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Arbeitsgruppe Nichtlineare Partielle Differentialgleichungen

Kollegiengebäude Mathematik (20.30)
Zimmer 3.029

Karlsruher Institut für Technologie
Institut für Analysis
Englerstraße 2
76131 Karlsruhe

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Dr. Stephan Rave, Universität Münster

Mittwoch 14.01.2015, 15:45
Raum 1C-04 (Allianz-Gebäude, 5.20)

'Reduced Basis Methods: From Theory to Implementation'

Reduced basis approximation is a very generic approach for model order reduction of parametric partial differential equation problems: Given some high-dimensional discretization of the equation to be solved, a reduced approximation space is computed from the liner span of the solutions of the discretization for certain well-chosen parameters. A reduced model is then obtain by Galerkin projection of the original equation onto the reduced space. Typically, the so obtained reduced model can be solved several orders of magnitude faster than the original discretization while retaining the same approximation quality. Applications are many-query problems like design optimization, where the same equation has to be solved repeatedly for many different parameters, or real-time scenarios, where the equation has to be solved quickly with limited resources (think of mobile devices) for unknown parameters.

Starting with results from approximation theory motivating the approach, I will give a short overview on the main ingredients of the reduced basis methodology and present recent work on the reduction of microscale lithium-ion battery models as an application example. Moreover, I will show how the combination of reduced basis techniques with the 'method of freezing' leads to a nonlinear approximation approach for handling advection-driven problems, which are particularly hard to approximate using traditional methods. Finally, I will discuss the technical difficulties in implementing reduced basis schemes and present the open-source software library pyMOR which has been specifically designed for easy integration of reduced basis methods with existing PDE solvers.