Application of the Meshless Local Radial Point Interpolation Method on Vector Eigenvalue Problems

In this work, the meshless Local Radial Point Interpolation Method is applied on 2D and 3D vector eigenvalue problems. The method is entirely nodal based, and each node is associated with a vector basis that allows direct enforcement of essential boundary conditions. Unlike traditional methods, the problems themselves are described by a mixed formulation, in which, the vector wave equation and the divergence-free constraint are coupled by using a Lagrange multiplier. The complete proposed technique provides a novel approach to the solution of vector problems in computational  electromagnetism. The numerical results are compared with Finite Element solutions using the same model, and analytical ones as well.