A Supernodal Out-of-Core Sparse Gaussian-Elimination Method

Abstract

We present an out-of-core sparse direct solver for unsymmetric linear systems. The solver factors the coefficient matrix A into A = PLU using Gaussian elimination with partial pivoting. It assumes that A fits within main memory, but it stores the L and U factors on disk (that is, in files). Experimental results indicate that on small to moderately-large matrices (whose factors fit or almost fit in main memory), our code achieves high performance, comparable to that of SuperLU. In some of these cases it is somewhat slower than SuperLU due to overheads associated with the out-of-core behavior of the algorithm (in particular the fact that it always writes the factors to files), but not by a large factor. But in other cases it is faster than SuperLU, probably due to more efficient use of the cache. However, it is able to factor matrices whose factors are much larger than main memory, although at lower computational rates.

This research was supported by an IBM Faculty Partnership Award, by grant 848/04 from the Israel Science Foundation (founded by the Israel Academy of Sciences and Humanities), and by grant 2002261 from the United-States-Israel Binational Science Foundation.