Online Reduced Basis Construction Procedure for Model Reduction of Parametrized Evolution Systems

The reduced basis method is a model reduction technique for parametrized PDEs. It approximates the parameter-dependent solutions in a low dimensional space constructed by “snapshots” of high dimensional discrete solutions for selected parameters. Usually this reduced space is built up in advance in a costly offline phase and is suited to approximate well all solutions for parameters stemming from a given parameter domain. For the case of time dependent problems we propose a new method which rapidly builds up a locally adapted approximation space for a given parameter by selection from and combination of a set of POD bases. Instead of generating a globally valid reduced space for the whole parameter domain we will show how to construct online a low dimensional approximation space which is more performant with respect to the online cost.