Second-Order Tetrahedral Elements Multiprocessing Gradient Recovery Method Using Modified Polynomial-Preserving Recovery

The use of the finite element method (FEM) to compute electric potential is widely used in the field of electrical engineering. In some cases, we are more concerned with the distribution of the electric field than the electric potential. The process of accurately computing the electric field from the FEM numerical solution involves gradient recovery. We analyze the particular cases of boundary nodes in the Polynomial-Preserving Recovery (PPR) process of second-order tetrahedral elements and provide the solution strategy. In order to improve the accuracy of boundary nodes' gradient recovery, we adopt a weighted average method based on the PPR. In addition, we propose the multiprocessing parallel computing method to improve the computing speed of the gradient recovery process.