PDE-constrained optimization, where the underlying PDE is recast as a boundary integral model, will be discussed form a modeling perspective focusing on computational and numerical issues.

To start with, the talk will provide a brief introduction to boundary integral models for Laplace, Stokes and Helmholtz equations, and outline advantages and disadvantages in choosing such models over classical discretization strategies. Then it will proceed with defining a few optimization problems on these models, considering both full-field design variables, and reduced space ones, as is the case for shape optimization over suitably parametrized surfaces.  

The main point of the talk will be to outline differences between continuous and discrete adjoints, together with their limitations, and complementary considerations, such as the use of automatic differentiation, adjoint consistency, conditions for self-adjointness, and adjoints for many-body problems.