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


Mathematical and Numerical Modeling of the Cardiovascular System and Applications




M. Tezzele, F. Ballarin, and G. Rozza

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.

  author = {Tezzele, Marco and Ballarin, Francesco and Rozza, Gianluigi},
  title = {Combined parameter and model reduction of cardiovascular problems by means of active subspaces and POD-Galerkin methods},
  address = {Cham},
  booktitle = {Mathematical and Numerical Modeling of the Cardiovascular System and Applications},
  doi = {10.1007/978-3-319-96649-6_8},
  editor = {Boffi, Daniele and Pavarino, Luca F. and Rozza, Gianluigi and Scacchi, Simone and Vergara, Christian},
  isbn = {978-3-319-96649-6},
  pages = {185--207},
  publisher = {Springer International Publishing},
  year = {2018}