A new method based on SOM network to generate coarse meshes for overlapping unstructured multigrid algorithm

A new method to generate coarse meshes for overlapping unstructured multigrid algorithm based on self-organizing map (SOM) neural network is presented in this paper. The application of SOM neural network can overcome some limitations of conventional methods and which is designed to pursuit the best...

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Published in:	Applied mathematics and computation Vol. 140; no. 2; pp. 353 - 360
Main Authors:	Lu, Hong-qiang, Wu, Yi-zhao, Chen, Song-can
Format:	Journal Article
Language:	English
Published:	New York, NY Elsevier Inc 10.08.2003 Elsevier
Subjects:	Calculus of variations and optimal control Exact sciences and technology Fluid dynamics Fundamental areas of phenomenology (including applications) Laminar flows Low-reynolds-number (creeping) flows Mathematical analysis Mathematics Mesh generation Nonlinear algebraic and transcendental equations Numerical analysis Numerical analysis. Scientific computation Numerical approximation Optimization Overlapping unstructured multigrid Physics Sciences and techniques of general use SOM network SOM network Overlapping unstructured multigrid Optimization Mesh generation Convergence of numerical methods Three-dimensional calculations Grid pattern Fluid dynamics Numerical method Overlap Window function Grids Finite element method Selforganizing map Algorithms Self organization Multigrid Neural networks Two-dimensional calculations Mesh method Learning algorithm
ISSN:	0096-3003, 1873-5649
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Abstract	A new method to generate coarse meshes for overlapping unstructured multigrid algorithm based on self-organizing map (SOM) neural network is presented in this paper. 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.
AbstractList	A new method to generate coarse meshes for overlapping unstructured multigrid algorithm based on self-organizing map (SOM) neural network is presented in this paper. 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.
Author	Chen, Song-can Lu, Hong-qiang Wu, Yi-zhao
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Keywords	SOM network Overlapping unstructured multigrid Optimization Mesh generation Convergence of numerical methods Three-dimensional calculations Grid pattern Fluid dynamics Numerical method Overlap Window function Grids Finite element method Selforganizing map Algorithms Self organization Multigrid Neural networks Two-dimensional calculations Mesh method Learning algorithm
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References	Mavriplis (BIB1) 1988 Vesanto (BIB2) 1999; 3 T. Kohonen, The self-organizing map (SOM), Available from Z.-q. Bian, X.-g. Zhang, ≪Pattern recognition≫, Tsing Hua University Press, January, 2000 > Vesanto (10.1016/S0096-3003(02)00232-1_BIB2) 1999; 3 10.1016/S0096-3003(02)00232-1_BIB4 10.1016/S0096-3003(02)00232-1_BIB3 Mavriplis (10.1016/S0096-3003(02)00232-1_BIB1) 1988
References_xml	– year: 1988 ident: BIB1 article-title: Multigrid solution of the two-dimensional Euler equations on unstructured triangular meshes publication-title: AIAA Journal – reference: Z.-q. Bian, X.-g. Zhang, ≪Pattern recognition≫, Tsing Hua University Press, January, 2000 – reference: T. Kohonen, The self-organizing map (SOM), Available from < – reference: > – volume: 3 start-page: 111 year: 1999 end-page: 126 ident: BIB2 article-title: SOM-based data visualization methods publication-title: Intelligent Data Analysis – volume: 3 start-page: 111 year: 1999 ident: 10.1016/S0096-3003(02)00232-1_BIB2 article-title: SOM-based data visualization methods publication-title: Intelligent Data Analysis doi: 10.1016/S1088-467X(99)00013-X – ident: 10.1016/S0096-3003(02)00232-1_BIB4 – year: 1988 ident: 10.1016/S0096-3003(02)00232-1_BIB1 article-title: Multigrid solution of the two-dimensional Euler equations on unstructured triangular meshes publication-title: AIAA Journal doi: 10.2514/3.9975 – ident: 10.1016/S0096-3003(02)00232-1_BIB3
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SubjectTerms	Calculus of variations and optimal control Exact sciences and technology Fluid dynamics Fundamental areas of phenomenology (including applications) Laminar flows Low-reynolds-number (creeping) flows Mathematical analysis Mathematics Mesh generation Nonlinear algebraic and transcendental equations Numerical analysis Numerical analysis. Scientific computation Numerical approximation Optimization Overlapping unstructured multigrid Physics Sciences and techniques of general use SOM network
Title	A new method based on SOM network to generate coarse meshes for overlapping unstructured multigrid algorithm
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