Newton-Krylov-Schwarz Methods: Interfacing Sparse Linear Solvers with Nonlinear Applications

摘要

Parallel implicit solution methods are increasingly important in large-scale applications, since reliable low-residual solutions to individual steady-state analyses are often needed repeatedly in multidisciplinary analysis and optimization. We review a class of linear implicit methods called Krylov-Schwarz and a class of nonlinear implicit methods called Newton-Krylov. Newton-Krylov methods are suited for problems in which it is unreasonable to compute or store a true Jacobian, given a strong enough preconditioner for the inner linear system that needs to be solved for each Newton correction. Schwarz-type domain decomposition preconditioning provides good data locality for paraljel implementations over a range of granularities. Their composition forms a class of methods called Newton-Krylov-Schwarz with strong potential for parallel implicit solution, as illustrated on an aerodynamics application.