L. McInnes, B. Norris, S. Bhowmick, P. Raghavan, "Adaptive Sparse Linear Solvers for Implicit CFD using Newton-Krylov Algorithms," Preprint ANL/MCS-P998-0902, September 2002. [pdf]
We consider the simulation of three-dimensional transonic Euler flow using pseudo-transient Newton-Krylov methods. The main computation involves solving a large, sparse linear system at each Newton (nonlinear) iteration. We develop a technique for adaptively selecting the linear solver method to match better the numeric properties of the linear systems as they evolve during the course of the nonlinear iterations. We show how such adaptive methods can be implemented using advanced software environments, leading to significant improvements in simulation time.