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SUMMARY:Fast algorithms for the dense matrices arising from the Method of
Regularized Stokeslets
DTSTART;VALUE=DATE-TIME:20180709T060000Z
DTEND;VALUE=DATE-TIME:20180709T063000Z
DTSTAMP;VALUE=DATE-TIME:20241104T174955Z
UID:indico-contribution-40@conferences.maths.unsw.edu.au
DESCRIPTION:Speakers: Minghao Rostami (Syracuse University)\nThe swimming
motion of microorganisms such as sperm and cilia can be modelled by severa
l methods\, all of which entail solving equations of fluid-structure inter
action. Among them\, the Method of Regularized Stokeslets (MRS) and the Ro
tne-Prager-Yamakawa tensor have the advantage of not requiring a 3D Euleri
an grid and using the fundamental solutions to the underlying equations in
stead. However\, the computations required by both methods entail the use
of dense matrices\, and they tend to be large and very costly to work with
for practical models in which the number of micro-swimmers is large. \n\n
The 'data-sparse' structure of these matrices enables the development of f
ast algorithms. To compute the matrix-vector products efficiently\, we ext
end the Kernel-Independent Fast Multipole Method (KIFMM) to the kernels as
sociated with the MRS. To solve linear systems with the same matrices eff
iciently\, we consider both a data-sparser preconditioner and a block-diag
onal preconditioner\; to expedite the application of the preconditioners\,
we employ a number of techniques such as Krylov subspace recycling. We ap
ply the proposed algorithms to study the dynamics of a large group of sper
m and the flow field induced by a carpet of cilia.\n\nhttps://conferences.
maths.unsw.edu.au/event/2/contributions/40/
LOCATION:University of Sydney New Law School/--106
URL:https://conferences.maths.unsw.edu.au/event/2/contributions/40/
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