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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Higher order convergent trial methods for Bernoull
i's free boundary problem - Mitrou\, G (University
of Southampton)
DTSTART;TZID=Europe/London:20140626T163000
DTEND;TZID=Europe/London:20140626T170000
UID:TALK53181AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/53181
DESCRIPTION:Co-author: Helmut Harbrecht (University of Basel)
\n\nFree boundary problem is a partial differentia
l equation to be solved in a domain\, a part of wh
ose boundary is unknown the so-called free bounda
ry. Beside the standard boundary conditions that a
re needed in order to solve the partial differenti
al equation\, an additional boundary condition is
imposed at the free boundary. One aims thus to det
ermine both\, the free boundary and the solution o
f the partial differential equation. \n\nThis work
is dedicated to the solution of the generalized e
xterior Bernoulli free boundary problem which is a
n important model problem for developing algorithm
s in a broad band of applications such as optimal
design\, fluid dynamics\, electromagnentic shaping
etc. For its solution the trial method\, which is
a fixed-point type iteration method\, has been ch
osen. \n\nThe iterative scheme starts with an init
ial guess of the free boundary. Given one boundary
condition at the free boundary\, the boundary ele
ment method is applied to compute an approximation
of the violated boundary data. The free boundary
is then updated such that the violated boundary co
ndition is satisfied at the new boundary. Taylor's
expansion of the violated boundary data around th
e actual boundary yields the underlying equation\,
which is formulated as an optimization problem fo
r the sought update function. When a target tolera
nce is achieved\, the iterative procedure stops an
d the approximate solution of the free boundary pr
oblem is detected. \n\nThe efficiency of the trial
method as well as its speed of convergence depend
s significantly on the update rule for the free bo
undary\, and thus on the violated boundary conditi
on. This talk focuses on the trial method with vio
lated Dirichlet boundary data and on the developme
nt of higher order convergent versions of the tria
l method with the help of shape sensitivity analys
is. \n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
CONTACT:Mustapha Amrani
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