Syllabus
Sensitivity analysis in optimal shape design problems:
- the algebraic sensitivity analysis of algebraic systems arising from discretizations of optimization problems
- sensitivity analysis in sizing optimization problems
- sensitivity analysis in shape optimization problems , material and shape derivative of solutions to PDE's.
- differentiation of cost functionals, optimality conditions.
- application of the shape optimization approach for solving free boundary problems of Bernoulli type.
Annotation
The second part of this course (summer semester) is devoted to practical aspects of shape optimization problems.
It concerns sensitivity analysis, i.e. the differentiability of solutions to state problems and of cost functionals with respect to design parameters for both, continuous as well as the discrete setting of the problem.