Title: Multilevel preconditioner of Polynomial Chaos Method for quantifying uncertainties in a blood pump,
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.