A New Fill-in Strategy for IC Factorization Preconditioning Considering SIMD Instructions

Most of current processors are equipped with single instruction multiple data (SIMD) instructions that are used to increase the performance of application programs. In this paper, we analyze the effective use of SIMD instructions in the Incomplete Cholesky (IC) preconditioned Conjugate Gradient (CG) solver, which we employ in a variety of simulations. A new fill-in strategy in the IC factorization is proposed for the SIMD vectorization of the preconditioning step and to increase the convergence rate. Our numerical results confirm that the proposed method has better solver performance than the conventional IC(0)-CG method.