Robust Parallel Iterative Solvers for Linear and Least-Squares Systems
The new generation of complex physical models encountered today in DOE mission-critical applications often result in large sparse linear and least-squares systems of equations which are very difficult to solve. Our goal is to investigate robust parallel reconditioning techniques for solving difficult large sparse linear systems, such as those that arise in circuit simulation, and the simulation of wave phenomena. We have recently developed a solution technique based on a form of a multilevel implementation of complete-pivoting incomplete LU factorization. The starting point for this research is to consider parallel implementations of this strategy. We will also develop multilevel strategies for least-squares problems, which are similar in spirit to those of the Algebraic Recursive Multilevel Solvers.