Optimization with PDEs considers nonlinear optimization problems, where constraints are given by partial differential equations.
Optimization with PDEsCoordination: Prof. Dr. Anton Schiela
Contact: Prof. Dr. Anton Schiela
Represented in MODUS since September 2016
Members with experience in this area:
The method "Optimization with PDEs":
What is this?
Optimization with PDEs considers nonlinear optimization problems, where constraints are given by partial differential equations. They can be formulated as optimization problems in infinite dimensional function spaces and solved by the combination of techniques from simulation of partial differential equations and nonlinear optimization. Since the resulting problems are of very large scale it is important to exploit problem inherent structure to obtain efficient solution algorithms
What is it good for?
These problems always occur if one wants to infulence a distributed physical process in an optimal way. Important examples are the control of heating and cooling processes in manufacturing, optimization of shapes in aerodynamics, and medical therapy planning.
Where have we applied it?
The members of MODUS have covered application problems in this field of research
- planning of hyperthermia cancer treatment
- optimization of facial bone implants
- identification of muscle fibres by measurements at the skin surface
- control of probability density functions via the Fokker-Planck equation
- optimal control of molten carbonate fuel cell modells
- trajectory optimization of hypersonic planes s.t. heat constraints