In the third lecture we will give an overview over the rich set of problems arising in the parallel implementation of sparse Gaussian elimination. We will discuss ordering methods, and the multifrontal method. SuperLU, a sparse solver for general unsymmetric problems on shared memory machines will be presented in detail.
Lecture notes by Jim Demmel:
Lectures 27, 4/23/96: Parallel Sparse Cholesky.
Lectures 28, 4/25/96: Parallel Sparse Gaussian Elimination.
Numerical Linear Algebra chapter of the Computational Science Education Project (section 8 on sparse Gaussian elimination).
"Parallel Direct Methods for Sparse Linear Equations" by Michael Heath, pp 55 - 90, in Parallel Numerical Algorithms, Kluwer, 1997.
"An Asynchronous Parallel Supernodal Algorithm for Sparse Gaussian Elimination" by Sherry Li, J. Demmel, and J. Gilbert. Submitted to SIAM J. Matrix Anal. Appl., special issue on "Sparse and Structured Matrix Computations and Their Applications", February 27, 1997.
Numerical Linear Algebra: Math 221 home page and many links from there.