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SUMMARY:Numerical shape optimization with finite elements: a bit of theory
  and a bit of practice - Alberto Paganini (University of Leicester)
DTSTART:20250529T140000Z
DTEND:20250529T150000Z
UID:TALK226756@talks.cam.ac.uk
CONTACT:Georg Maierhofer
DESCRIPTION:Shape optimization is about finding domain geometries that min
 imize a given objective function. Dido’s isoperimetric problem of findin
 g a geometry with maximal area for a given perimeter is a classical exampl
 e. In most applications\, evaluating the objective function requires solvi
 ng a boundary value problem on the domain to be optimized. For example\, t
 o compute the energy dissipated by a fluid flowing in a pipe one must firs
 t compute a solution to a fluid model. The presence of such constraints ma
 kes shape optimization problems particularly challenging. Even computing a
 pproximate solutions with numerical methods is not straightforward because
  this requires solving a boundary value problem on a computational domain 
 that changes at each iteration of the optimization algorithm.\nIn this tal
 k\, I will describe how the finite element method enables a natural implem
 entation of the moving-mesh shape optimization method that generalizes str
 aightforwardly to higher-order discretizations. I will also explain how fi
 nite element software can automated the evaluation of shape derivatives al
 ong finite element directions. Finally\, I will present how these aspects 
 have been realized in the automated PDE-constrained shape optimization too
 lbox Fireshape.\nThe talk is designed to be accessible to a general academ
 ic audience interested in applied mathematics. Prior knowledge of the fini
 te element method is not assumed.
LOCATION:Centre for Mathematical Sciences\, MR14
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