Deflated GMRES with multigrid for lattice QCD
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 a...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2020-04-01
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| Series: | Physics Letters B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S037026932030085X |
| _version_ | 1818983387309801472 |
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| author | Travis Whyte Walter Wilcox Ronald B. Morgan |
| author_facet | Travis Whyte Walter Wilcox Ronald B. Morgan |
| author_sort | Travis Whyte |
| collection | DOAJ |
| description | 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 multigrid 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. Keywords: Lattice QCD, Matrix deflation, Multigrid |
| first_indexed | 2024-12-20T18:02:09Z |
| format | Article |
| id | doaj.art-f3386608368741098c097b0c981d90fd |
| institution | Directory Open Access Journal |
| issn | 0370-2693 |
| language | English |
| last_indexed | 2024-12-20T18:02:09Z |
| publishDate | 2020-04-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Physics Letters B |
| spelling | doaj.art-f3386608368741098c097b0c981d90fd2022-12-21T19:30:36ZengElsevierPhysics Letters B0370-26932020-04-01803Deflated GMRES with multigrid for lattice QCDTravis Whyte0Walter Wilcox1Ronald B. Morgan2Department of Physics, Baylor University, Waco, TX 76798-7316, United States of AmericaDepartment of Physics, Baylor University, Waco, TX 76798-7316, United States of America; Corresponding author.Department of Mathematics, Baylor University, Waco, TX 76798-7316, United States of AmericaLattice 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 multigrid 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. Keywords: Lattice QCD, Matrix deflation, Multigridhttp://www.sciencedirect.com/science/article/pii/S037026932030085X |
| spellingShingle | Travis Whyte Walter Wilcox Ronald B. Morgan Deflated GMRES with multigrid for lattice QCD Physics Letters B |
| title | Deflated GMRES with multigrid for lattice QCD |
| title_full | Deflated GMRES with multigrid for lattice QCD |
| title_fullStr | Deflated GMRES with multigrid for lattice QCD |
| title_full_unstemmed | Deflated GMRES with multigrid for lattice QCD |
| title_short | Deflated GMRES with multigrid for lattice QCD |
| title_sort | deflated gmres with multigrid for lattice qcd |
| url | http://www.sciencedirect.com/science/article/pii/S037026932030085X |
| work_keys_str_mv | AT traviswhyte deflatedgmreswithmultigridforlatticeqcd AT walterwilcox deflatedgmreswithmultigridforlatticeqcd AT ronaldbmorgan deflatedgmreswithmultigridforlatticeqcd |