%0 Generic %1 Frommer2012Deflation %A Frommer, Andreas %A Nobile, Andrea %A Zingler, Paul %D 2012 %K na %T Deflation and Flexible SAP-Preconditioning of GMRES in Lattice QCD Simulation %U http://arxiv.org/abs/1204.5463 %X 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.

@misc{Frommer2012Deflation, abstract = {{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.}}, added-at = {2019-02-23T22:09:48.000+0100}, archiveprefix = {arXiv}, author = {Frommer, Andreas and Nobile, Andrea and Zingler, Paul}, biburl = {https://www.bibsonomy.org/bibtex/2969b308a5ce9718d89dafb862d7982fc/cmcneile}, citeulike-article-id = {14223159}, citeulike-linkout-0 = {http://arxiv.org/abs/1204.5463}, citeulike-linkout-1 = {http://arxiv.org/pdf/1204.5463}, day = 24, eprint = {1204.5463}, interhash = {775f87da30b185e8137af58d2851b334}, intrahash = {969b308a5ce9718d89dafb862d7982fc}, keywords = {na}, month = apr, posted-at = {2016-12-07 15:08:06}, priority = {2}, timestamp = {2019-02-23T22:15:27.000+0100}, title = {{Deflation and Flexible SAP-Preconditioning of GMRES in Lattice QCD Simulation}}, url = {http://arxiv.org/abs/1204.5463}, year = 2012 }