The Numerical Solution of Large-Scale Generalized Eigenvalue Problems Arising from Finite-Element Modeling of Electroelastic Materials

Numerical Solution of Large Nonsymmetric Eigenvalue Problems

The Spectral Transformation Lanczos Method for the Numerical Solution of Large Sparse Generalized Symmetric Eigenvalue Problems

A new algorithm is developed which computes a specified number of eigenvalues in any part of the spectrum of a generalized symmetric matrix eigenvalue problem. It uses a linear system routine (factorization and solution) as a tool for applying the Lanczos algorithm to a shifted and inverted problem. The algorithm determines a sequence of shifts and checks that all eigenvalues get computed in th...

Parallel Solution of Some Large-Scale Eigenvalue Problems Arising in Chemistry and Physics

We consider the numerical solution on distributed-memory parallel arrays of vector processors of some large-scale eigenvalue problems which arise in chemistry and physics. Applications from a variety of areas are discussed, including molecular dynamics, quantum chemistry, optical physics, chemical reactions, and hydrodynamic stability.

Finite Element Solution of Optimal Control Problems Arising in Semiconductor Modeling

Optimal design, parameter estimation, and inverse problems arising in the modeling of semiconductor devices lead to optimization problems constrained by systems of PDEs. We study the impact of different state equation discretizations on optimization problems whose objective functionals involve flux terms. Galerkin methods, in which the flux is a derived quantity, are compared with mixed Galerki...

The Numerical Treatment of Large Eigenvalue Problems

This paper surveys techniques for calculating eigenvalues and eigenvectors of very large matrices.