Parallel SSOR preconditioning for lattice QCD |
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| Affiliation: | 1. Dukhov Research Institute of Automatics (VNIIA), Moscow, Russia;2. Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region, Russia;3. Joint Institute for High Temperatures of the Russian Academy of Sciences, Moscow, Russia;4. Landau Institute for Theoretical Physics, Chernogolovka, Russia;1. Lab. MIA, Univ. La Rochelle, France;2. Lab. L3i - Lab. MIA, Univ. La Rochelle, France;3. Kyungpook National University, Republic of Korea;4. Lab. L3i, Univ. La Rochelle, France;1. School of Mathematical Science, Peking University, China;2. Beijing International Center for Mathematical Research & Institute for Artificial Intelligence, Peking University, China;3. Department of Mathematics, Pennsylvania State University, United States of America;1. Helmut Schmidt University, Holstenhofweg 85, 22043 Hamburg, Germany;2. Siemens AG, Corporate Technology, Otto-Hahn-Ring 6, 81739 Munich, Germany;3. University of Magdeburg, Institute for Simulation and Graphics, Universitätsplatz 2, 39104 Magdeburg, Germany;4. University of Magdeburg, Institute for Analysis and Numerics, Universitätsplatz 2, 39104 Magdeburg, Germany |
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| Abstract: | The locally lexicographic symmetric successive overrelaxation algorithm (ll-SSOR) is the most effective parallel preconditioner known for iterative solvers used in lattice gauge theory. After reviewing the basic properties of ll-SSOR, the focus of this contribution is put on its parallel aspects: the administrative overhead of the parallel implementation of ll-SSOR, which is due to many conditional operations, decreases its efficiency by a factor of up to one third. A simple generalization of the algorithm is proposed that allows the application of the lexicographic ordering along specified axes, while along the other dimensions odd–even preconditioning is used. In this way one can tune the preconditioner towards optimal performance by balancing ll-SSOR effectivity and administrative overhead. |
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