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An Efficient Multigrid Solver based on Distributive Smoothing for Poroelasticity Equations

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Abstract

In this paper, we present a robust distributive smoother in a multigrid method for the system of poroelasticity equations. Within the distributive framework, we deal with a decoupled system, that can be smoothed with basic iterative methods like an equation-wise red-black Jacobi point relaxation. The properties of the distributive relaxation are optimized with the help of Fourier smoothing analysis. A highly efficient multigrid method results, as is confirmed by Fourier two-grid analysis and numerical experiments.

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Authors and Affiliations

  1. University of Cologne, Mathematical Institute, Weyertal 86-90, 50931, Cologne, Germany

    R. Wienands

  2. Departamento de Mathemática Aplicada, University of Zaragoza, Pedro Cerbuna 12, 50009, Zaragoza, Spain

    F. J. Gaspar

  3. Departamento de Mathemática Aplicada, University of Zaragoza, Pedro Cerbuna 12, 50009, Zaragoza, Spain

    F. J. Lisbona

  4. Delft University of Technology, Faculty of Information Technology Systems, Department of Applied Mathematical Analysis, Mekelweg 4, 2628 CD, Delft, The Netherlands

    C. W. Oosterlee

Authors
  1. R. Wienands
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  2. F. J. Gaspar
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  3. F. J. Lisbona
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  4. C. W. Oosterlee
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Corresponding author

Correspondence to R. Wienands.

Additional information

AMS Subject Classifications: 65N55, 74F10, 74S10, 65M12.

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Wienands, R., Gaspar, F., Lisbona, F. et al. An Efficient Multigrid Solver based on Distributive Smoothing for Poroelasticity Equations. Computing 73, 99–119 (2004). https://doi.org/10.1007/s00607-004-0078-y

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  • DOI: https://doi.org/10.1007/s00607-004-0078-y

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