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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Cauchy and log transforms on intervals\, curves\,
wedges and polygons - Sheehan Olver (Imperial Coll
ege London)
DTSTART;TZID=Europe/London:20230208T094500
DTEND;TZID=Europe/London:20230208T103000
UID:TALK194776AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/194776
DESCRIPTION:Green's integral representations for two-dimension
al PDEs arising in scattering can be expressed as
smooth modifications of logarithmic and Cauchy ker
nels. An efficient way to numerically solve these
is to find exact expressions for the logarithmic a
nd Cauchy kernels on the underlying geometries. Th
is talk explores how this can be accomplished usin
g orthogonal polynomials on an interval\, and by m
apping the interval to a curve or wedge by a polyn
omial\, rational\, or algebraic map. The Cauchy tr
ansform over the mapped domain can be expressed ex
actly in terms of the unmapped Cauchy transform us
ing new change-of-variable formulae\, and multiple
wedges can be combined to solve PDEs on polygons\
, that is\, by breaking the polygon into elements
but where the elements have a corner in the middle
. These maps exactly capture the singularities tha
t arise in corners for solutions ot PDEs leading t
o spectral convergence. \;
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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