Journal
JOURNAL OF SCIENTIFIC COMPUTING
Volume 68, Issue 2, Pages 803-825Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-015-0159-4
Keywords
Krylov method; BiCGStab; Variable preconditioning; Extreme-scale simulation
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Funding
- Office of Advanced Scientific Computing Research, Office of Science, U.S. Department of Energy [DE-AC02-06CH11357]
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A flexible version of the BiCGStab algorithm for solving a linear system of equations is analyzed. We show that under variable preconditioning, the perturbation to the outer residual norm is of the same order as that to the application of the preconditioner. Hence, in order to maintain a similar convergence behavior to BiCGStab while reducing the preconditioning cost, the flexible version can be used with a moderate tolerance in the preconditioning Krylov solves. We explored the use of flexible BiCGStab in a large-scale reacting flow application, PFLOTRAN, and showed that the use of a variable multigrid preconditioner significantly accelerates the simulation time on extreme-scale computers using - processor cores.
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