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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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  2. Hackbusch, W.: Iterative Solution of Large Sparse Systems of Equations. Applied Mathematical Sciences, vol. 95. Springer-Verlag, New York (1994). https://doi.org/10.1007/978-1-4612-4288-8. Translated and revised from the 1991 German original

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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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Correspondence to Jan Valdman .

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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

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