Newton-krylov-schwarz: an Implicit Solver for Cfd

Newton Krylov methods and Krylov Schwarz domain decomposition methods have begun to become established in computational uid dynamics CFD over the past decade The former employ a Krylov method inside of Newton s method in a Jacobian free manner through directional di erencing The latter employ an overlapping Schwarz domain decomposition to derive a preconditioner for the Krylov accelerator that relies primarily on local information for data parallel concurrency They may be composed as Newton Krylov Schwarz NKS methods which seem particularly well suited for solving nonlinear elliptic systems in high latency distributed memory environments We give a brief description of this family of algorithms with an emphasis on domain decomposition iterative aspects We then describe numerical simulations with Newton Krylov Schwarz methods on aerodynamics applications emphasizing comparisons with a standard defect correction approach subdomain preconditioner consistency subdomain preconditioner quality and the e ect of a coarse grid