Adaptive Aggregation-based Domain Decomposition Multigrid for Twisted Mass Fermions

@article{Alexandrou2016AdaptiveAD,
  title={Adaptive Aggregation-based Domain Decomposition Multigrid for Twisted Mass Fermions},
  author={C. Alexandrou and S. Bacchio and J. Finkenrath and A. Frommer and K. Kahl and M. Rottmann},
  journal={Physical Review D},
  year={2016},
  volume={94},
  pages={114509}
}
The Adaptive Aggregation-based Domain Decomposition Multigrid method (arXiv:1303.1377) is extended for two degenerate flavors of twisted mass fermions. By fine-tuning the parameters we achieve a speed-up of the order of hundred times compared to the conjugate gradient algorithm for the physical value of the pion mass. A thorough analysis of the aggregation parameters is presented, which provides a novel insight into multigrid methods for lattice QCD independently of the fermion discretization. 

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References

SHOWING 1-10 OF 36 REFERENCES
DDalphaAMG for Twisted Mass Fermions
We present the Adaptive Aggregation-based Domain Decomposition Multigrid method extended to the twisted mass fermion discretization action. We show comparisons of results as a function of tuning theExpand
Adaptive Aggregation-Based Domain Decomposition Multigrid for the Lattice Wilson-Dirac Operator
TLDR
This work presents a domain decomposition adaptive algebraic multigrid method used as a preconditioner to solve the “clover improved” Wilson discretization of the Dirac equation and shows considerable speedup can be achieved compared to conventional Krylov subspace methods,domain decomposition methods, and other hierarchical approaches for realistic system sizes. Expand
An adaptive aggregation based domain decomposition multilevel method for the lattice wilson dirac operator: multilevel results
In lattice QCD computations a substantial amount of work is spent in solving linear systems arising in Wilson's discretization of the Dirac equations. We show first numerical results of the extensionExpand
Multigrid Algorithms for Domain-Wall Fermions
We describe an adaptive multigrid algorithm for solving inverses of the domain-wall fermion operator. Our multigrid algorithm uses an adaptive projection of near-null vectors of the domain-wallExpand
Adaptive multigrid algorithm for the lattice Wilson-Dirac operator.
TLDR
An adaptive multigrid solver for application to the non-Hermitian Wilson-Dirac system of QCD is presented, demonstrating that the algorithm nearly eliminates critical slowing down in the chiral limit and that it has weak dependence on the lattice volume. Expand
Adaptive multigrid algorithm for lattice QCD.
TLDR
A new multigrid solver that is suitable for the Dirac operator in the presence of disordered gauge fields is presented that has weak dependence on the gauge coupling and exhibits very little critical slowing down in the chiral limit. Expand
The role of multigrid algorithms for LQCD
TLDR
The first successful QCD multigrid algorithm which demonstrates constant conver-gence rates independent of quark mass and lattice volume for the Wilson Dirac operator is reported on. Expand
Adaptive Domain Decomposition Multigrid for Lattice QCD
In this thesis we present a multigrid approach for systems of linear equations involving the Wilson Dirac operator from lattice quantum chromodynamics (lattice QCD), the fundamental physical theoryExpand
Multigrid solver for clover fermions
We present an adaptive multigrid Dirac solver developed for Wilson clover fermions which offers order-of-magnitude reductions in solution time compared to conventional Krylov solvers. The solverExpand
Solution of the Dirac equation in lattice QCD using a domain decomposition method
Efficient algorithms for the solution of partial differential equations on parallel computers are often based on domain decomposition methods. Schwarz preconditioners combined with standard KrylovExpand
...
1
2
3
4
...