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The simulation of lattice QCD on massively parallel computers stimulated thedevelopment of scalable algorithms for the solution of sparse linear systems.We tackle the problem of the Wilson-Dirac operator inversion by combining aSchwarz alternating procedure (SAP) in multiplicative form with a flexiblevariant of the GMRES-DR algorithm. We show that restarted GMRES is not able toconverge when the system is poorly conditioned. By adding deflation in the formof the FGMRES-DR algorithm, an important fraction of the information producedby the iterates is kept between successive restarts leading to convergence incases in which FGMRES stagnates.

Deflation and Flexible SAP-Preconditioning of GMRES in Lattice QCD Simulation