Computing and Visualization in Science

, Volume 16, Issue 1, pp 1–14

Parallel algebraic multilevel Schwarz preconditioners for a class of elliptic PDE systems

  • Alfio Borzì
  • Valentina De Simone
  • Daniela di Serafino

DOI: 10.1007/s00791-014-0220-0

Cite this article as:
Borzì, A., De Simone, V. & di Serafino, D. Comput. Visual Sci. (2013) 16: 1. doi:10.1007/s00791-014-0220-0


Algebraic multilevel preconditioners for algebraic problems arising from the discretization of a class of systems of coupled elliptic partial differential equations (PDEs) are presented. These preconditioners are based on modifications of Schwarz methods and of the smoothed aggregation technique, where the coarsening strategy and the restriction and prolongation operators are defined using a point-based approach with a primary matrix corresponding to a single PDE. The preconditioners are implemented in a parallel computing framework and are tested on two representative PDE systems. The results of the numerical experiments show the effectiveness and the scalability of the proposed methods. A convergence theory for the twolevel case is presented.


Systems of elliptic PDEs Algebraic multilevel preconditioners Schwarz methods Smoothed aggregation Parallel computing 

Mathematics of Subject Classification

65F08 65N55 49J20 

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Alfio Borzì
    • 1
  • Valentina De Simone
    • 2
  • Daniela di Serafino
    • 2
    • 3
  1. 1.Institut für MathematikUniversität WürzburgWürzburgGermany
  2. 2.Dipartimento di Matematica e FisicaSeconda Università degli Studi di NapoliCasertaItaly
  3. 3.Istituto di Calcolo e Reti ad Alte Prestazioni (ICAR), CNRNaplesItaly

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