A Vectorized Conjugate-Gradient Solver for Sparse Systems of Algebraic Equations

M.M. El-Awad, M.Z. Yusoff, and M.H. Boosroh (Malaysia)


Conjugate-Gradient Method, Algebraic Systems, Vectorization.


This paper describes a diagonally pre-conditioned conjugate-gradient (CG) solver for large, but sparse, systems of algebraic equations. The diagonally-scaled CG scheme adopted by the solver has three important advantages when compared to other preconditioning schemes such as the incomplete Cholesky factorisation. Firstly, it retains the low storage requirement of the basic CG method. Secondly, like the basic method, it is readily vectorizable and can perform better than the incomplete Cholesky CG algorithm on vector processors. Thirdly, it is easy to implement and requires only minor modifications to the basic CG method. The performance of the solver is evaluated using the standard test case of a flow in a differentially-heated square cavity at three values of the Rayleigh number. The paper also shows the computer-time requirements of the solver on two vector processors, in both scalar and vectorized modes. These clearly show the benefit of vectorization.

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