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Block-preconditioners for conforming and non-conforming FEM discretizations of the Cahn-Hilliard equation
KTH, School of Engineering Sciences (SCI), Mechanics, Physicochemical Fluid Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0003-2830-0454
2012 (English)In: Large-Scale Scientific Computing, Springer Science+Business Media B.V., 2012, Vol. 7116 LNCS, 549-557 p.Conference paper (Refereed)
Abstract [en]

We consider preconditioned iterative solution methods to solve the algebraic systems of equations arising from finite element discretizations of multiphase flow problems, based on the phase-field model. The aim is to solve coupled physics problems, where both diffusive and convective processes take place simultaneously in time and space. To model the above, a coupled system of partial differential equations has to be solved, consisting of the Cahn-Hilliard equation to describe the diffusive interface and the time-dependent Navier-Stokes equation, to follow the evolution of the convection field in time. We focus on the construction and efficiency of preconditioned iterative solution methods for the linear systems, arising after conforming and non-conforming finite element discretizations of the Cahn-Hilliard equation in space and implicit discretization schemes in time. The non-linearity of the phase-separation process is treated by Newton's method. The resulting matrices admit a two-by-two block structure, utilized by the preconditioning techniques, proposed in the current work. We discuss approximation estimates of the preconditioners and include numerical experiments to illustrate their behaviour.

Place, publisher, year, edition, pages
Springer Science+Business Media B.V., 2012. Vol. 7116 LNCS, 549-557 p.
, Lecture Notes in Computer Science, ISSN 0302-9743 ; 7116
Keyword [en]
Algebra, Linear systems, Navier Stokes equations, Newton-Raphson method, Partial differential equations
National Category
Fluid Mechanics and Acoustics
URN: urn:nbn:se:kth:diva-99904DOI: 10.1007/978-3-642-29843-1_62ScopusID: 2-s2.0-84861740603ISBN: 978-364229842-4OAI: diva2:542658
8th International Conference on Large-Scale Scientific Computations,LSSC 2011;Sozopol;6 June 2011 through 10 June 2011
Swedish e‐Science Research Center

QC 20120802

Available from: 2012-08-02 Created: 2012-08-02 Last updated: 2013-09-16Bibliographically approved

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Do-Quang, Minh
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Physicochemical Fluid MechanicsLinné Flow Center, FLOW
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