A Comparison of the Element Free Galerkin Method and the Meshless Local Petrov-Galerkin Method for Solving Electromagnetic Problems

In this paper, the element free Galerkin (EFG) method and the local Petrov-Galerkin (MLPG) method are compared for solving the electromagnetic problems. The EFG method and MLPG method are introduced at first. Both of the EFG and the MLPG methods are formulated in detail with Poisson's equation. Based on basic electromagnetic problems, the numerical results from the EFG method and MLPG method are given in this paper. The numerical results show that the EFG method and MLPG method both work well for the solution of electromagnetic problems. The EFG method, based on global weak form, needs background meshes for integration, and it needs more nodes to get an accurate result but it requires less cost in computational time. The MLPG method as a true meshless method doesn't needs any meshes in the implementation and can obtain an accurate result using fewer nodes than EFG. However, because the MLPG Method needs more integration nodes and has asymmetric matrices, it needs more CPU time than the EFG method with the condition that the same number of nodes is used in the problem domain.