ALGEBRAIC MULTIGRID PRECONDITIONER FOR SECOND ORDER FINITE ELEMENT APPROXIMATIONS IN RECTANGULAR DOMAINS. II. MULTIGRID PRECONDITIONER

Authors

  • Yu. H. Hakopian Chair of Mathematical Methods and Modeling, YSU, Armenia
  • H. A. Hovhannisyan Chair of Mathematical Methods and Modeling, YSU, Armenia

DOI:

https://doi.org/10.46991/PYSUA.2003.37.2.018

Keywords:

algebraic multigrid preconditioner, elliptic boundary value problems, stiffness matrix, second-order finite element approximation

Abstract

The present paper, consisting of two parts, is devoted to constructing an algebraic multigrid preconditioner for stiffness matrices arising in second-order finite element approximation of elliptic boundary value problems. In the second part of the paper, being based on the two-level preconditioner described in the first part, the multigrid preconditioner is constructed. The multigrid preconditioner is proved to be spectrally equivalent to the initial stiffness matrix and its arithmetic cost is proportional to the dimensionality of the finest-grid algebraic problem.

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Published

2003-06-03

Issue

Vol. 37 No. 2 (201) (2003)

Section

Mathematics

License

Copyright (c) 2003 Proceedings of the YSU

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

How to Cite

Hakopian, Y. H., & Hovhannisyan, H. A. (2003). ALGEBRAIC MULTIGRID PRECONDITIONER FOR SECOND ORDER FINITE ELEMENT APPROXIMATIONS IN RECTANGULAR DOMAINS. II. MULTIGRID PRECONDITIONER. Proceedings of the YSU A: Physical and Mathematical Sciences, 37(2 (201), 18-24. https://doi.org/10.46991/PYSUA.2003.37.2.018
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