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On Superlinear PCG Methods for FDM Discretizations of Convection-Diffusion Equations

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Numerical Analysis and Its Applications (NAA 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5434))

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Abstract

The numerical solution of linear convection-diffusion equations is considered. Finite difference discretization leads to an algebraic system solved by a suitable preconditioned CG method, where the preconditioning approach is based on equivalent operators. Our goal is to study the superlinear convergence of the preconditioned CG iteration and to find mesh independent behaviour on a model problem. This is an analogue of previous results where FEM discretization was used.

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Authors and Affiliations

  1. Department of Applied Analysis and Computational Mathematics, ELTE University, H-1117, Budapest, Hungary

    János Karátson & Tamás Kurics

Authors
  1. János Karátson
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  2. Tamás Kurics
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Editors and Affiliations

  1. Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Bl. 25-A, 1113, Sofia, Bulgaria

    Svetozar Margenov

  2. FNSE, Department of Numerical Methods and Statistics, University of Rousse, 8 Studentska str., 7017, Rousse, Bulgaria

    Lubin G. Vulkov

  3. Department of Informatics and Mathematical Modelling, Technical University of Denmark, 2800, Kongens, Lyngby, Denmark

    Jerzy Waśniewski

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© 2009 Springer-Verlag Berlin Heidelberg

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Karátson, J., Kurics, T. (2009). On Superlinear PCG Methods for FDM Discretizations of Convection-Diffusion Equations. In: Margenov, S., Vulkov, L.G., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2008. Lecture Notes in Computer Science, vol 5434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00464-3_38

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  • DOI: https://doi.org/10.1007/978-3-642-00464-3_38

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00463-6

  • Online ISBN: 978-3-642-00464-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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