High performance sparse Cholesky factorization algorithm for scalable parallel computers

This paper presents a new parallel algorithm for sparse matrix factorization. This algorithm uses subforest-to-subcube mapping instead of the subtree-to-subcube mapping of another recently introduced scheme by Gupta and Kumar. Asymptotically, both formulations are equally scalable on a wide range of architectures and a wide variety of problems. But the subtree-to-subcube mapping of the earlier formulation causes significant load imbalance among processors, limiting overall efficiency and speedup. The new mapping largely eliminates the load imbalance among processors. Furthermore, the algorithm has a number of enhancements to improve the overall performance substantially. This new algorithm achieves up to 20 GFlops on a 1024-processor Cray T3D for moderately large problems. To our knowledge, this is the highest performance ever obtained on an MPP for sparse Cholesky factorization.