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.

Information is spatially distributed over data servers and for many services online it has to be available at all times, but those servers are not always available. If we store the information in a smart way, we might be able to still get our information even if we can not reach the servers.
There are two factors we have to keep in mind when we restore the servers and information. Those are the repair bandwidth, this is the amount of data you need to download to repair a failed server, and the repair degree, this is the amount of other servers you have to access before you can repair your server.
We will look at two methods for restoring information with focusing on the repair degree, which means to access the least amount of other servers.
First we discuss how we can repair one and multiple failures or erasures using the cooperative and sequential repairing method. Then we discuss the parameters for a sequential locally repairable code and its locality or repair degree. Next we will discuss the parameters for the Hamming code and the extended Hamming code and their locality for which we have constructed a function to calculate the generalized Hamming weight with kappa smaller than or equal to 3. Now we can compare the sequential locally repairable code with the Hamming code for two erasures and we can compare the sequential locally repairable code with the extended Hamming code for three erasures. The result is that the sequential locally repairable code has a much lower locality than the Hamming code and the extended Hamming code, but they have a higher information rate.