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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Solving Wiener-Hopf type problems numerically: a s
pectral method approach - Matthew Colbrook (Univer
sity of Cambridge)
DTSTART;TZID=Europe/London:20190816T140000
DTEND;TZID=Europe/London:20190816T143000
UID:TALK128701AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/128701
DESCRIPTION:The unified transform is typically associated with
the solution of integrable nonlinear PDEs. Howeve
r\, after an appropriate linearisation\, one can a
lso apply the method to linear PDEs and develop a
spectral boundary-based method. I will discuss rec
ent advances of this method\, in particular\, the
application of the method to problems in unbounded
domains with solutions having corner singularitie
s. Consequently\, a wide variety of mixed boundary
condition problems can be solved without the need
for the Wiener-Hopf technique. Such problems aris
e frequently in acoustic scattering or in the calc
ulation of electric fields in geometries involving
finite and/or multiple plates. The new approach c
onstructs a global relation that relates known bou
ndary data\, such as the scattered normal velocity
on a rigid plate\, to unknown boundary values\, s
uch as the jump in pressure upstream of the plate.
This can be viewed formally as a domain dependent
Fourier transform of the boundary integral equati
ons. By approximating the unknown boundary functio
ns in a suitable basis expansion and evaluating th
e global relation at collocation points\, one can
accurately obtain the expansion coefficients of th
e unknown boundary values. The local choice of bas
is functions is flexible\, allowing the user to de
al with singularities and complicated boundary con
ditions such as those occurring in elasticity mode
ls or spatially variant Robin boundary conditions
modelling porosity.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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