The Fourier-Galerkin Method for Band Structure Computations of 2D and 3D Photonic Crystals

In this dissertation we consider the band structure computation of 2D and 3D photonic crystals with the Fourier-Galerkin method. For the 2D Helmholtz equation we discuss the efficient implementation and the convergence. For the three-dimensional problem we use the so-called Harmonic Restarted Arnoldi method for solving the discrete eigenvalue problems without preconditioning.