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MATLAB Implementation of Element-Based Solvers

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Large-Scale Scientific Computing (LSSC 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11958))

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Abstract

Rahman and Valdman (2013) introduced a vectorized way to assemble finite element stiffness and mass matrices in MATLAB. Local element matrices are computed all at once by array operations and stored in multi-dimensional arrays (matrices). We build some iterative solvers on available multi-dimensional structures completely avoiding the use of a sparse matrix.

The work of the 1st author was partially supported by Polish Scientific Grant: National Science Center 2016/21/B/ST1/00350.

The work of the 2nd and the corresponding author was supported by the Czech Science Foundation (GACR), through the grant GA17-04301S.

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References

  1. Anjam, I., Valdman, J.: Fast MATLAB assembly of FEM matrices in 2D and 3D: edge elements. Appl. Math. Computat. 267, 252–263 (2015)

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  3. Rahman, T., Valdman, J.: Fast MATLAB assembly of FEM matrices in 2D and 3D: nodal elements. Appl. Math. Computat. 219, 7151–7158 (2013)

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  4. Samarskii, A.A., Nikolaev, E.S.: Numerical Methods for Grid Equations. Vol. II. Iterative Methods. Birkhäuser Verlag, Basel (1989). https://doi.org/10.1007/978-3-0348-9272-8. Translated from the Russian and with a note by Stephen G. Nash

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Author information

Authors and Affiliations

  1. Faculty of Mathematics, University of Warsaw, Warszawa, Poland

    Leszek Marcinkowski

  2. Faculty of Science, University of South Bohemia, České Budějovice, and The Czech Academy of Sciences, Institute of Information Theory and Automation, Prague, Czechia

    Jan Valdman

Authors
  1. Leszek Marcinkowski
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  2. Jan Valdman
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Corresponding author

Correspondence to Jan Valdman .

Editor information

Editors and Affiliations

  1. Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Lirkov

  2. Bulgarian Academy of Sciences, Sofia, Bulgaria

    Svetozar Margenov

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Marcinkowski, L., Valdman, J. (2020). MATLAB Implementation of Element-Based Solvers. In: Lirkov, I., Margenov, S. (eds) Large-Scale Scientific Computing. LSSC 2019. Lecture Notes in Computer Science(), vol 11958. Springer, Cham. https://doi.org/10.1007/978-3-030-41032-2_69

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  • DOI: https://doi.org/10.1007/978-3-030-41032-2_69

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-41031-5

  • Online ISBN: 978-3-030-41032-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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