Argonne National Laboratory

Analysis and Practical Use of Flexible Bicgstab

TitleAnalysis and Practical Use of Flexible Bicgstab
Publication TypeReport
Year of Publication2012
AuthorsChen, J, McInnes, LCurfman, Zhang, H
Date Published09/2012
Other NumbersANL/MCS-P3039-0912
AbstractA flexible version of the BiCGStab algorithm (FBiCGStab) for solving a linear system of equations is analyzed. We show that under flexible preconditioning, the perturbation to the outer residual norm is of the same order as that to the preconditioner. In addition, we formulate a mathematically equivalent variant, FBiCGStab-R, in order to reduce the global synchronization cost for performing inner product calculations. FBiCGStab-R is numerically stable and sometimes far outperforms FBiCGStab if high accuracy of the solution is required. Both analysis and numerical experiments show that a strong preconditioner is often favored for the practical use of flexible BiCGStab. We demonstrate in a large-scale reacting flow application (PFLOTRAN) that the use of flexible BiCGStab leads to signifi cantly accelerated simulation time on extreme-scale computers using O(10^4) -(10^5) processor cores.