A Meshless Local Petrov–Galerkin Method for Three-Dimensional Scalar Problems

In this paper, we apply a meshless method based on local boundary integral equations (LBIEs) to solve electromagnetic problems. The discretization process is carried out through the use of special basis functions that, unlike the Finite Element Method, are not confined to an element and do not require the support of an underlying mesh. The approach herein developed can be applied to general three-dimensional scalar boundary value problems arising in electromagnetism.