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

In this work, the meshless local radial point interpolation method (LRPIM) is applied to 2-D and 3-D 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 (FEM) solutions as well as analytical ones.