Communication-hiding pipelined BiCGSafe methods for solving large linear systems

Recently, a new variant of the BiCGStab method, known as the pipelined BiCGStab, has been proposed. This method can achieve a higher degree of scalability and speed-up rates through a mechanism in which the communication phase for the computation of the inner product can be overlapped with the computation of the matrix-vector prod-uct. Meanwhile, several generalized iteration methods with better convergence behavior than BiCGStab exist, such as ssBiCGSafe, BiCGSafe, and GPBi-CG. Among these methods, ssBiCGSafe, which requires a single phase of computing inner products per iteration, is best suited for high-performance computing systems. As described herein, inspired by the success of the pipelined BiCGStab method, we propose pipelined variations of the ss-BiCGSafe method in which only one phase of inner product computation per iteration is required and this phase of inner product computation can be overlapped with the matrix -vector computation. Through numerical experimentation, we demonstrate that the pro-posed methods engender improvements in convergence behavior and execution time com-pared to the pipelined BiCGStab and ssBiCGSafe methods.(c) 2023 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license( http://creativecommons.org/licenses/by/4.0/ )

Automated summary

Recently, a new variant of the BiCGStab method called pipelined BiCGStab has been proposed. It achieves higher scalability and speed-up rates by overlapping the communication phase for inner product computation with matrix-vector computation. Other generalized iteration methods like ssBiCGSafe, BiCGSafe, and GPBi-CG have better convergence behavior than BiCGStab, with ssBiCGSafe being best suited for high-performance computing systems. Inspired by pipelined BiCGStab, we propose pipelined variations of the ss-BiCGSafe method that only require one phase of inner product computation per iteration, showing improved convergence and execution time compared to pipelined BiCGStab and ssBiCGSafe.