Meshless numerical method based on tensor product

doi:10.1007/s11709-008-0021-y

Frontiers of Architecture and Civil Engineering in China - Selected Publications from Chinese Universities

2008, Vol. 2

Issue (2): 166-171 https://doi.org/10.1007/s11709-008-0021-y

本期目录

Meshless numerical method based on tensor product

SUN Haitao, WANG Yuanhan, MIAO Yu

School of Civil Engineering and Mechanics, Huazhong University of Science and Technology;

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Abstract：A normalized space constructed by tensor product is used in field function approach to give a special case of moving least squares (MLS) interpolation scheme. In the regular domain, the field function which meets homogenous boundary conditions is constructed by spanning base space to make the MLS interpolation scheme simpler and more efficient. Owing to expanded basis functions selection, some drawbacks in general MLS method, for example repeated inversion, low calculation efficiency, and complex criterions, can be avoided completely. Numerical examples illustrate that the proposed method is characterized by simple mathematical concept, convenient repeat calculations with high accuracy, good continuity, less computation and rapid convergence.

出版日期: 2008-06-05

引用本文:

. Meshless numerical method based on tensor product[J]. Frontiers of Architecture and Civil Engineering in China - Selected Publications from Chinese Universities, 2008, 2(2): 166-171.
SUN Haitao, WANG Yuanhan, MIAO Yu. Meshless numerical method based on tensor product. Front. Struct. Civ. Eng., 2008, 2(2): 166-171.

链接本文:

https://academic.hep.com.cn/fsce/CN/10.1007/s11709-008-0021-y
https://academic.hep.com.cn/fsce/CN/Y2008/V2/I2/166

1	Belytschko T Krongauz Y Organ D et al.Meshless methods: an overview and recent developmentsCompute Methods Appl Mech Engrg 1996 139347. doi:10.1016/S0045‐7825(96)01078‐X
	Belytschko T, Krongauz Y, Organ D, et al. Meshless methods: an overview and recent developments. Compute Methods Appl Mech Engrg.1996, 139: 3-47 doi: 10.1016/S0045‐7825(96)01078‐X
	Belytschko T, Krongauz Y, Organ D, et al. Meshless methods: an overview and recent developments. Compute Methods Appl Mech Engrg.1996, 139: 3-47 doi: 10.1016/S0045‐7825(96)01078‐X
2	Donning B M Liu W K Meshless methods for shear-deformablebeams and platesComputer Methods in AppliedMechanics and Engineering 1998 1524771. doi:10.1016/S0045‐7825(97)00181‐3
	Donning B M, Liu W K. Meshless methods for shear-deformablebeams and plates. Computer Methods in Applied Mechanics and Engineering.1998, 152: 47-71 doi: 10.1016/S0045‐7825(97)00181‐3
	Donning B M, Liu W K. Meshless methods for shear-deformablebeams and plates. Computer Methods in Applied Mechanics and Engineering.1998, 152: 47-71 doi: 10.1016/S0045‐7825(97)00181‐3
3	Nayroles B Touzot G Villon P Generalizing the finite element method: diffuse approximationand diffuse elementsComputational Mechanics 1992 10307318. doi:10.1007/BF00364252
	Nayroles B, Touzot G, Villon P. Generalizing the finite element method: diffuse approximationand diffuse elements. Computational Mechanics.1992, 10: 307-318 doi: 10.1007/BF00364252
	Nayroles B, Touzot G, Villon P. Generalizing the finite element method: diffuse approximationand diffuse elements. Computational Mechanics.1992, 10: 307-318 doi: 10.1007/BF00364252
4	Atluri S N Zhu T A new meshless local Petrov-Galerkin(MLPG) approach in computational mechanicsComputational Mechanics 1998 22117127. doi:10.1007/s004660050346
	Atluri S N, Zhu T. A new meshless local Petrov-Galerkin(MLPG) approach in computational mechanics. Computational Mechanics.1998, 22: 117-127 doi: 10.1007/s004660050346
	Atluri S N, Zhu T. A new meshless local Petrov-Galerkin(MLPG) approach in computational mechanics. Computational Mechanics.1998, 22: 117-127 doi: 10.1007/s004660050346
5	Braun J Malcolm S A numerical method for solvingpartial differential equations on highly irregular envolving gridsNature 1995 376(24)655660. doi:10.1038/376655a0
	Braun J, Malcolm S. A numerical method for solvingpartial differential equations on highly irregular envolving grids. Nature.1995, 376(24):655-660 doi: 10.1038/376655a0
	Braun J, Malcolm S. A numerical method for solvingpartial differential equations on highly irregular envolving grids. Nature.1995, 376(24):655-660 doi: 10.1038/376655a0
6	De S Bathe K J The method of finite sphereComputational Mechanics 2000 25329345. doi:10.1007/s004660050481
	De S, Bathe K J. The method of finite sphere. Computational Mechanics.2000, 25: 329-345 doi: 10.1007/s004660050481
	De S, Bathe K J. The method of finite sphere. Computational Mechanics.2000, 25: 329-345 doi: 10.1007/s004660050481
	Shen Pengcheng, He Peixiang. Multi-variables spline finiteelement method. Acta Solida Mechanic.1994, 15(3):234-243(in Chinese)
7	Shen Pengcheng He Peixiang Multi-variables spline finiteelement methodActa Solida Mechanic 1994 15(3)234243 (in Chinese)
	Shen Pengcheng, He Peixiang. Multi-variables spline finiteelement method. Acta Solida Mechanic.1994, 15(3):234-243(in Chinese)
	Qin Rong. Spline Boundary Element Method. Nanning, Guangxi Science & Technique Press, 1988(in Chinese)
8	Qin Rong Spline Boundary Element MethodNanningGuangxi Science & Technique Press 1988 (in Chinese)
	Qin Rong. Spline Boundary Element Method. Nanning, Guangxi Science & Technique Press, 1988(in Chinese)
	Liu Xiaoyao. Spline Functions and Structure Mechanics. Beijing, People Communication Press, 1990(in Chinese)
9	Liu Xiaoyao Spline Functions and Structure MechanicsBeijingPeople Communication Press 1990 (in Chinese)
	Liu Xiaoyao. Spline Functions and Structure Mechanics. Beijing, People Communication Press, 1990(in Chinese)
	Hollig K. FiniteElement Methods with B-spline. Stuttgart,Germany, SIAM, Philadelphia, 2003
10	Hollig K FiniteElement Methods with B-splineStuttgart,GermanySIAM, Philadelphia 2003
	Hollig K. FiniteElement Methods with B-spline. Stuttgart,Germany, SIAM, Philadelphia, 2003

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