Blog
About

364
views
1
recommends
+1 Recommend
2 collections
    49
    shares
      • Record: found
      • Abstract: found
      • Poster: found
      Is Open Access

      Combining POD Model Order Reduction with Adaptivity

      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

          A crucial challenge within snapshot-based POD model order reduction for time-dependent systems lies in the input dependency. In the ‘offline phase’, the POD basis is computed from snapshot data obtained by solving the high-fidelity model at several time instances. If a dynamical structure is not captured by the snapshots, this feature will be missing in the ROM simulation. Thus, the quality of the POD approximation can only ever be as good as the input material. In this sense, the accuracy of the POD surrogate solution is restricted by how well the snapshots represent the underlying dynamical system. If one restricts the snapshot sampling process to uniform and static discretizations, this may lead to very fine resolutions and thus large-scale systems which are expensive to solve or even can not be realized numerically. Therefore, offline adaptation strategies are introduced which aim to filter out the key dynamics. On the one hand, snapshot location strategies detect suitable time instances at which the snapshots shall be generated. On the other hand, adaptivity with respect to space enables us to resolve important structures within the spatial domain. Motivated from an infinite-dimensional perspective, we explain how POD in Hilbert spaces can be implemented. The advantage of this approach is that it only requires the snapshots to lie in a common Hilbert space. This results in a great flexibility concerning the actual discretization technique, such that we even can consider r-adaptive snapshots or a blend of snapshots stemming from different discretization methods. Moreover, in the context of optimal control problems adaptive strategies are crucial in order to adjust the POD model according to the current optimization iterate.

          Related collections

          Author and article information

          Journal
          ScienceOpen Posters
          ScienceOpen
          27 April 2018
          Affiliations
          [1 ]University Hamburg
          [* ]Correspondence: carmen.graessle@ 123456uni-hamburg.de
          Article
          10.14293/P2199-8442.1.SOP-MATH.RVMIXZ.v1
          Copyright © 2018

          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.

          Comments

          Comment on this article