Parallel Symmetric Eigenvalue Problem Solvers
Abstract
Sparse symmetric eigenvalue problems arise in many computational science and engineering applications: in structural mechanics, nanoelectronics, and spectral reordering, for example. Often, the large size of these problems requires the development of eigensolvers that scale well on parallel computing platforms. In this dissertation, I describe two such eigensolvers, TraceMin and TraceMin-Davidson. These methods are different from many other eigensolvers in that they do not require accurate linear solves to be performed at each iteration in order to find the smallest eigenvalues and their associated eigenvectors. After introducing these closely related eigensolvers, I discuss alternative methods for solving saddle point problems arising in each iteration, which can improve the overall running time. Additionally, I present TraceMin-Multisectioning, a new TraceMin implementation geared towards finding large numbers of eigenpairs in any interval of the spectrum. I conclude with numerical experiments comparing my trace-minimization solvers to other popular eigensolvers (such as Krylov-Schur, LOBPCG, Jacobi- Davidson, and FEAST), establishing the competitiveness of my methods.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 2015
- Accession Number
- ADA626022
Entities
People
- Alicia M. Klinvex
Organizations
- Purdue University