Improved finite element based on gradient recovery algorithm for electric field calculation

In electric field calculation, the accuracy of electric field strength obtained by traditional finite element method is not ideal, and the applicability of weighted average method is insufficient. In order to improve the accuracy of electric field strength solution, the improved finite element based on gradient recovery algorithm for electric field calculation is proposed. The algorithm selects superconvergence sampling points in the element slices near the nodes, and performs least square fitting on the gradient of the finite element solution of the sampling points, so as to obtain high-precision gradient approximation. The algorithm is applied to solve the two-dimensional electric field problem, the results show that the numerical algorithm is simple to implement, the cost involved in the calculation can be ignored, compared with the weighted average method, it has better solution accuracy, faster convergence speed and wider applicability.

I. Introduction

Finite element method (FEM) is a numerical method based on variational principle and piecewise interpolation[1]. Since its proposal in the 1950s, under the impetus of computer technology, finite element method has expanded from the initial aviation technology field to civil engineering, mechanical manufacturing, hydraulic engineering, shipbuilding, electronic technology and other fields, from simple static analysis to the solution of complex problems, and its application breadth and depth have been greatly expanded[2]. Because of its high computational efficiency and many element division methods, it can simulate various complex geometry. The finite element method has become an important analysis method in engineering and scientific numerical simulation.