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An Aggregation-Based Algebraic Multigrid Method with Deflation Techniques and Modified Generic Factored Approximate Sparse Inverses

Author

Listed:
  • Anastasia A. Natsiou

    (School of Computing, Technological University of Dublin, D07 H6K8 Dublin, Ireland)

  • George A. Gravvanis

    (Department of Electrical and Computer Engineering, School of Engineering, Democritus University of Thrace, Kimmeria, 67100 Xanthi, Greece)

  • Christos K. Filelis-Papadopoulos

    (Department of Computer Science, University College Cork, T12 XF62 Cork, Ireland)

  • Konstantinos M. Giannoutakis

    (Department of Applied Informatics, School of Information Sciences, University of Macedonia, 54636 Thessaloniki, Greece)

Abstract

In this paper, we examine deflation-based algebraic multigrid methods for solving large systems of linear equations. Aggregation of the unknown terms is applied for coarsening, while deflation techniques are proposed for improving the rate of convergence. More specifically, the V-cycle strategy is adopted, in which, at each iteration, the solution is computed by initially decomposing it utilizing two complementary subspaces. The approximate solution is formed by combining the solution obtained using multigrids and deflation. In order to improve performance and convergence behavior, the proposed scheme was coupled with the Modified Generic Factored Approximate Sparse Inverse preconditioner. Furthermore, a parallel version of the multigrid scheme is proposed for multicore parallel systems, improving the performance of the techniques. Finally, characteristic model problems are solved to demonstrate the applicability of the proposed schemes, while numerical results are given.

Suggested Citation

  • Anastasia A. Natsiou & George A. Gravvanis & Christos K. Filelis-Papadopoulos & Konstantinos M. Giannoutakis, 2023. "An Aggregation-Based Algebraic Multigrid Method with Deflation Techniques and Modified Generic Factored Approximate Sparse Inverses," Mathematics, MDPI, vol. 11(3), pages 1-15, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:640-:d:1047993
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    References listed on IDEAS

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    1. P. E. Kyziropoulos & C. K. Filelis-Papadopoulos & G. A. Gravvanis, 2015. "Parallel N -Body Simulation Based on the PM and P3M Methods Using Multigrid Schemes in conjunction with Generic Approximate Sparse Inverses," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-12, April.
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    Cited by:

    1. Xu Xu & Jinyu Guo & Peixin Ye & Wenhui Zhang, 2023. "Approximation Properties of the Vector Weak Rescaled Pure Greedy Algorithm," Mathematics, MDPI, vol. 11(9), pages 1-23, April.

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