Full matrix techniques in sparse Gaussian elimination

TLDR: The benefits of using full matrix techniques in the later stages of Gaussian elimination are indicated and frontal and multi-frontal schemes where such benefits are obtained automatically are described.

Abstract: We discuss ways in which code for Gaussian elimination on full systems can be used in crucial parts of the code for the solution of sparse linear equations. We indicate the benefits of using full matrix techniques in the later stages of Gaussian elimination and describe frontal and multi-frontal schemes where such benefits are obtained automatically. We also illustrate the advantages of such approaches when running sparse codes on vector machines.