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.

The growing demand for sustainable energy generation has often pointed to solar energy as a very promising alternative. A new way to harvest solar energy is through solar rectennas. These systems are the integration of micro size antennas and nano diodes. In this way, electromagnetic energy can be captured and converted to the form of direct current. The challenges for the development of this technology are due to the submicron sizes since the theory that describes the operation of antennas moves away from classical electromagnetic behavior and incorporates quantum effects. At the same time, diodes operating in tens or hundreds of THz need specific properties. Within this context, this work presents an investigative study on solar rectennas for operation in THz range by using a bowtie antenna and a geometric diode, both based on graphene.