Development and study of Newton-Krylov-Schwarz algorithms

In this paper we develop and study a combination of Newton-Krylov matrix-fr ee methodology with Schwarz-based domain decomposition methods. To illustra te the performance of the resulting algorithms we present numerical applica tions to the steady solution of compressible Euler flow together with some comparisons with the more standard Schwarz-based methods, namely, Schwarz m ethods combined with defect-correction procedures.