Multilevel preconditioner of Polynomial Chaos Method for quantifying uncertainties in a blood pump

TL;DR

This paper develops a multilevel preconditioner for Polynomial Chaos methods to efficiently quantify uncertainties in blood pump simulations, demonstrating improved computational performance for large-scale stochastic blood flow models.

Contribution

It introduces a multilevel preconditioning technique tailored for Polynomial Chaos methods applied to unsteady blood pump simulations, enhancing computational efficiency for large-scale problems.

Findings

Effective preconditioning reduces computation time.

Successful simulation of large-scale stochastic blood flow.

Demonstrated scalability on supercomputers with 30 million degrees of freedom.

Abstract

More than 23 million people are suffered by Heart failure worldwide. Despite the modern transplant operation is well established, the lack of heart donations becomes a big restriction on transplantation frequency. With respect to this matter, ventricular assist devices (VADs) can play an important role in supporting patients during waiting period and after the surgery. Moreover, it has been shown that VADs by means of blood pump have advantages for working under different conditions. While a lot of work has been done on modeling the functionality of the blood pump, but quantifying uncertainties in a numerical model is a challenging task. We consider the Polynomial Chaos (PC) method, which is introduced by Wiener for modeling stochastic process with Gaussian distribution. The Galerkin projection, the intrusive version of the generalized Polynomial Chaos (gPC), has been densely studied and applied for various problems. The intrusive Galerkin approach could represent stochastic process directly at once with Polynomial Chaos series expansions, it would therefore optimize the total computing effort comparing with classical non-intrusive methods. We compared different preconditioning techniques for a steady state simulation of a blood pump configuration in our previous work, the comparison shows that an inexact multilevel preconditioner has a promising performance. In this work, we show an instationary blood flow through a FDA blood pump configuration with Galerkin Projection method, which is implemented in our open source Finite Element library Hiflow3. Three uncertainty sources are considered: inflow boundary condition, rotor angular speed and dynamic viscosity, the numerical results are demonstrated with more than 30 Million degrees of freedom by using supercomputer.