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DTSTART:20171105T020000
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UID:calendar.96191.field_date.0@www.wpi.edu
DTSTAMP:20200809T205401Z
CREATED:20180205T192105Z
DESCRIPTION:Description of Event: \n\n\n\nPhD Dissertation Proposal Present
ation\n\n\n\nKyle Dunn\n\n\n\nTitle: A Cut Finite Element Immersed Boundar
y Method and its Application to a Chemotaxis Model\n\n\n\nAbstract: Origin
ally developed for numerical analysis of cardiac blood flow\, the immersed
boundary method introduced in 1977 by Peskin has gained popularity in var
ious computational applications. Peskin’s method solves for the velocity a
nd pressure of the fluid\, then uses the local velocity to move the immers
ed boundary. Due to its growth in popularity across many applications\, in
cluding cell mechanics and fluid dynamics\, there has been a recent surge
in effort to further study this method. Many advances have been made to be
tter incorporate the forces applied to the fluid by the elastic structure.
Specifically\, we consider the finite element approach.\nWe will introduc
e a finite element method for the Stokes equations with a massless immerse
d membrane. We design and implement a high-accuracy cut finite element met
hod (CutFEM) for the steady-state problem which enables the use of a struc
tured mesh that is not aligned with the immersed membrane. Allowing the me
mbrane to move in the time-dependent Stokes problem\, we design a semi-imp
licit time discretization. We then prove that this semi-implicit scheme is
unconditionally energy stable and illustrate this theoretical result with
numerical simulations. Further advances of this method will be discussed\
, such as improved accuracy and preconditioning. Finally\, we will apply t
hese techniques to a chemotaxis model\, combining aspects of multiple exis
ting models and fully integrating the dynamics of the interior\, exterior\
, and cell membrane.
DTSTART;TZID=America/New_York:20180214T100000
DTEND;TZID=America/New_York:20180214T120000
LAST-MODIFIED:20180205T192228Z
LOCATION:Stratton Hall
SUMMARY:Mathematical Sciences - PhD Dissertation Proposal Presentation - 'A
Cut Finite Element Immersed Boundary Method and its Application to a Chem
otaxis Model' by Kyle Dunn
URL;TYPE=URI:https://www.wpi.edu/news/calendar/events/mathematical-sciences
-phd-dissertation-proposal-presentation-cut-finite-element
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