Reduced Basis Methods for Higher Order Evolution Problems and Application in Optimization

Prof. Dr. Bernard Haasdonk

Markus Dihlmann

15.11.2009

14.11.2012

In the current project, we will extend the RB-methodology to a general class of higher-order evolution systems. Furthermore we will investigate more goal oriented basis-generation techniques to improve the RB-methodology.

Many problems in natural and engineering sciences can be described by parametrized partial differential equations (PDEs). Modern discretization techniques result in simulation models, which are computationally intensive and not suited for a multi-query setting, i.e situations where multiple simulations for varying parameters are required, e.g. optimization, optimal control, inverse problems, statistical analysis, etc. Reduced Basis (RB) methods aim at producing hierarchical low-dimensional parametrized models for approximating the parametrized PDE solution, providing estimates for output functionals and error bounds.

As a multi-query setting, we consider parameter optimization problems. Relations between the detailed and reduced optimization problem and their solutions will be investigated analytically and experimentally. The algorithms will be realized in the software environment RBmatlab, a MATLAB library for RB-simulations. The generality and modularity of the model reduction technique will allow automatic reduction of various real-world problems. Primarily, we aim to solve optimization problems from the SimTech application fields.