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UID:calendar.103851.field_date.0@www.wpi.edu
DTSTAMP:20191211T085404Z
CREATED:20180614T121335Z
DESCRIPTION:Description of Event: \n\n\n\nKyle Dunn\n\n\n\nPhD Candidate\n
\n\n\nMathematical Sciences\n\n\n\nPhD Dissertation Presentation\n\n\n\nTi
tle: A Cut Finite Element Immersed Boundary Method and its Application to
a Chemotaxis Model\n\n\n\nAbstract: Originally developed for numerical ana
lysis of cardiac blood flow\, the immersed boundary method introduced in 1
977 by Peskin has gained popularity in various computational applications
involving a fluid with an immersed elastic structure. Peskin's method solv
es for the velocity and pressure of the fluid\, then uses the local veloci
ty to move the immersed boundary. There has been a recent surge in efforts
to further study this method due to its growth in popularity across many
applications\, including cell mechanics and fluid dynamics. Many advances
have been made to better incorporate the forces applied to the fluid by th
e elastic structure. Specifically\, we will consider the finite element ap
proach first introduced by Boffi\, Gastaldi\, and Heltai.\n\n\n\nWe will i
ntroduce a finite element method for Stokes equations with a massless imme
rsed membrane. We design and implement a high-accuracy cut finite element
method (CutFEM) which enables the use of a structured mesh that is not ali
gned with the immersed membrane. Allowing the membrane to move in the time
-dependent Stokes problem\, we design a semi-implicit time discretization.
We then prove that this semi-implicit scheme is unconditionally energy st
able and illustrate this theoretical result with numerical simulations. We
improve the first-order temporal accuracy of the semi-implicit algorithm
by implementing and analyzing an unconditionally stable Crank-Nicolson sch
eme. Next\, we turn our attention to the steady state Stokes problem to im
prove computational efficiency. A domain decomposition approach and a Diri
chlet-Neumann preconditioner are developed for the two-subdomain problem.
Finally\, we will use the immersed boundary method to incorporate interior
and exterior fluid flow into a local excitation\, global inhibition chemo
taxis model.\n\n\n\nDissertation Committee:\n\n\n\nDr. Marcus Sarkis\, WPI
(Advisor)\n\n\n\nDr. Roger Lui\, WPI (Co-advisor)\n\n\n\nDr. Zhongqiang Z
hang\, WPI\n\n\n\nDr. Sarah Olson\, WPI\n\n\n\nDr. Johnny Guzmán\, Brown U
niversity\n\n\n\nDr. Blanca Ayuso de Dios\, University of Bologna
DTSTART;TZID=America/New_York:20180713T120000
DTEND;TZID=America/New_York:20180713T140000
LAST-MODIFIED:20180626T193833Z
LOCATION:Stratton Hall
SUMMARY:Mathematical Sciences - PhD Dissertation Presentation 'A Cut Finite
Element Immersed Boundary Method and its Application to a Chemotaxis Mode
l' by Kyle Dunn
URL;TYPE=URI:https://www.wpi.edu/news/calendar/events/mathematical-sciences
-phd-dissertation-presentation-cut-finite-element-immersed
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