Frommer, Andreas and Kahl, Karsten and Knechtli, Francesco and Rottmann, Matthias and Strebel, Artur and Zwaan, Ian (2021) A multigrid accelerated eigensolver for the Hermitian Wilson-Dirac operator in lattice QCD. COMPUTER PHYSICS COMMUNICATIONS, 258: 107615. ISSN 0010-4655, 1879-2944
Full text not available from this repository. (Request a copy)Abstract
Eigenvalues of the Hermitian Wilson-Dirac operator are of special interest in several lattice QCD simulations, e.g., for noise reduction when evaluating all-to-all propagators. In this paper we present a Davidson-type eigensolver that utilizes the structural properties of the Hermitian Wilson-Dirac operator Q to compute eigenpairs of this operator corresponding to small eigenvalues. The main idea is to exploit a synergy between the (outer) eigensolver and its (inner) iterative scheme which solves shifted linear systems. This is achieved by adapting the multigrid DD-aAMG algorithm to a solver for shifted systems involving the Hermitian Wilson-Dirac operator. We demonstrate that updating the coarse grid operator using eigenvector information obtained in the generalized Davidson method is crucial to achieve good performance when calculating many eigenpairs, as our study of the local coherence shows. We compare our method with the commonly used software-packages PARPACK and PRIMME in numerical tests, where we are able to achieve significant improvements, with speed-ups of up to one order of magnitude and a near-linear scaling with respect to the number of eigenvalues. For illustration we compare the distribution of the small eigenvalues of Q on a 64 x 32(3) lattice with what is predicted by the Banks-Casher relation in the infinite volume limit. (C) 2020 Elsevier B.V. All rights reserved.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | OPTIMAL PRECONDITIONED METHODS; JACOBI-DAVIDSON; LIMITED MEMORY; EIGENPROBLEMS; EIGENVALUES; SEEKING; Lattice QCD; Eigensolver; Multigrid; Wilson-Dirac operator; Parallel computing |
| Subjects: | 500 Science > 530 Physics |
| Divisions: | Physics > Institute of Experimental and Applied Physics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 05 Jul 2022 11:15 |
| Last Modified: | 05 Jul 2022 11:15 |
| URI: | https://pred.uni-regensburg.de/id/eprint/46095 |
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