Abstract:
We examine shape optimization problems in the context of inexact
sequential quadratic programming.
Inexactness is a consequence of using adaptive finite element methods
(AFEM) to approximate the
state equation, update the boundary, and compute the geometric
functional. We present a novel algorithm
that uses a dynamic tolerance and equidistributes the errors due to
shape optimization and discretization,
thereby leading to coarse resolution in the early stages and fine
resolution upon convergence. We discuss the
ability of the algorithm to detect whether or not geometric
singularities such as corners are genuine to the
problem or simply due to lack of resolution - a new paradigm in adaptivity.
(Joint work with P. Morin, R.H Nochetto and M.S.Pauletti)