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      A generalized POD space-time Galerkin scheme for parameter dependent dynamical systems

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      MoRePaS 2015 - Model Reduction of Parametrized Systems III
      proper orhogonal decomposition, POD, Burgers equation, MOR, model order reduction, parameterized systems
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            Abstract

            In a recent work [Baumann et al. 'Discrete Input/Output Maps and their Relation to Proper Orthogonal Decomposition' (2015)], a generalized version of Proper Orthogonal Decomposition (POD) has been formulated based on generalized measurements replacing the snapshot matrix of the standard POD. We extend this approach in two directions. Firstly, we add a parameter dependence as a third dimension of the measurement matrix. Secondly, we use a higher-order SVD to obtain optimized low-dimensional bases for both the space and the time discretization. Then, applying a space-time Galerkin scheme, a time-dependent PDE can be transformed into a small system of algebraic equations -- the reduced model. We illustrate the properties and benefits of this approach for an example of nonlinear Burgers equation with varying diffusion parameters.

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            Author and article information

            Conference
            ScienceOpen Posters
            ScienceOpen
            December 1 2015
            Author information
            https://orcid.org/0000-0003-0228-8522
            https://orcid.org/0000-0002-2198-3080
            https://orcid.org/0000-0003-3362-4103
            Article
            10.14293/P2199-8442.1.SOP-MATH.P8ECXQ.v1
            47383ae1-fc56-48b1-b059-b52f4a130795

            This work has been published open access under Creative Commons Attribution License CC BY 4.0 , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Conditions, terms of use and publishing policy can be found at www.scienceopen.com .

            MoRePaS 2015 - Model Reduction of Parametrized Systems III
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            Applied mathematics,Numerical methods
            proper orhogonal decomposition, POD, Burgers equation, MOR, model order reduction, parameterized systems

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