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Multigrid for Q k Finite Element Matrices Using a (Block) Toeplitz Symbol Approach

Author

Listed:
  • Paola Ferrari

    (Dipartimento di Scienza ed Alta Tecnologia, Università dell’Insubria-Sede di Como, Via Valleggio 11, 22100 Como, Italy)

  • Ryma Imene Rahla

    (University of Tunis El Manar, ENIT-LAMSIN, BP 37, Tunis 1002, Tunisia)

  • Cristina Tablino-Possio

    (Dipartimento di Matematica e Applicazioni, Università di Milano Bicocca, via Cozzi 53, 20125 Milano, Italy)

  • Skander Belhaj

    (University of Tunis El Manar, ENIT-LAMSIN, BP 37, Tunis 1002, Tunisia)

  • Stefano Serra-Capizzano

    (Dipartimento di Scienze Umane e dell’Innovazione per il Territorio, Università dell’Insubria-Sede di Como, Via Valleggio 11, 22100 Como, Italy)

Abstract

In the present paper, we consider multigrid strategies for the resolution of linear systems arising from the Q k Finite Elements approximation of one- and higher-dimensional elliptic partial differential equations with Dirichlet boundary conditions and where the operator is div − a ( x ) ∇ · , with a continuous and positive over Ω ¯ , Ω being an open and bounded subset of R 2 . While the analysis is performed in one dimension, the numerics are carried out also in higher dimension d ≥ 2 , showing an optimal behavior in terms of the dependency on the matrix size and a substantial robustness with respect to the dimensionality d and to the polynomial degree k .

Suggested Citation

  • Paola Ferrari & Ryma Imene Rahla & Cristina Tablino-Possio & Skander Belhaj & Stefano Serra-Capizzano, 2019. "Multigrid for Q k Finite Element Matrices Using a (Block) Toeplitz Symbol Approach," Mathematics, MDPI, vol. 8(1), pages 1-17, December.
    • Handle: RePEc:gam:jmathe:v:8:y:2019:i:1:p:5-:d:299447
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