Nodal Meshless Method With Vectorial Shape Functions Based on H(Curl)

The aim of this article is to deepen the idea of vectorial meshless methods, creating a nodal meshless method for vector problems, which we will call the vector nodal meshless method. In this proposal, a set of nodes is distributed in the domain and on its boundary, and each node has an associated unit vector. The vector shape functions are based on the H(curl) spaces and Nédélec's first type elements polynomial space. The method is applied in the solution of the eigenvalues problem on waveguides filled with different materials. The numerical solution is not corrupted by spurious modes, it satisfies the tangential field continuity at the interface among different materials, and it overcomes problems of field singularities caused by corners and edges of the geometry.