Department of Mathematics - Seminar on Applied Mathematics - Computational Optimization of Spectral Band-gap for Periodic Wave Operators

In this talk, we consider the optimization problem of maximizing the shared gap between two spectral bands of two periodic wave operators that attain different topological invariant. I will present an efficient semi-definite optimization approach to solve the underlying optimization problem subject to the PDE constraints in the form of the eigenvalue problem. I will also introduce a computational strategy to preserve the topology of the photonic crystal during the optimization.