Descriptif

Plan of the course (subject to slight changes):

1. Introduction (motivation, PDEs, variational formulations, finite elements, FreeFEM)
2. Introduction to optimization (basic optimization algorithms, gradient descent, Newton, implementations and applications)
3. First Examples of PDE constrained optimization problems (existence of solutions, computing the sensitivity, adjoint method, FreeFem examples)
4. Time dependent problems, special cases (backward adjoint, alternate minimization)
5. Shape optimization: introduction, existence questions, shape derivatives
6. Shape derivatives, first numerical methods and examples
7. Various ways of parametrizing shapes in numerical shape optimization
8. Spectral problems: optimizing the eigenvalues of operators depending on PDEs defined on variable domains
9. Actual research questions related to shape optimization problems and Partial Differential Equations