Hierarchical Preconditioning for P^T AP-Systems arising from particulate flows

Particulate flows, i.e. flow of an incompressible, Newtonian carrier fluid loaded with (many) rigid bodies, play an important role in diverse technical applications. In [1] a finite element method was introduced to simulate such flows. The method relies on a splitting method and a subspace projection method to incorporate the rigid body motion of the particles in a so called one domain approach [2]. The resulting systems arising after discretization are ill conditioned in general. Thus preconditioning is mandatory for instance when using an iterative Krylov subspace methods. In this paper we present a Schur complement based preconditioner well suited for this type of application. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)