Adaptive Aggregation Based Domain Decomposition Multigrid for the Lattice Wilson Dirac Operator

In lattice QCD computations a substantial amount of work is spent in solving discretized versions of the Dirac equation. Conventional Krylov solvers show critical slowing down for large system sizes and physically interesting parameter regions. We present a domain decomposition adaptive algebraic multigrid method used as a precondtioner to solve the "clover improved" Wilson discretization of the Dirac equation. This approach combines and improves two approaches, namely domain decomposition and adaptive algebraic multigrid, that have been used seperately in lattice QCD before. We show in extensive numerical test conducted with a parallel production code implementation that considerable speed-up over conventional Krylov subspace methods, domain decomposition methods and other hierarchical approaches for realistic system sizes can be achieved.Comment: Additional comparison to method of arXiv:1011.2775 and to mixed-precision odd-even preconditioned BiCGStab. Results of numerical experiments changed slightly due to more systematic use of odd-even preconditionin

Parallel SSOR preconditioning for lattice QCD

The locally lexicographic symmetric successive overrelaxation algorithm (ll-SSOR) is the most effective parallel preconditioner known for iterative solvers used in lattice gauge theory. After reviewing the basic properties of ll-SSOR, the focus of this contribution is put on its parallel aspects: the administrative overhead of the parallel implementation of ll-SSOR, which is due to many conditional operations, decreases its efficiency by a factor of up to one third. A simple generalization of the algorithm is proposed that allows the application of the lexicographic ordering along specified axes, while along the other dimensions odd–even preconditioning is used. In this way one can tune the preconditioner towards optimal performance by balancing ll-SSOR effectivity and administrative overhead