Abstract The Adaptive Finite Element Method (AFEM) for approximating solutions of PDE
boundary value and eigenvalue problems is a numerical scheme that automatically and …

Background We discuss the numerical solution of large scale nonlinear eigenvalue
problems and frequency response problems that arise in the analysis, simulation and …

In several applications, one needs to solve a sequence of linear systems with changing
matrices and right hand sides. This thesis concentrates on the analysis and application of …

We present a perturbed subspace iteration algorithm to approximate the lowermost
eigenvalue cluster of an elliptic eigenvalue problem. As a prototype, we consider the …

We discuss adaptive numerical methods for the solution of eigenvalue problems arising
either from the finite element discretization of a partial differential equation (PDE) or from …

In mathematical modeling, the description of reality via some system of differential or integral
equations can be considered a kind of model reduction. This omits, for sake of clarity and …

We consider PDE eigenvalue problems as they occur in two-dimensional photonic crystal
modeling. If the permittivity of the material is frequency-dependent, then the eigenvalue …

We briefly survey the recent developments in adaptive finite element approximations of
eigenvalue problems arising from elliptic, second-order, selfadjoint partial differential …

The first part of this paper is devoted to the modeling of wave propagation inside a perfect
two-dimensional photonic crystal and the spectral analysis of the resulting eigenvalue …