Publications
Publication Information
| Title | Multigrid deflation for Lattice QCD |
| Authors | Eloy Romero Alcalde, Andreas Stathopoulos, Konstantinos Orginos |
| JLAB number | JLAB-THY-19-3023 |
| LANL number | arXiv:1909.12234 |
| Other number | DOE/OR/23177-4771 |
| Document Type(s) | (Journal Article) |
| Associated with EIC: | No |
| Supported by Jefferson Lab LDRD Funding: | No |
| Funding Source: | Nuclear Physics (NP) |
|
Journal Compiled for Journal of Computational Physics Volume 409 Page(s) 109356 Refereed | |
| Publication Abstract: | Computing the trace of the inverse of large matrices is typically ad- dressed through statistical methods. Deflating out the lowest eigenvectors or singular vectors of the matrix reduces the variance of the trace estimator. This work summarizes our efforts to reduce the computational cost of computing the deflation space while achieving the desired variance reduction for Lattice QCD applications. Previous efforts computed the lower part of the singular spectrum of the Dirac operator by using an eigensolver preconditioned with a multigrid linear system solver. Despite the improvement in performance in those appli- cations, as the problem size grows the runtime and storage demands of this approach will eventually dominate the stochastic estimation part of the compu- tation. In this work, we propose to compute the deflation space in one of the following two ways. First, by using an inexact eigensolver on the Hermitian, but maxi- mally indefinite, operator A?5. Second, by exploiting the fact that the multigrid prolongator for this operator is rich in components toward the lower part of the singular spectrum. We show experimentally that the inexact eigensolver can approximate the lower part of the spectrum even for ill-conditioned operators. Also, the deflation based on the coarser grid is more efficient to compute and ap- ply, and, despite its limitation to approximate the fine level spectrum, it obtains similar variance reduction on the trace estimator. |
| Experiment Numbers: | |
| Group: | THEORY CENTER |
| Document: | |
| DOI: | https://doi.org/10.1016/j.jcp.2020.109356 |
| Accepted Manuscript: | 1909.12234.pdf |
| Supporting Documents: | |
| Supporting Datasets: | |