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

Abstract

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.