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SUMMARY:Convergence theory for adaptive smoothed aggregation multigrid met
hods used in lattice QCD
DTSTART;VALUE=DATE-TIME:20170619T133000Z
DTEND;VALUE=DATE-TIME:20170619T135000Z
DTSTAMP;VALUE=DATE-TIME:20200225T072648Z
UID:indico-contribution-414@cern.ch
DESCRIPTION:Speakers: Mr. WHITE\, JR.\, Edward (Johns Hopkins University)\
nIn recent years adaptive smoothed aggregation algebraic multigrid ($\\alp
ha$SA-AMG) methods have been developed and subsequently adapted for use in
lattice quantum chromodynamics (QCD). The purpose of these efforts has b
een to reduce the critical slowdown that occurs in lattice QCD algorithms
when working on state-of-the-art problems. Convergence theorems can estab
lish the robustness of such methods and lead to ways to improve them. Most
convergence theorems for $\\alpha$SA-AMG methods require the underlying m
atrix to be Hermitian\, which the lattice Wilson-Dirac matrix is not. A ge
neral two-level $\\alpha$SA-AMG convergence theorem for non-Hermitian matr
ices is known\, and it suggests convergence in O(k$^2$) iterations\, where
k is an error scaling constant. However\, the general theory does not co
nsider the $\\Gamma_5$-symmetry of the Wilson-Dirac matrix\, or the use of
spin symmetry in adaptive smoothed aggregation procedures. This paper co
nsiders both $\\Gamma_5$ symmetry and spin symmetry in analyzing the conve
rgence of two recently introduced lattice QCD algebraic multigrid methods.
One of these is an $\\alpha$SA-AMG method\, and the other is a bootstrap
multigrid method. The conclusion reached is that both of these methods s
hould converge in O(k) iterations\, the same order of magnitude that would
be expected for Hermitian matrices. The question of whether it is prefer
able to use singular vectors or eigenvectors to build intergrid interpolat
ion operators for multigrid methods is reexamined. The investigation here
suggests that both may lead to similar convergence results.\n\nhttps://ma
kondo.ugr.es/event/0/session/97/contribution/414
LOCATION: Seminarios 8
URL:https://makondo.ugr.es/event/0/session/97/contribution/414
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