Discretization and optimal control of Lagrangian and Hamiltonian field theories

Institute of Applied Dynamics (LTD) in the Department of Mechanical Engineering of the Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)

Ihre Aufgaben

Description

Classical Lagrangian and Hamiltonian field theories are at the core of continuum mechanics, electromagnetismand general relativity- These theories have a rich geometric structure of which multisymplecticity may provehighly valuable when performing numerical simulations-The structure of optimal control problems is analogous to that of Lagrangian and Hamiltonian mechanics andfield theories- Therefore, the numerical treatment of these, particularly when applied to mechanical and fieldtheoretical 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 systemswith and without constraints- These discretisations will be then applied in optimal control problems- Wewill 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 ICMAT in Madrid, Spain whose expertise in geometric mechanics is well-known-

Ihr Profil

Notwendige Qualifikationen:

• Highly motivated candidates with degrees in mathematics, physics, engineering, computer science, or related fields-
• Knowledge of analytical mechanics, differential geometry, numerical methods and programming-
• Good written and oral communication skills in English (German desirable)-

Entgelt

TV-L E 13

Arbeitszeit

Vollzeit