The IBiCGStab method on bulk synchronous parallel architectures

Abstract

In this paper, an improved version of the BiCGStab method for the solutions of large and sparse linear systems of equations with unsymmetric coefficient matrices is proposed. The method combines elements of numerical stability and parallel algorithm design without increasing the computational costs. The algorithm is derived such that all inner products of a single iteration step are independent and communication time required for inner product can be overlapped efficiently with computation time of vector updates. Therefore, the cost of global communication can be significantly reduced. In this paper, the bulk synchronous parallel (BSP) model is used to design a fully efficient, scalable and portable parallel proposed algorithm and to provide accurate performance prediction of the algorithm for a wide range of architectures including the Cray T3D, the Parsytec, and a cluster of workstations connected by an Ethernet. This performance model provides us useful insight in the time complexity of the method using only a few system dependent parameters based on a simple and accurate cost modelling. The theoretical performance prediction are compared with some preliminary measured timing results of a numerical application from ocean flow simulation.