Efficient Numerical Solution of Large Scale Algebraic Matrix Equations in PDE Control and Model Order Reduction

in accordance with the requirements for the degree Dr. rer. nat. M ˙ x(t)= N x(t)+ B u(t); y(t)= C x(t) ˆ M ˙ ˆ x(t) = ˆ N ˆ x(t)+ ˆ B u(t); y(t)= ˆ C ˆ x(t) ii iii to S ¸enay iv ACKNOWLEDGEMENTS Financial Support. Large parts of this research have been refined in the projects Parallele numerische Lösung von Optimalsteuerungsproblemen f ¨ ur instationäre Diffusions-Konvektions-Reaktionsgleichungen (project A15 in SFB393 Parallele Numerische Simulation f ¨ ur Physik und Kontinuumsmechanik), Numerische Lösung von Optimalsteuerungsproblemen f ¨ ur instationäre Diffusions-Konvektions-und Diffusions-Reaktionsgleichungen and Integrierte Simulation des Systems " Werkzeugmaschine-Antrieb-Zerspanprozess " auf der Grundlage ord-nungsreduzierter FEM-Strukturmodelle supported by the German Research Foundation (DFG) over the past years. Besides these, the integration and exchange project Parallele Algorithmen f ¨ ur hochdimensionale, d ¨ unnbesetzte algebraische Riccatigleichungen und Anwen-dungen in der Regelungstheorie inside the Acciones Integradas Hispano-Alemanas program of the German Academic Exchange Service (DAAD) has enabled me to undertake some very helpful and inspiring trips to Universitat Jaume I in Castelí on (Spain). Personal Thanks. My primary thanks go to my advisor and teacher Peter Benner for the introduction to and the guidance in this highly fascinating field of research with all its interesting types of applications. On the other hand the best mentor still depends on the many people working in the background. Therefore my thanks go to the colleagues and friends that I had the pleasure to work with at TU Chemnitz during the past almost 6 years. I cannot mention single persons without forgetting other important ones. So I will only pick the three most important ones, Ulrike Baur, Sabine Hein and Hermann Mena. As for Hermann I can only cite himself. I am particularly grateful to my dear friend Hermann Mena together with whom (among the most interesting topics in life) large parts of this work were discussed in our mid-afternoon coffee breaks. The countless inspiring discussions with Sabine have given me an increasingly deeper insight to many aspects of LQR and LQG design for parabolic PDEs. Also, I would know hardly half as much as I do today about model order reduction, if there had not been Ulrike providing me with endless advice and numerous suggestions regarding the field. I also want to thank Enrique S. Quintana-Ortí and his workgroup at Universitat Jaume I for the warm welcomes in Spain and for providing me a quiet place …

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