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DTSTART:19700329T010000
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CATEGORIES:RSE Seminars
SUMMARY:A Reynolds-robust preconditioner for the 3D statio
nary Navier-Stokes equations - Patrick Farrell\, M
athematical Institute\, University of Oxford
DTSTART;TZID=Europe/London:20191029T130000
DTEND;TZID=Europe/London:20191029T140000
UID:TALK133327AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/133327
DESCRIPTION:When approximating PDEs with the finite element me
thod\, large sparse\nlinear systems must be solved
. The ideal preconditioner yields\nconvergence tha
t is algorithmically optimal and parameter robust\
, i.e.\nthe number of Krylov iterations required t
o solve the linear system to a\ngiven accuracy doe
s not grow substantially as the mesh or problem\np
arameters are changed.\n\nAchieving this for the s
tationary Navier-Stokes has proven challenging:\nL
U factorisation is Reynolds-robust but scales poor
ly with degree of\nfreedom count\, while Schur com
plement approximations such as PCD and LSC\ndegrad
e as the Reynolds number is increased.\n\nBuilding
on the ideas of Schöberl\, Benzi & Olshanskii\, i
n this talk we\npresent the first preconditioner f
or the Newton linearisation of the\nstationary Nav
ier–Stokes equations in three dimensions that achi
eves\nboth optimal complexity and Reynolds-robustn
ess. The scheme combines\naugmented Lagrangian sta
bilisation to control the Schur complement\, the\n
convection stabilisation proposed by Burman & Hans
bo\, a\ndivergence-capturing additive Schwarz rela
xation method on each level\,\nand a specialised p
rolongation operator involving non-overlapping loc
al\nStokes solves. The properties of the precondit
ioner are tailored to the\ndivergence-free Scott–V
ogelius discretisation.\n\nWe present 3D simulatio
ns with over one billion degrees of freedom with\n
robust performance from Reynolds numbers 10 to 500
0.
LOCATION:JJ Thomson Seminar Room\, Maxwell Centre\, Cavendi
sh Laboratory
CONTACT:Chris Richardson
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