Parallel Hybrid Preconditioning: Incomplete Factorization with Selective Sparse Approximate Inversion

• Authors: Padma Raghavan;Keita Teranishi
• Venue: SIAM Journal on Scientific Computing
• Year: 2010

We consider parallel preconditioning to solve large sparse linear systems $Ax=b$ using conjugate gradients when $A$ is symmetric and positive definite. We develop a preconditioner that can be viewed as a hybrid of incomplete factorization and sparse approximate inversion schemes. Such a hybrid can potentially enable fast and reliable solution through a preconditioner with low memory requirements that allows latency-tolerant construction and application on multiprocessor systems. We propose a parallel hybrid scheme which yields a preconditioner as a tree-structured aggregate of sparse incomplete factors and inverses of selected submatrices. We analyze the computation and communication costs of our hybrid preconditioner and report on its parallel performance on some well-known test matrices. Our results indicate that our hybrid has significant advantages over sparse approximate inverse preconditioners and incomplete Cholesky preconditioners using either drop-threshold or zero-level-of-fill schemes.