Algorithms for calculating quark propagators on large lattices

Chalmers, C.B.; Kenway, R.D.; Roweth, Duncan

doi:10.1016/0021-9991(87)90192-6

Cited by 4 publications

(3 citation statements)

References 19 publications

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“…It is well known [1] that the convergence rate of iterative algorithms for propagators is governed by the condition number 1) of (−∆ + m 2 ) or (− D 2 + m 2 ). Therefore the CSD scaling relation for relaxation times τ reads…”

Section: Results For Propagators In 4-dimensional Su (2) Gauge Fieldsmentioning

confidence: 99%

“…Retaining Ξ yields little difference in performance. 1) i. e. the ratio of the largest to the smallest eigenvalue 2) Using SOR as a smoother contradicts the conventional MG wisdom. However, in nontrivial gauge fields any over-relaxation yields better performance than Gauss-Seidel and much better performance than damped Jacobi or MR. A similar result was reported in a recent paper on MG gauge fixing [13].…”

Section: Bosonic Propagators In Nontrivial Gauge Fieldsmentioning

confidence: 99%

“…In Monte Carlo simulations of lattice gauge theories with fermions the most time-consuming part is the computation of the gauge field dependent fermion propagators. Conjugate gradient (CG) or minimal residual (MR) algorithms are state of the art [1]. Great hopes to do better are attached to multigrid (MG) methods [2][3][4][5][6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

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Improving Multigrid and Conventional Relaxation Algorithms for Propagators

Kalkreuter

1992

Int. J. Mod. Phys. C

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Practical modifications of deterministic multigrid and conventional relaxation algorithms are discussed. New parameters need not be tuned but are determined by the algorithms themselves. One modification can be thought of as "updating on a last layer consisting of a single site". It eliminates critical slowing down in computations of bosonic and fermionic propagators in a fixed volume. Here critical slowing down means divergence of asymptotic relaxation times as the propagators approach criticality. A remaining volume dependence is weak enough in case of bosons so that conjugate gradient can be outperformed. However, no answer can be given yet if the same is true for staggered fermions on lattices of realizable sizes. Numerical results are presented for propagators of bosons and of staggered fermions in 4-dimensional SU (2) gauge fields.

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Section: Results For Propagators In 4-dimensional Su (2) Gauge Fieldsmentioning

confidence: 99%