Abstract:

Shape optimization is indispensable for designing and constructing 
industrial components. Many problems that arise in application, particularly in 
structural mechanics and in the optimal control of distributed parameter 
systems, can be formulated as the minimization of functionals which 
are defined over a class of admissible domains.

The application of gradient based minimization algorithms involves the 
shape functionals’ derivative with respect to the domain under consideration. 
Such derivatives can analytically be computed by means of shape calculus 
and enable the paradigm first optimize then discretize. Especially, by identifying 
the sought domain with a parametrization of its boundary, the solution of the 
shape optimization problem will be equivalent to solving a nonlinear 
pseudodifferential equation for the unknown parametrization.

The present talk aims at surveying on analytical and numerical methods 
for shape optimization. In particular, besides several applications of 
shape optimization, the following items will be addressed:

• first and second order optimality conditions
• discretization of shapes
• existence and convergence of approximate shapes
• efficient numerical techniques to compute the state equation

Afternoon tea will be provided at 3:30pm