A simple and efficient local Petrov-Galerkin meshless method and its application

In the MLPG method of this paper, only the boundary integrations over local subdomains is involved, which make the MLPG method is very easy to carry out because the local sub-domains are chosen in MLPG method as simple circular or rectangular ranges. In order to simplify the MLPG method, the radius of local sub-domains has been adjusted for the nodes close to the global boundary but not exactly on the boundary. In addition, the boundary conditions including the essential and natural boundary are imposed directly by the nodes which are exactly on the global boundary. Two electromagnetic models have been studied in this paper to investigate the accuracy and computational efficiency of the MLPG method. The results, which are compared with the solutions obtained from the MLPG in the reference and the FEM, show that the MLPG method in this paper can obtain more accurate results by using fewer nodes.