interpolation functions to approximate the field distribution within the element. In order to describe the distribution of ion flow field more accurately, this paper proposes a finite element calculation method based on Hermite interpolation basis function in two dimensions. Compared with the traditional finite element method, the proposed algorithm uses a higher-precision Hermite interpolation function to approximate the electric potential and space charge density distribution. At the same time, this paper proposes an update formula for the surface charge density of conductors, which makes the algorithm converge very well. In this paper, the algorithm program is compiled by MATLAB and compared with the analytical solution, which proves the correctness of the algorithm. Subsequently, a comparison with the traditional finite element method proved that the algorithm has higher accuracy and faster convergence speed. Finally, it is compared with the actual measurement data, which proves the effectiveness of the algorithm.