Using Postordering and Static Symbolic Factorization for Parallel Sparse LU
Abstract
In this report we present several improvements of widely used parallel LU factorization methods on sparse matrices. First we characterize the L, U factors in terms of their corresponding LU elimination forest. This characterization can be used as a compact storage scheme of the matrix as well as of the task dependence graph. To improve the use of BLAS in the numerical factorization, we perform a postorder traversal of the LU eforest thus obtaining larger supernodes. To expose more task parallelism for a sparse matrix, we build a more accurate task dependence graph that includes only the least necessary dependencies. Experiments compared favorably our methods against methods implemented in the S* environment on the SGI's Origin2000 multiprocessor.