Preconditioned solvers for large eigenvalue problems on massively parallel computers and workstation clusters

We present parallel preconditioned solvers to compute a few extreme eigenvalues and vectors of large sparse matrices based on the Jacobi-Davidson (JD) method by G.L.G. Sleijpen and H.A. van der vorst. For preconditioning, we apply banded matrices and a new adaptive approach using the QMR iteration. To parallelize the solvers developed, we investigate matrix and vector partitioning as well as division of the spectrum of the matrix into independent parts. The efficiency of these strategies is demonstrated on the massively parallel systems NEC Cenju-3, Cray T3E, and on workstation clusters