High-performance implementation of Chebyshev filter diagonalization for interior eigenvalue computations

Wellein G, Alvermann A, Fehske H, Hager G, Kreutzer M, Lang B, Pieper A, Galgon M (2016)

Publication Status: Published

Publication Type: Journal article

Publication year: 2016

Journal

Publisher: Elsevier

Book Volume: 325

Pages Range: 226-243

DOI: 10.1016/j.jcp.2016.08.027

Abstract

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(2) innermost eigenpairs of a topological insulator matrix with dimension 10(9) derived from quantum physics applications. (C) 2016 Elsevier Inc. All rights reserved.

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Involved external institutions

Universität Greifswald Germany (DE) Bergische Universität Wuppertal Germany (DE)

How to cite

APA:

Wellein, G., Alvermann, A., Fehske, H., Hager, G., Kreutzer, M., Lang, B.,... Galgon, M. (2016). High-performance implementation of Chebyshev filter diagonalization for interior eigenvalue computations. Journal of Computational Physics, 325, 226-243. https://doi.org/10.1016/j.jcp.2016.08.027

MLA:

Wellein, Gerhard, et al. "High-performance implementation of Chebyshev filter diagonalization for interior eigenvalue computations." Journal of Computational Physics 325 (2016): 226-243.

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