Postdoctoral position in Geometric integration of field theories at ICMAT

The Institute of Mathematical Sciences (ICMAT), Madrid, Spain seeks highly motivated candidates to fill a 2-year Postdoctoral position for the AEI-DFG project Discretization and optimal control of Lagrangian and Hamiltonian field theories.

Description :

Classical Lagrangian and Hamiltonian field theories are at the core of continuum mechanics, electromagnetism and general relativity. These theories have a rich geometric structure of which multisymplecticity may prove highly valuable when performing numerical simulations.

The structure of optimal control problems is analogous to that of Lagrangian and Hamiltonian mechanics and field theories. Therefore, the numerical treatment of these, particularly when applied to mechanical and field theoretical systems, may benefit from the use of structure-preserving numerical methods.

In this project we will study and develop high-order multisymplectic numerical integrators for continuum systems with and without constraints. These discretisations will be then applied in optimal control problems. We will also attempt to imbue structure-preserving properties to non-preserving methods using neural networks.

The project will be carried out in collaboration with our partner team at Institute of Applied Dynamics (LTD) in the Department of Mechanical Engineering of the Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU).

Qualifications :

• Highly motivated candidates with PhD. in mathematics, physics, engineering, computer science, or

related fields.

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