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SUMMARY:Higher order convergent trial methods for Bernoulli's free boundar
 y problem - Mitrou\, G (University of Southampton)
DTSTART:20140626T153000Z
DTEND:20140626T160000Z
UID:TALK53181@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Co-author: Helmut Harbrecht (University of Basel) \n\nFree bou
 ndary problem is a partial differential equation to be solved in a domain\
 , a part of whose boundary is unknown  the so-called free boundary. Beside
  the standard boundary conditions that are needed in order to solve the pa
 rtial differential equation\, an additional boundary condition is imposed 
 at the free boundary. One aims thus to determine both\, the free boundary 
 and the solution of the partial differential equation. \n\nThis work is de
 dicated to the solution of the generalized exterior Bernoulli free boundar
 y problem which is an important model problem for developing algorithms in
  a broad band of applications such as optimal design\, fluid dynamics\, el
 ectromagnentic shaping etc. For its solution the trial method\, which is a
  fixed-point type iteration method\, has been chosen. \n\nThe iterative sc
 heme starts with an initial guess of the free boundary. Given one boundary
  condition at the free boundary\, the boundary element method is applied t
 o compute an approximation of the violated boundary data. The free boundar
 y is then updated such that the violated boundary condition is satisfied a
 t the new boundary. Taylor's expansion of the violated boundary data aroun
 d the actual boundary yields the underlying equation\, which is formulated
  as an optimization problem for the sought update function. When a target 
 tolerance is achieved\, the iterative procedure stops and the approximate 
 solution of the free boundary problem is detected. \n\nThe efficiency of t
 he trial method as well as its speed of convergence depends significantly 
 on the update rule for the free boundary\, and thus on the violated bounda
 ry condition. This talk focuses on the trial method with violated Dirichle
 t boundary data and on the development of higher order convergent versions
  of the trial method with the help of shape sensitivity analysis. \n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
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