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

Understand

The simulation of lattice QCD on massively parallel computers stimulated the development of scalable algorithms for the solution of sparse linear systems.

• We tackle the problem of the Wilson-Dirac operator inversion by combining a Schwarz alternating procedure (SAP) in multiplicative form with a flexible variant of the GMRES-DR algorithm.
• We show that restarted GMRES is not able to converge when the system is poorly conditioned.
• By adding deflation in the form of the FGMRES-DR algorithm, an important fraction of the information produced by the iterates is kept between successive restarts leading to convergence in cases in which FGMRES stagnates.