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Incomplete double-cone factorizations of centrosymmetric matrices arising in spectral methods

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Abstract

We develop structure-preserving incomplete LU type factorizations for preconditioning centrosymmetric matrices and use them to numerically solve centrosymmetric and nearly centrosymmetric linear systems arising from spectral methods for partial differential equations. Our algorithm builds in part on direct solution techniques previously developed for this type of linear systems, featuring double-cone factorizations. We illustrate our findings on discretizations of model problems involving the Poisson, diffusion, Helmholtz, and biharmonic equations in one, two, and three dimensions.

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The numerical code for solving the problems described in this paper is available at tinyurl.com/2uf3645d.

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Acknowledgements

The authors thank the anonymous referees for their careful reading and valuable suggestions.

Funding

This work was partially funded by Natural Sciences and Engineering Research Council of Canada (NSERC).

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  1. Chen Greif, Sarah Nataj and Manfred Trummer contributed equally to this work.

Authors and Affiliations

  1. Department of Computer Science, University of British Columbia, Vancouver, BC, Canada

    Chen Greif & Sarah Nataj

  2. Department of Mathematics, Simon Fraser University, Burnaby, BC, Canada

    Sarah Nataj & Manfred Trummer

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  1. Chen Greif
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  2. Sarah Nataj
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  3. Manfred Trummer
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The authors contributed equally to this work.

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Correspondence to Sarah Nataj.

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Greif, C., Nataj, S. & Trummer, M. Incomplete double-cone factorizations of centrosymmetric matrices arising in spectral methods. Numer Algor 95, 1359–1386 (2024). https://doi.org/10.1007/s11075-023-01612-y

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