Eigenvalue spectrum estimation and photonic crystals

We have developed an algorithm for the estimation of eigenvalue spectra and have applied it to the determination of the density of states in a photonic crystal, which requires the repeated solution of a generalized eigenvalue problem. We demonstrate that the algorithm offers significant advantages in time, memory, and ease of parallelization over conventional subspace iteration algorithms. In particular it is possible to obtain more than two orders of magnitude speedup in time over subspace methods for modestly sized matrices. For larger matrices the savings are even greater, whilst retaining accurate resolution of features of the eigenspectru