High-performance implementation of Chebyshev filter diagonalization for interior eigenvalue computations
- Ernst-Moritz-Arndt-Universität Greifswald (Germany)
- Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany)
- Bergische Universität Wuppertal (Germany)
We study Chebyshev filter diagonalization as a tool for the computation of many interior eigenvalues of very large sparse symmetric matrices. In this technique the subspace projection onto the target space of wanted eigenvectors is approximated with filter polynomials obtained from Chebyshev expansions of window functions. After the discussion of the conceptual foundations of Chebyshev filter diagonalization we analyze the impact of the choice of the damping kernel, search space size, and filter polynomial degree on the computational accuracy and effort, before we describe the necessary steps towards a parallel high-performance implementation. Because Chebyshev filter diagonalization avoids the need for matrix inversion it can deal with matrices and problem sizes that are presently not accessible with rational function methods based on direct or iterative linear solvers. To demonstrate the potential of Chebyshev filter diagonalization for large-scale problems of this kind we include as an example the computation of the 10{sup 2} innermost eigenpairs of a topological insulator matrix with dimension 10{sup 9} derived from quantum physics applications.
- OSTI ID:
- 22622211
- Journal Information:
- Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 325; ISSN JCTPAH; ISSN 0021-9991
- Country of Publication:
- United States
- Language:
- English
Similar Records
A Thick-Restart Lanczos Algorithm with Polynomial Filtering for Hermitian Eigenvalue Problems
Scalable implementation of polynomial filtering for density functional theory calculation in PARSEC