An Unsymmetric-Pattern Multifrontal Method for Sparse LU Factorization

An Unsymmetric-Pattern Multifrontal Method for Sparse LU Factorization

Sparse matrix factorization algorithms for general problems are typically characterized by irregular memory access patterns that limit their performance on parallel-vector supercomputers. For symmetric problems, methods such as the multifrontal method avoid indirect addressing in the innermost loops by using dense matrix kernels. However, no efficient LU factorization algorithm based primarily ...

Unsymmetric-pattern Multifrontal Methods for Parallel Sparse Lu Factorization

Sparse matrix factorization algorithms are typically characterized by irregular memory access patterns that limit their performance on parallel-vector supercomputers. For symmetric problems, methods such as the multifrontal method replace irregular operations with dense matrix kernels. However, no e cient method based primarily on dense matrix kernels exists for matrices whose pattern is very u...

Performance of an unsymmetric-pattern multifrontal method for sparse LU factorization

An Unsymmetrized Multifrontal LU Factorization

A well-known approach to compute the LU factorization of a general unsymmetric matrix A is to build the elimination tree associated with the pattern of the symmetric matrix A + A and use it as a computational graph to drive the numerical factorization. This approach, although very eÆcient on a large range of unsymmetric matrices, does not capture the unsymmetric structure of the matrices. We in...

Hypergraph-Based Unsymmetric Nested Dissection Ordering for Sparse LU Factorization

In this paper we present HUND, a hypergraph-based unsymmetric nested dissection ordering algorithm for reducing the fill-in incurred during Gaussian elimination. HUND has several important properties. It takes a global perspective of the entire matrix, as opposed to local heuristics. It takes into account the assymetry of the input matrix by using a hypergraph to represent its structure. It is ...