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      Advances in Hierarchical Model Reduction and combination with other computational reduction methods

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          Abstract

          In this work we present address the combination of the Hierarchical Model (Hi-Mod) reduction approach with projection-based reduced order methods, exploiting either on Greedy Reduced Basis (RB) or Proper Orthogonal Decomposition (POD), in a parametrized setting. The Hi-Mod approach, introduced in, is suited to reduce problems in pipe-like domains featuring a dominant axial dynamics, such as those arising for instance in haemodynamics. The Hi-Mod approach aims at reducing the computational cost by properly combining a finite element discretization of the dominant dynamics with a modal expansion in the transverse direction. In a parametrized context, the Hi-Mod approach has been employed as the high-fidelity method during the offline stage of model order reduction techniques based on RB or POD. The resulting combined reduction methods, which have been named Hi-RB and Hi-POD, respectively, will be presented with applications in diffusion-advection problems, fluid dynamics and optimal control problems, focusing on the approximation stability of the proposed methods and their computational performance.

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          Author and article information

          Journal
          ScienceOpen Posters
          ScienceOpen
          27 April 2018
          Affiliations
          [1 ]MOX, Department of Mathematics, Politecnico di Milano, Milano, Italy
          [2 ]mathLab, Mathematics Area, SISSA, Trieste, Italy
          [* ]Correspondence: mzancana@ 123456sissa.it
          Article
          10.14293/P2199-8442.1.SOP-MATH.JOWNZF.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.

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