Deflated GMRES with Multigrid for Lattice QCD
arXiv:1912.02868 · doi:10.1016/j.physletb.2020.135281
Abstract
Lattice QCD solvers encounter critical slowing down for fine lattice spacings and small quark mass. Traditional matrix eigenvalue deflation is one approach to mitigating this problem. However, to improve scaling we study the effects of deflating on the coarse grid in a hierarchy of three grids for adaptive mutigrid applications of the two dimensional Schwinger model. We compare deflation at the fine and coarse levels with other non deflated methods. We find the inclusion of a partial solve on the intermediate grid allows for a low tolerance deflated solve on the coarse grid. We find very good scaling in lattice size near critical mass when we deflate at the coarse level using the GMRES-DR and GMRES-Proj algorithms.
12 pages, 5 figures
References in corpus (6)
- Adaptive multigrid algorithm for the lattice Wilson-Dirac operator
- Deflated Iterative Methods for Linear Equations with Multiple Right-Hand Sides
- Multigrid for Staggered Lattice Fermions
- Multi-Grid Lanczos
- QCDLAB: Designing Lattice QCD Algorithms with MATLAB
- Adaptive Multigrid Algorithm for the QCD Dirac-Wilson Operator