An Efficient Block-Oriented Approach to Parallel Sparse Cholesky Factorization

This paper explores the use of a subblock decomposition strategy for parallel sparse Cholesky factorization in which the sparse matrix is decomposed into rectangular blocks. Such a strategy has enormous theoretical scalability advantages over more traditional column-oriented and panel-oriented decompositions. However, little progress has been made in producing a practical subblock method. This paper describes and evaluates an approach that is simple to implement, provides slightly higher performance than column (and panel) methods on small parallel machines, and has the potential to provide much higher performance on large parallel machines.