The Meshless Local Petrov–Galerkin Method in Two-Dimensional Electromagnetic Wave Analysis

This paper deals with one member of the class of meshless methods, namely the Meshless Local Petrov-Galerkin (MLPG) method, and explores its application to boundary-value problems arising in the analysis of two-dimensional electromagnetic wave propagation and scattering. This method shows some similitude with the widespread finite element method (FEM), like the discretization of weak forms and sparse global matrices. MLPG and FEM differ in what regards the construction of an unstructured mesh. In MLPG, there is no mesh, just a cloud of nodes without connection to each other spread throughout the domain. The suppression of the mesh is counterbalanced by the use of special shape functions, constructed numerically. This paper illustrates how to apply MLPG to wave scattering problems through a number of cases, in which the results are compared either to analytical solutions or to those provided by other numerical methods.