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Inexact Additive Schwarz Solvers for hp-FEM Discretizations in Three Dimensions

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Advanced Finite Element Methods and Applications

Part of the book series: Lecture Notes in Applied and Computational Mechanics ((LNACM,volume 66))

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Abstract

In this paper, a boundary value problem of second order in three space dimensions is discretized by means of the hp-version of the finite element method. The system of linear algebraic equations is solved by the preconditioned conjugate gradient method with an overlapping domain decomposition preconditioner with in-exact subproblem solvers. In addition to a global solver for the low order functions, the ingredients of this preconditioner are local solvers for the patches. Here, a solver is used which utilizes the tensor product structure of the patches. The efficiency in time and iteration numbers of the presented solver is shown in several numerical examples for diffusion like problems as well as for problems in linear elasticity.

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Authors and Affiliations

  1. Institut für Numerische Simulation, Rheinische Friedrich–Wilhelms–Universität Bonn, Wegelerstraße 6, 53115, Bonn, Germany

    Sven Beuchler

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  1. Sven Beuchler
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Correspondence to Sven Beuchler .

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Editors and Affiliations

  1. Inst. Mathematik und Bauinformatik, Universität der Bundeswehr München, Neubiberg, 85579, Germany

    Thomas Apel

  2. Institut für Numerische Mathematik, Technische Universität Graz, Steyrergasse 30, Graz, 8010, Austria

    Olaf Steinbach

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Beuchler, S. (2013). Inexact Additive Schwarz Solvers for hp-FEM Discretizations in Three Dimensions. In: Apel, T., Steinbach, O. (eds) Advanced Finite Element Methods and Applications. Lecture Notes in Applied and Computational Mechanics, vol 66. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30316-6_4

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  • DOI: https://doi.org/10.1007/978-3-642-30316-6_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-30315-9

  • Online ISBN: 978-3-642-30316-6

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