Modern Numerical Methods for Huge-Scale Optimization Problems with Time-Dependent PDE Constraints

My research interests are centered around the numerical study of optimal control problems.

I am especially interested in computational methods for large-scale systems arising from real-world problems, and their challenges from a numerical linear algebra point of view.

More specifically, my approaches enhance parallel-in-time methods for solving challenging PDE-constrained optimization problems, and require the development of robust preconditioners that can exploit the full potential of parallelization.

Moreover, I am interested in the numerical analysis of feedback controls, including model predictive control, and solving the associated operator equations.

Applications of this include sparse tree-coupled systems, such as domain decomposition of PDEs and scenario-based model predictive control, and flow control problems governed by unsteady Stokes and Oseen equations.