Skip to main content
SpringerLink
Log in

On some parallel iterative methods for solving elliptic equations on triangular grids

  • Numerical Methods
  • Published:
Differential Equations Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Meijerink, J.A. and van der Vorst, H.A., Math. Comp., 1977, vol. 31, no. 137, pp. 148–162.

    Article  MATH  MathSciNet  Google Scholar 

  2. Ortega, J., Introduction to Parallel and Vector Solution of Linear Systems, New York: Plenum, 1988. Translated under the title Vvedenie v parallel’nye i vektornye metody resheniya lineinykh sistem, Moscow: Mir, 1991.

    Google Scholar 

  3. Gustafsson, I., BIT, 1978, vol. 18, pp. 142–156.

    Article  MATH  MathSciNet  Google Scholar 

  4. Axelsson, O. and Barker, V.A., Finite Element Solution of Boundary Value Problems. Theory and Computations, New York: Academic, 1984.

    Google Scholar 

  5. Axelsson, O. and Lindskog, G., Numer. Math., 1986, vol. 48, pp. 479–498.

    Article  MATH  MathSciNet  Google Scholar 

  6. Kershaw, D., J. Comp. Phys., 1978, vol. 26, pp. 43–65.

    Article  MATH  MathSciNet  Google Scholar 

  7. Doi, S., Appl. Numer. Math., 1991, vol. 7, no. 5, pp. 417–436.

    Article  MATH  MathSciNet  Google Scholar 

  8. Milyukova, O.Yu., Parallel Comput., 2001, vol. 27, pp. 1365–1379.

    Article  MATH  MathSciNet  Google Scholar 

  9. Milyukova, O.Yu., Zh. Vychisl. Mat. Mat. Fiz., 2001, vol. 41, no. 11, pp. 1619–1636.

    MATH  MathSciNet  Google Scholar 

  10. Milyukova, O.Yu., Comput. Methods Sci. Engng., 2002, vol. 2, no. 1–2, pp. 195–200.

    MATH  Google Scholar 

  11. Notay, Y., Parallel Comput., 1995, vol. 21, pp. 1725–1748.

    Article  MathSciNet  Google Scholar 

  12. Notay, Y., Numer. Linear Algebra Appl., 1994, vol. 1, pp. 511–533.

    Article  MATH  MathSciNet  Google Scholar 

  13. Milyukova, O.Yu. and Popov, I.V., Mat. Model., 2003, vol. 15, no. 10, pp. 3–16.

    MATH  MathSciNet  Google Scholar 

  14. Milyukova, O.Yu., Mat. Model., 2005, vol. 17, no. 2, pp. 65–80.

    MATH  MathSciNet  Google Scholar 

  15. Milyukova, O.Yu., Mat. Model., 2003, vol. 15, no. 4, pp. 3–15.

    MATH  MathSciNet  Google Scholar 

  16. Duff, I.S. and Meurant, G.A., BIT, 1989, vol. 29, pp. 635–657.

    Article  MATH  MathSciNet  Google Scholar 

  17. George, A. and Liu, J.W.-H., Computer Solution of Large Sparse Positive Definite Systems, New York: Springer-Verlag, 1993. Translated under the title Chislennoe reshenie bol’shikh razrezhennykh sistem uravnenii, Moscow: Mir, 1984.

    Google Scholar 

  18. Boldyrev, S.N., Levanov, E.I., Sukov, S.A., and Yakobovskii, M.V., in Setochnye metody dlya kraevykh zadach i prilozheniya: Mater. chetvertogo vseros. sem. Kazan’, 13–16 sentyabrya 2002 g. (Grid Methods for Boundary Value Problems and Applications: Proc. IVth All-Russia Sem. Kazan, Russia, September, 13–16, 2002), Kazan, 2002, pp. 33–39.

  19. Pascal, J.F. and Paul-Louis, G., Mesh Generation Application to Finite Elements, Oxford, 2000.

  20. Samarskii, A.A. and Nikolaev, E.S., Metody resheniya setochnykh vravnenii (Methods for the Solution of Difference Equations), Moscow: Nauka, 1978.

    Google Scholar 

  21. Milyukova, O.Yu., Zh. Vychisl. Mat. Mat. Fiz., 1998, vol. 38, no. 12, pp. 2002–2012.

    MATH  MathSciNet  Google Scholar 

  22. Samarskii, A.A., Teoriya raznostnykh skhem (Theory of Difference Schemes), Moscow: Nauka, 1989.

    Google Scholar 

  23. Popov, I.V. and Polyakov, S.V., Mat. Model., 2002, vol. 14, no. 6, pp. 25–35.

    MATH  MathSciNet  Google Scholar 

  24. Milyukova, O.Yu. and Tishkin, V.F., in Voprosy atomnoi nauki i tekhniki. Matematicheskoe modelirovanie fizicheskikh protsessov (Problems of Nuclear Science and Engineering. Mathematical Modeling of Physical Processes), Moscow, 2005, pp. 3–14.

Download references

Author information

Authors and Affiliations

  1. Institute for Mathematical Modeling, Russian Academy of Sciences, Moscow, Russia

    O. Yu. Milyukova

Authors
  1. O. Yu. Milyukova
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © O.Yu. Milyukova, 2006, published in Differentsial’nye Uravneniya, 2006, Vol. 42, No. 7, pp. 956–968.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Milyukova, O.Y. On some parallel iterative methods for solving elliptic equations on triangular grids. Diff Equat 42, 1018–1030 (2006). https://doi.org/10.1134/S0012266106070111

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0012266106070111

Keywords

Search

Navigation