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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Anjam, I., Valdman, J.: Fast MATLAB assembly of FEM matrices in 2D and 3D: edge elements. Appl. Math. Computat. 267, 252–263 (2015)
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
Rahman, T., Valdman, J.: Fast MATLAB assembly of FEM matrices in 2D and 3D: nodal elements. Appl. Math. Computat. 219, 7151–7158 (2013)
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
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/978-3-030-41032-2_69
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-41031-5
Online ISBN: 978-3-030-41032-2
eBook Packages: Computer ScienceComputer Science (R0)