Meshless methods in electromagnetic wave scattering

Abstract

This work is concerned with the application of meshless methods to some problems of mathematical physics described either by integral or by partial differential equations. Meshless methods are a recent alternative to the widespread Finite Element Method. However, differently from the latter, they do not, according to their name, require the use of whatever kind of mesh or grid. After developing the theoretical framework, these methods are applied to a number of problems from areas relevant to Electrical Engineering such as Electrostatics (three- dimensional Poisson equation), Electromagnetic Wave Scattering (Electric and Magnetic field integral equations, and Helmholtz equation), Photonic Crystals (photonic bandgap) and Quantum Mechanics (band structure of solids, linear and non-linear Schrdinger equation).