Journal of Advanced Simulation in Science and Engineering
Online ISSN : 2188-5303
ISSN-L : 2188-5303
Special Issue on Recent Advances in Simulation in Science and Engineering
Improvement of Convergence Property of Communication Avoiding Conjugate Gradient Method for Linear System Obtained from Meshless Approaches
Akira MatsumotoYoshihisa FujitaTaku ItohKuniyoshi AbeSoichiro Ikuno
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2019 Volume 6 Issue 1 Pages 43-55

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Abstract

An improvement strategy of a convergence property of a communication-avoiding Krylov subspace method is numerically investigated, and the method is adopted for a linear system obtained from the Element-Free Galerkin (EFG) method. Although a communication-avoiding Krylov subspace method such as k-skip Conjugate Gradient (k-skip CG) improves parallelization efficiency, a convergence property of the method is degraded. To improve this degradation, we propose two improvement techniques, calculating a true residual vector once in several iterations and adopting weighted average of the a true residual and a numerical residual. As the result, the convergence of k-skip CG becomes more stabilized and faster.

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© 2019 Japan Society for Simulation Technology
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