Composite Algorithm for Adaptive Mesh Construction Based on Self-Organizing Maps

  • Olga Nechaeva
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4131)


A neural network approach for the adaptive mesh construction based on Kohonen’s Self-Organizing Maps (SOM) is considered. The approach belongs to a class of methods in which an adaptive mesh is a result of mapping of a computational domain onto a physical domain. There are some imperfections in using the SOM for mesh construction in a pure form. The composite algorithm to overcome these imperfections is proposed. The algorithm is based on the idea to alternate mesh construction on the border and inside the physical domain and includes techniques to control the consistency between boundary and interior mesh nodes and to provide an appropriate distribution of boundary nodes along the border of the domain. To increase the quality and the speed of mesh construction, a number of experiments are held to improve the learning rate. It has been shown that the quality of meshes constructed using the proposed algorithm is admissible according to the generally accepted quality criteria for finite difference meshes.


Physical Domain Boundary Node Adaptive Mesh Neural Network Approach Mesh Node 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Lebedev, A.S., Liseikin, V.D., Khakimzyanov, G.S.: Development of methods for generating adaptive grids. Vychislitelnye tehnologii 7(3), 29 (2002)MATHMathSciNetGoogle Scholar
  2. 2.
    Khakimzyanov, G.S., Shokin, Y.I., Barakhnin, V.B., Shokina, N.Y.: Numerical Modelling of Fluid Flows with Surface Waves. SB RAS, Novosibirsk (2001)Google Scholar
  3. 3.
    Thompson, J.F., Warsi, Z.U.A., Mastin, C.W.: Numerical grid generation, foundations and applications. North-Holland, Amsterdam (1985)MATHGoogle Scholar
  4. 4.
    Nechaeva, O.I.: Neural network approach for adaptive mesh construction. In: Proc. of VIII National scientific conference NeuroInformatics-2006. Part 2, MEPhI, Moscow, pp. 172–179 (2006)Google Scholar
  5. 5.
    Kohonen, T.K.: Self-organization and associative memory. Springer, New York (1989)Google Scholar
  6. 6.
    Flexer, A.: On the use of self-organizing maps for clustering and visualization. Intelligent Data Analysis, vol. 5, pp. 373–384. IOS Press, Amsterdam (2001)Google Scholar
  7. 7.
    Nechaeva, O.I.: Adaptive curvilinear mesh construction on arbitrary two-dimensional convex area with applying of Kohonen’s Self Organizing Map. Neuroinformatics and its applications. In: The XII National Workshop. ICM SB RAS, Krasnoyarsk, pp. 101–102 (2004)Google Scholar
  8. 8.
    Manevitz, L., Yousef, M., Givoli, D.: Finite Element Mesh Generation Using Self-Organizing Neural Networks. Special Issue on Machine Learning of MicroComputers in Civil Engineering 12(4), 233–250 (1997)Google Scholar
  9. 9.
    Manevitz, L.: Interweaving Kohonen Maps of Different Dimensions to Handle Measure Zero Constraints on Topological Mappings. Neural Processing Letters 5(2), 83–89 (1997)CrossRefGoogle Scholar
  10. 10.
    Nechaeva, O.: Neural Network Approach for Parallel Construction of Adaptive Meshes. In: Malyshkin, V.E. (ed.) PaCT 2005. LNCS, vol. 3606, pp. 446–451. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  11. 11.
    Ghahramani, Z.: Unsupervised Learning. In: Bousquet, O., von Luxburg, U., Rätsch, G. (eds.) Machine Learning 2003. LNCS (LNAI), vol. 3176, pp. 72–112. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  12. 12.
    Prokopov, G.P.: About organization of comparison of algorithms and programs for 2D regular difference mesh construction. Preprint / Keldysh’s Institute for Applied Mathematics AS USSA, No. 18. Moscow (1989)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Olga Nechaeva
    • 1
  1. 1.Novosibirsk State UniversityNovosibirskRussia

Personalised recommendations