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SUMMARY:Hermitian/skew-Hermitian preconditioners for the indefinite Helmho
 ltz equation - Colin Cotter (Imperial)
DTSTART:20230427T140000Z
DTEND:20230427T150000Z
UID:TALK198040@talks.cam.ac.uk
CONTACT:Matthew Colbrook
DESCRIPTION:The indefinite Helmholtz equation\, obtained by Fourier transf
 ormation of the wave equation in time\, arises in many applications includ
 ing acoustics\, elasticity\, electromagnetism\, geophysics\, and quantum m
 echanics. Scalable iterative solvers for discretisations of the indefinite
  Helmholtz equation remain a challenging problem in scientific computing a
 nd numerical analysis. I will present such an iterative solver that combin
 es shift preconditioning\, Hermitian/skew-Hermitian splitting and multigri
 d methods. Standard multigrid methods can be used with local smoothers (su
 ch as Jacobi smoothers) that can be parallelised by domain decomposition w
 ith minimal overlaps\, unlike some other solver approaches for the indefin
 ite Helmholtz equation. I will present a proof that the solver converges a
 t a rate that is independent of the frequency k\, the mesh size h\, and al
 l other parameters of the problem\, provided that O(k) inner iterations ar
 e performed. I will also present numerical experiments that confirm this r
 esult.
LOCATION:Centre for Mathematical Sciences\, MR14
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