Hierarchical Methods for Simulation and Optimal Design with Applications to Magnetic Field Problems (Subprojekt des SFB F-13)
Sprache der Bezeichnung:
Hierarchical Methods for Simulation and Optimal Design with Applications to Magnetic Field Problems (project of the SFB "Numerical and Symbolic Scientific Computing")
The subject of this project is the development, analysis and implementation of numerically efficient algorithms for solving optimal design problems arising, e.g., in magnetostatics. The project aims at a unified treatment of direct simulation and optimization based on hierarchical methods. The development of both numerical algorithms and the power of hardware components during the last few years enables us today to solve direct simulation problems with some 100.000 unknowns in seconds. However, most of the practical problems are inverse or are given implicitly by a functional which is to be optimized. This project deals with the second case, for which until now no efficient numerical methodology exists. Our approach aims at a uniform algorithm involving both, direct simulation and optimization, instead of just using some direct simulation within an optimization algorithm.
Additionally, optimal design problems cause the need for handling parameter-dependent geometries. Thus, new flexible data structures describing the geometry have to be defined. Moreover, in order to construct efficient algorithms, inter-grid transfer operators have to be defined. Furthermore, adaptive strategies based on error estimates should be applied in order to reduce the total complexity of the discrete problems. Parallel computers offer the opportunity to speed up the solution of direct problems which is indispensable with respect to optimization. 2D applications have shown that Domain Decomposition (DD) methods or methods based on DD data partitions are well suited for this purpose in the field of magnetostatics. Computer aided optimal design of electromagnetic machines is the ultimate aim of practical applications.
However, the crucial goal of this project is the development of new and much faster methods based on the hierarchical coupling of simulation and optimization by a "Multilevel-Nested-Iteration" and the parallelization of the coupled method.