Model Order Reduction Methods for Topology Optimization

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Topology optimization is a branch of mechanical engineering in which the topology of a structure is created and optimized to certain conditions and restrictions. In the last few decades, the demand for highly accurate and complex models of these structures has increased and it has a big effect on the computational power needed. To ease the computational load for the dynamical systems one can use model order reduction methods to reduce the size of the models.
Classic Arnoldi is a widely used method for model order reduction (MOR) with topology optimization. In this thesis, we discuss two-sided Arnoldi and IRKA to help find a suitable moment-matching MOR method for topology optimization. These two reduction methods are implemented and improved to create a high fidelity reduced model. For improvements in the accuracy, the use of orthogonalization methods is analysed and discussed as well as including rigid body modes for IRKA and a preconditioner for two-sided Arnoldi. Lastly, a participation factor is discussed and improved to help reduce the model created with two-sided Arnoldi.
In the end, we find that two-sided Arnoldi in combination with the participation factor performs better than IRKA by creating a smaller and more accurate reduced model.