MATLAB Implementation of Element-Based Solvers

  • Leszek Marcinkowski
  • Jan ValdmanEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11958)


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.


MATLAB code vectorization Finite elements Stiffness and mass matrices Iterative solvers 


  1. 1.
    Anjam, I., Valdman, J.: Fast MATLAB assembly of FEM matrices in 2D and 3D: edge elements. Appl. Math. Computat. 267, 252–263 (2015)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Hackbusch, W.: Iterative Solution of Large Sparse Systems of Equations. Applied Mathematical Sciences, vol. 95. Springer-Verlag, New York (1994). Translated and revised from the 1991 German originalCrossRefzbMATHGoogle Scholar
  3. 3.
    Rahman, T., Valdman, J.: Fast MATLAB assembly of FEM matrices in 2D and 3D: nodal elements. Appl. Math. Computat. 219, 7151–7158 (2013)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Samarskii, A.A., Nikolaev, E.S.: Numerical Methods for Grid Equations. Vol. II. Iterative Methods. Birkhäuser Verlag, Basel (1989). Translated from the Russian and with a note by Stephen G. NashCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Faculty of MathematicsUniversity of WarsawWarszawaPoland
  2. 2.Faculty of ScienceUniversity of South Bohemia, České Budějovice, and The Czech Academy of Sciences, Institute of Information Theory and AutomationPragueCzechia

Personalised recommendations