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Limited Memory Block Preconditioners for Fast Solution of Fractional Partial Differential Equations

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Abstract

An innovative block structured with sparse blocks multi iterative preconditioner for linear multistep formulas used in boundary value form is proposed here to accelerate GMRES, FGMRES and BiCGstab(l). The preconditioner is based on block \(\omega \)-circulant matrices and a short-memory approximation of the underlying Jacobian matrix of the fractional partial differential equations. Convergence results, numerical tests and comparisons with other techniques confirm the effectiveness of the approach.

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Acknowledgements

We wish to thank two anonymous referees for their constructive comments which have improved the readability of the paper.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Roma “Tor Vergata”, viale della Ricerca Scientifica 1, 00133, Rome, Italy

    Daniele Bertaccini

  2. Istituto per le Applicazioni del Calcolo (IAC) “M. Picone”, National Research Council (CNR), Rome, Italy

    Daniele Bertaccini

  3. Dipartimento di Informatica, Università di Pisa, Largo Bruno Pontecorvo 3, 56127, Pisa, Italy

    Fabio Durastante

Authors
  1. Daniele Bertaccini
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  2. Fabio Durastante
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Corresponding author

Correspondence to Daniele Bertaccini.

Additional information

The authors are members of the INdAM research group GNCS and this work has been partially supported by the GNCS 2018 Project “Tecniche innovative per problemi di algebra lineare”.

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Bertaccini, D., Durastante, F. Limited Memory Block Preconditioners for Fast Solution of Fractional Partial Differential Equations. J Sci Comput 77, 950–970 (2018). https://doi.org/10.1007/s10915-018-0729-3

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  • DOI: https://doi.org/10.1007/s10915-018-0729-3

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