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.
We discuss the implementation and optimization challenges for a Wilson-Dirac solver with Clover term on QPACE, a parallel machine based on Cell processors and a torus network. We choose the mixed-precision Schwarz preconditioned FGCR algorithm in ord
er to circumvent network bandwidth and latency constraints, to make efficient use of the multicore parallelism and on-chip memory, and to achieve flexibility in the choice of lattice sizes. We present benchmarks on up to 256 QPACE nodes showing an aggregate sustained performance of about 10 TFlops for the complete solver and very good scaling.
We give an overview of the QPACE project, which is pursuing the development of a massively parallel, scalable supercomputer for LQCD. The machine is a three-dimensional torus of identical processing nodes, based on the PowerXCell 8i processor. The no
des are connected by an FPGA-based, application-optimized network processor attached to the PowerXCell 8i processor. We present a performance analysis of lattice QCD codes on QPACE and corresponding hardware benchmarks.
