Plan of the course (subject to slight changes):
- Introduction (motivation, PDEs, variational formulations, finite elements, FreeFEM)
- Introduction to optimization (basic optimization algorithms, gradient descent, Newton, implementations and applications)
- First Examples of PDE constrained optimization problems (existence of solutions, computing the sensitivity, adjoint method, FreeFem examples)
- Time dependent problems, special cases (backward adjoint, alternate minimization)
- Shape optimization: introduction, existence questions, shape derivatives
- Shape derivatives, first numerical methods and examples
- Various ways of parametrizing shapes in numerical shape optimization
- Spectral problems: optimizing the eigenvalues of operators depending on PDEs defined on variable domains
- Actual research questions related to shape optimization problems and Partial Differential Equations
- Teaching coordinator: Bogosel Beniamin