Abstract
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.
This work is supported by Grant of Rosobrazovanie, contract PH(.2.2.1.1.3653 and Program for Basic Research of RAS Presidium No. 14.15-2006.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Lebedev, A.S., Liseikin, V.D., Khakimzyanov, G.S.: Development of methods for generating adaptive grids. Vychislitelnye tehnologii 7(3), 29 (2002)
Khakimzyanov, G.S., Shokin, Y.I., Barakhnin, V.B., Shokina, N.Y.: Numerical Modelling of Fluid Flows with Surface Waves. SB RAS, Novosibirsk (2001)
Thompson, J.F., Warsi, Z.U.A., Mastin, C.W.: Numerical grid generation, foundations and applications. North-Holland, Amsterdam (1985)
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)
Kohonen, T.K.: Self-organization and associative memory. Springer, New York (1989)
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)
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)
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)
Manevitz, L.: Interweaving Kohonen Maps of Different Dimensions to Handle Measure Zero Constraints on Topological Mappings. Neural Processing Letters 5(2), 83–89 (1997)
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)
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)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Nechaeva, O. (2006). Composite Algorithm for Adaptive Mesh Construction Based on Self-Organizing Maps. In: Kollias, S.D., Stafylopatis, A., Duch, W., Oja, E. (eds) Artificial Neural Networks – ICANN 2006. ICANN 2006. Lecture Notes in Computer Science, vol 4131. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11840817_47
Download citation
DOI: https://doi.org/10.1007/11840817_47
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-38625-4
Online ISBN: 978-3-540-38627-8
eBook Packages: Computer ScienceComputer Science (R0)