A latency tolerant hybrid sparse solver using incomplete Cholesky factorization 3

Consider the solution of large sparse symmetric positive de nite linear systems using the preconditioned conjugate gradient method. On sequential architectures, incomplete Cholesky factorizations provide ef13 fective preconditioning for systems from a variety of application domains, some of which may have widely di ering preconditioning requirements. However, incomplete factorization based preconditioners 15 are not considered suitable for multiprocessors. This is primarily because the triangular solution step required to apply the preconditioner (at each iteration) does not scale well due to the large latency of 17 inter-processor communication. We propose a new approach to overcome this performance bottleneck by coupling incomplete factorization with a selective inversion scheme to replace triangular solutions by 19 scalable matrix–vector multiplications. We discuss our algorithm, analyze its communication latency for model sparse linear systems, and provide empirical results on its performance and scalability. Copyright 21 ? 2003 John Wiley & Sons, Ltd.