Combined Parameter and Model Reduction of Cardiovascular Problems by Means of Active Subspaces and POD-Galerkin Methods

  • Marco Tezzele
  • Francesco Ballarin
  • Gianluigi RozzaEmail author
Part of the SEMA SIMAI Springer Series book series (SEMA SIMAI, volume 16)


In this chapter we introduce a combined parameter and model reduction methodology and present its application to the efficient numerical estimation of a pressure drop in a set of deformed carotids. The aim is to simulate a wide range of possible occlusions after the bifurcation of the carotid. A parametric description of the admissible deformations, based on radial basis functions interpolation, is introduced. Since the parameter space may be very large, the first step in the combined reduction technique is to look for active subspaces in order to reduce the parameter space dimension. Then, we rely on model order reduction methods over the lower dimensional parameter subspace, based on a POD-Galerkin approach, to further reduce the required computational effort and enhance computational efficiency.



This work was partially supported by the INDAM-GNCS 2017 project “Advanced numerical methods combined with computational reduction techniques for parameterised PDEs and applications”, and by European Union Funding for Research and Innovation—Horizon 2020 Program—in the framework of European Research Council Executive Agency: H2020 ERC CoG 2015 AROMA-CFD project 681447 “Advanced Reduced Order Methods with Applications in Computational Fluid Dynamics” P.I. Gianluigi Rozza.


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Marco Tezzele
    • 1
  • Francesco Ballarin
    • 1
  • Gianluigi Rozza
    • 1
    Email author
  1. 1.Mathematics Area, mathLabSISSATriesteItaly

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