Adaptive Reduced Basis Methods for Parameterized Evolution Problems with Application in Optimization and State Estimation

Beschreibung

Simulations provide support in understanding and predicting the behavior of systems in engineering and science. However, if the problem setting is rather complex the computational costs for performing simulations can be extremely high. In those cases model order reduction techniques can help to lower the computational complexity and to speed up the computation of solutions. In the first part, this thesis gives an introduction to the Reduced Basis Method - a model reduction technique particularly suited for parameterized problems described by partial differential equations (PDEs) - while focusing on time dependent problems. Furthermore, adaptive basis generation methods are presented, allowing the construction of efficient reduced basis spaces. In the second part, the Reduced Basis Method is applied to accelerate parameter optimizations under PDE-constraints and to perform rapid state estimations for systems described by PDEs using measurements. Error bounds for these applications are derived in order to certify the use of reduced order models.

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Markus Dihlmann

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Kalman filter Reduced Basis Method adaptive data assimilation error estimation model reduction parameterized partial differential equation pde-constrained optimization state estimation

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