Evaluating Sparse Linear System Solvers on Scalable Parallel Architectures; Final technical rept. Aug 2006-May 2008

摘要

This report describes in detail studies developing and evaluating sparse linear systems on scalable architectures, with emphasis on preconditioned iterative solvers. The study was motivated primarily by the lack of robustness of Krylov subspace iterative schemes with generic, black-box, pre- conditioners such as approximate (or incomplete) LU-factorizations. In this report the authors advocate the use of banded pre-conditioners after suitable reordering of the sparse linear systems. The choice of the reordering scheme is based on: (1) minimizing the bandwidth, and (2) bringing as many of the largest elements of the coefficient matrix as possible to a narrow central band.