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Lu, Hong-qiang; Wu, Yi-zhao; Chen, Song-can

A new method based on SOM network to generate coarse meshes for overlapping unstructured multigrid algorithm. (English) Zbl 1027.65164

Appl. Math. Comput. 140, No. 2-3, 353-360 (2003).

Summary: A new method to generate coarse meshes for overlapping unstructured multigrid algorithm based on self-organizing map (SOM) neural network is presented. The application of SOM neural network can overcome some limitations of conventional methods and which is designed to pursuit the best structure relation between fine and coarse unstructured meshes with the object to ensure robust convergence for overlapping unstructured multigrid algorithm. Besides, this method can automate the generation of unstructured meshes and is suitable for both two and three dimensions conditions.

© Elsevier Science Inc.

Cited in 2 Documents

MSC:

65N50	Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
65N55	Multigrid methods; domain decomposition for boundary value problems involving PDEs

Keywords:

SOM network; overlapping unstructured multigrid; optimization; mesh generation; numerical examples; algorithm; self-organizing map neural network; convergence

Cite Review PDF

Full Text: DOI

References:

[1]	Mavriplis, D. J., Multigrid solution of the two-dimensional Euler equations on unstructured triangular meshes, AIAA Journal, 1988 · Zbl 0667.76088
[2]	Vesanto, J., SOM-based data visualization methods, Intelligent Data Analysis, 3, 111-126, 1999 · Zbl 0970.68570
[3]	Z.-q. Bian, X.-g. Zhang, ≪Pattern recognition≫, Tsing Hua University Press, January, 2000
[4]	T. Kohonen, The self-organizing map (SOM), Available from <http://www.cis.hut.fi/projects/somtoolbox/thoery/somalgorithm.shtml> · Zbl 0917.68176

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.

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