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Reduced Basis Methods: Success, Limitations and Future Challenges · Around

2015

Reduced Basis Methods: Success, Limitations and Future Challenges

Ohlberger, Mario, Rave, Stephan

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Parametric model order reduction using reduced basis methods can be an effective tool for obtaining quickly solvable reduced order models of parametrized partial differential equation problems.

With speedups that can reach several orders of magnitude, reduced basis methods enable high fidelity real-time simulations of complex systems and dramatically reduce the computational costs in many-query applications.
In this contribution we analyze the methodology, mainly focussing on the theoretical aspects of the approach.
In particular we discuss what is known about the convergence properties of these methods: when they succeed and when they are bound to fail.

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Chapter to appear in P. Benner, A. Cohen, M. Ohlberger and K. Willcox: ”Model Reduction and Approximation for Complex Systems”, Springer
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