Blog
About

833
views
0
recommends
+1 Recommend
2 collections
    43
    shares
      • Record: found
      • Abstract: found
      • Poster: found
      Is Open Access

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

      ScienceOpen Posters

      ScienceOpen

      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.

      proper orhogonal decomposition, POD, Burgers equation, MOR, model order reduction, parameterized systems

      Read this article at

      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          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.

          Related collections

          Author and article information

          Journal
          10.14293/P2199-8442.1.SOP-MATH.P8ECXQ.v1

          Comments

          Comment on this article