Theory and numerics of the coupled Maxwell-LLG system

In recent groundbreaking experiments, physicists managed to manipulate magnetic materials using ultrashort light pulses. This can be extremely useful for new data storage systems or magnetic sensors. This project aims to develop the mathematical theory and computational algorithms to simulate and predict this new technology. To that end, cutting edge mathematical theory for time dependent partial differential equations has to be developed. Those equations describe the behavior of magnets on a microscopic level and are notoriously hard to solve. The project will develop so-called adaptive approximation methods for those equations. Such methods automatically focus the bulk of the computational resources to hard subproblems, while not wasting them on easy parts of the problem. This will be supported by neural network models which are well suited to approximate solutions of the problem.