An improved meshless method based on strong-weak coupling algorithm for electric field calculation

The traditional numerical calculation methods of electrostatic field include finite element method, finite difference method and so on. Due to the time-consuming meshing, the meshless method is gradually used by scholars for physical field analysis. At present, the meshless local Petrov-Galerkin method and the meshfree weak-strong method have been reported in various fields with their better accuracy and wide applicability. This paper presents an improved meshless strong-weak coupling method based on test function. The scattered nodes are used to represent the problem domain and boundary, and the shape function is constructed by the moving least square method. For the nodes where the local integration domain does not intersect the global derivative boundary, the meshless strong form method is used to construct the basic equation. For other nodes, the meshless local weak formula method is used. The exponential function is used as a test function for weak formula expressions. By changing the coefficient of the exponential function, the shape of the test function is controlled, and the influence of the change in the size of the influence domain on the calculation accuracy is reduced. The case analysis shows that this method has higher accuracy and better convergence effect than the traditional meshless method. The proposed method has high precision and computational efficiency in processing electrical numerical calculations, and has strong astringency. This method has better application prospects than traditional methods.