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CATEGORIES:Applied and Computational Analysis
SUMMARY:Hermitian/skew-Hermitian preconditioners for the i
ndefinite Helmholtz equation - Colin Cotter (Imper
ial)
DTSTART;TZID=Europe/London:20230427T150000
DTEND;TZID=Europe/London:20230427T160000
UID:TALK198040AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/198040
DESCRIPTION:The indefinite Helmholtz equation\, obtained by Fo
urier transformation of the wave equation in time\
, arises in many applications including acoustics\
, elasticity\, electromagnetism\, geophysics\, and
quantum mechanics. Scalable iterative solvers for
discretisations of the indefinite Helmholtz equat
ion remain a challenging problem in scientific com
puting and numerical analysis. I will present such
an iterative solver that combines shift precondit
ioning\, Hermitian/skew-Hermitian splitting and mu
ltigrid methods. Standard multigrid methods can be
used with local smoothers (such as Jacobi smoothe
rs) that can be parallelised by domain decompositi
on with minimal overlaps\, unlike some other solve
r approaches for the indefinite Helmholtz equation
. I will present a proof that the solver converges
at a rate that is independent of the frequency k\
, the mesh size h\, and all other parameters of th
e problem\, provided that O(k) inner iterations ar
e performed. I will also present numerical experim
ents that confirm this result.
LOCATION:Centre for Mathematical Sciences\, MR14
CONTACT:Matthew Colbrook
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