Syllabus
Abstract formulation of shape optimization problems. Existence of solutions.
Discretization of shape optimization problems- abstract formulation. Convergence analysis
Application of abstract results to particular shape optimization problems with different state relations ( Dirichlet, Neumann, mixed Stokes)
Annotation
The first part of this course is devoted to comprehensive introduction to the mathematical theory of optimal shape design problems. The stability of solutions to elliptic PDE’s on parameters characterizing the geometry of systems ( thickness of plates, shape of domains where state problems are formulated) will be studied.
This property plays the key role in the existence analysis. This part deals not only with the continuous setting of problems but also with their discretizations (state problems by finite elements, shapes by Bezier curves) followed by the convergence analysis.