WG Modelling and Scientific Computing
Administration: Prof. Dr. Andreas Rademacher
Modelling processes from production engineering like grinding, cutting, drilling or deep-drawing leads to systems of nonsmooth partial differential equations. They are often written as variational inequalities. Due to the complexity of problems of this type, the efficient solution is indispensable in the simulation and the optimal control of these processes.Our working group deals in detail with the following topics:
- Modelling, simulation, and optimal control of processes from production engineering.
- Finite element methods for problems from structural mechanics
- A posteriori error estimators based on the dual weighted residual (DWR) method
- Adaptive techniques for finite element meshes and the choice of models
- Efficient solution techniques and their implementation
To simulate processes from production engineering an interdisciplinary collaboration is essential. We develop an adequate modeling together with working groups from production engineering and mechanics. The appropriate discretization of the models is the second step. Usually, we use finite element methods. In many cases, single components of the process are only represented in detail. Other parts are roughly considered by different simulation techniques. Consequently, we have to couple the different approaches.
The efficient realization of the finite element method is the core part of our work. Here, we consider two different aspects. On the one hand, we want to maximize the accuracy while minimizing the numerical effort. The accuracy is measured in a process specific quantity and the effort is described by the total number unknowns. We apply adaptive techniques on the basis of a posteriori error estimators to achieve this goal. Furthermore, efficient solution algorithms, which are implemented in parallel, are used to minimize the computing time.
The last step is the verification and validation of the simulation concept based on measurement results. In this context, the determination of the model parameters is crucial. We frequently use techniques from numerical parameter identification. Finally, the simulation is employed to enhance the process management, where we also use techniques from optimal control.