Parameter space and model reduction with shape parametrization, by means of active subspace and POD-Galerkin methods for industrial and biomedical applications

Marco Tezzele,Andrea Mola,Gianluigi Rozza,Francesco Ballarin

doi:10.14293/p2199-8442.1.sop-math.zkdilb.v1

Abstract

In this work we present both industrial and biomedical applications, focusing on shape parametrization and parameter space reduction by means of active subspaces. In particular we introduce a combined parameter and model reduction methodology using a POD-Galerkin approach, and its application to the efficient numerical estimation of a pressure drop in a set of deformed carotids [2]. The aim is to simulate a wide range of possible occlusions after the bifurcation of the carotid artery. A parametric description of the admissible deformations, based on radial basis functions interpolation technique implemented in the PyGeM python package, is introduced. The use of the reduced order model acting on the reduced parameter space allows significant computational savings and better performances. Moreover we present the reduction of heterogeneous parameter space in a naval engineering problem, that is the hydrodynamic flow past the hull of a ship advancing in calm water [3], considering structural and shape parameters. The geometrical parametrization is done via free form deformation. Some perspectives on a complete shape optimization pipeline by means of Dynamic Mode Decomposition (DMD) and POD with interpolation (PODI) are presented [1], together with the integration of the python packages PyDMD and EZyRB respectively.

Highlights

IntroductionWe introduce a new framework for parameters space reduction in naval and biomedical engineering obtained by coupling: Active Subspaces property to identify lower dimensional structure in the parameters space [1]; Free Form Deformation (FFD) and Radial Basis Functions (RBF), to morph the geometry; Response surfaces method (RS) and PODGalerkin methods
We introduce a new framework for parameters space reduction in naval and biomedical engineering obtained by coupling: Active Subspaces property to identify lower dimensional structure in the parameters space [1]; Free Form Deformation (FFD) and Radial Basis Functions (RBF), to morph the geometry; Response surfaces method (RS) and PODGalerkin methods.Geometrical Deformation: the PyGeM libraryPyGeM is a python library using Free Form Deformation, Inverse Distance Weighting, and Radial Basis Function interpolation to parametrize and morph complex geometries.It interacts with industrial file formats used for CAD management (.iges, .step, .stl), mesh files (.unv and OpenFOAM), and output files (.vtk)
The structural parameter is the displacement of the hull and the physical one is the velocity

Summary

Introduction

We introduce a new framework for parameters space reduction in naval and biomedical engineering obtained by coupling: Active Subspaces property to identify lower dimensional structure in the parameters space [1]; Free Form Deformation (FFD) and Radial Basis Functions (RBF), to morph the geometry; Response surfaces method (RS) and PODGalerkin methods. PyGeM is a python library using Free Form Deformation, Inverse Distance Weighting, and Radial Basis Function interpolation to parametrize and morph complex geometries. It interacts with industrial file formats used for CAD management (.iges, .step, .stl), mesh files (.unv and OpenFOAM), and output files (.vtk).

Carotid parametrization

Spectral and POD analysis

Eigenvalues and error analysis