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Hierarchical Preconditioning for P T AP ‐Systems arising from particulate flows
Author(s) -
Prignitz Rodolphe,
Reitsam Andreas,
Bänsch Eberhard
Publication year - 2012
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201210325
Subject(s) - preconditioner , subspace topology , schur complement , discretization , krylov subspace , projection (relational algebra) , finite element method , newtonian fluid , mathematics , iterative method , computer science , physics , mathematical analysis , mathematical optimization , mechanics , algorithm , eigenvalues and eigenvectors , thermodynamics , quantum mechanics
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)