Developing object-oriented parallel iterative methods
International Journal of High Performance Computing and Networking
An improved parallel hybrid bi-conjugate gradient method suitable for distributed parallel computing
Journal of Computational and Applied Mathematics
Diagnosing performance bottlenecks in emerging petascale applications
Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis
Direct pore-level modeling of incompressible fluid flow in porous media
Journal of Computational Physics
Minimizing synchronizations in sparse iterative solvers for distributed supercomputers
Computers & Mathematics with Applications
Hierarchical Krylov and nested Krylov methods for extreme-scale computing
Parallel Computing
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In this paper, an improved version of the BiCGStab(IBiCGStab) method for the solutions of large andsparse linear systems of equations with unsymmetriccoefficient matrices is proposed. The method combineselements of numerical stability and parallel algorithmdesign without increasing the computational costs. Thealgorithm is derived such that all inner products of asingle iteration step are independent and communication time required for inner product can be overlappedefficiently with computation time of vector updates.Therefore, the cost of global communication which represents the bottleneck of the parallel performance canbe signifficantly reduced. The resulting IBiCGStab algorithm maintains the favorable properties of the originalmethod while not increasing computational costs. Datadistribution suitable for both irregularly and regularlystructured matrices based on the analysis of the non-zero matrix elements is presented. Communicationscheme is supported by overlapping execution of computation and communication to reduce waiting times.The efficiency of this method is demonstrated by numerical experimental results carried out on a massivelyparallel distributed memory system.