Adaptive Trust Region POD Algorithms

• Applicant: Professor Dr. Ekkehard Sachs
• Subject Area: Mathematics
• Term: from 2009 to 2014
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 132832509

Dynamical systems described by general evolution equations, like a partial integro-differential equation, can be reduced in size through a proper orthogonal decomposition technique. If these systems are part of an optimization problem, one has to solve this problem numerically. While the optimization algorithm is working, the need for an update of the model might arise, which could prove to be a costly part in the overall computing budget. In order to alleviate this effect, a model management technique can be employed handling the coarse and fine grid models in the optimization phase. We base this on a multi-level trust region technique which is also able to deal with nonlinear models. Applications of this technique can be found in various fields of engineering (fluid flow problems) and finance (calibration of derivative products).

• DFG Programme: Priority Programmes
• Subproject of: SPP 1253: Optimisation with Partial Differential Equations