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

In lattice quantum chromodynamics (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 decomposit...

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Bibliographic Details
Published in:SIAM journal on scientific computing 2014-01, Vol.36 (4), p.A1581-A1608
Main Authors: Frommer, A., Kahl, K., Krieg, S., Leder, B., Rottmann, M.
Format: Article
Language:English
Subjects:
Algebra
Computation
Dirac equation
Domain decomposition
Lattices
Mathematical models
Quantum chromodynamics
Solvers
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Summary:In lattice quantum chromodynamics (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 preconditioner 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 separately in lattice QCD before. We show in extensive numerical tests conducted with a parallel production code implementation that considerable speedup can be achieved compared to conventional Krylov subspace methods, domain decomposition methods, and other hierarchical approaches for realistic system sizes.
ISSN:1064-8275
1095-7197
DOI:10.1137/130919507