Iterative solution of generalized eigenvalue problems from optoelectronics with trilinos

Abstract

In this paper, we study the iterative solution of generalized Hermitian eigenvalue problems arising from the finite-element discretization of k·p models of optoelectronic nano systems. We are interested in computing the eigenvalues close to the band-gap which determine electronic and optical properties of a given system. Our work is based on the Trilinos project which provides an object-oriented software framework of integrated algorithms for the solution of large-scale physics problems. Trilinos enables users to combine state-of-the-art eigensolvers with efficient preconditioners, sparse solvers, and partitioning methods. Our study illustrates these possibilities and evaluates various algorithms for their suitability in the context of our physical problem setting.