A Newton–Krylov solver with multiplicative Schwarz preconditioning for finite element compressible flow simulations.

The paper presents an implementation of the Newton–Krylov–Schwarz methodology for stabilized, adaptive finite element approximations of compressible Navier–Stokes equations. Special emphasis is laid on preconditioning of the GMRES method within Newton iterations. Several Schwarz preconditioners are compared on a benchmark problem, including a new implementation of multiplicative preconditioner for matrix-free GMRES, that can be interpreted as accelerated block Gauss–Seidel iterations. Numerical examples show a good performance of the new algorithm, for single step problems and overall simulations. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]