Reduced Basis Methods: Success, Limitations and Future Challenges

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Mario Ohlberger Stephan Rave

Abstract

Parametric model order reduction using reduced basis methods can be an effective tool for obtaining quickly solvable reduced order model  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. Moreover, we highlight some recent approaches employing nonlinear  approximation techniques which aim to overcome the current limitations of reduced basis methods.

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How to Cite
OHLBERGER, Mario; RAVE, Stephan. Reduced Basis Methods: Success, Limitations and Future Challenges. Proceedings of the Conference Algoritmy, [S.l.], p. 1-12, feb. 2016. Available at: <http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/389>. Date accessed: 22 sep. 2017.
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