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ON APPROXIMATION OF LAPLACIAN EIGENPROBLEM OVER A REGULAR HEXAGON WITH ZERO BOUNDARY CONDITIONS

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Sun Jiachang

文摘	In my earlier paper [4], an eigen-decompositions of the Laplacian operator is given on a unit regular hexagon with periodic boundary conditions. Since an exact decomposition with Dirichlet boundary conditions has not been explored in terms of any elementary form. In this paper, we investigate an approximate eigen-decomposition. The function space, corresponding all eigenfunction, have been decomposed into four orthogonal subspaces. Estimations of the first eight smallest eigenvalues and related orthogonal functions are given. In particulary we obtain an approximate value of the smallest eigenvalue λ_1 ～ (29)/(40)π~2 = 7.1555, the absolute error is less than 0.0001.
来源	Journal of Computational Mathematics ,2004,22(2):275-286 【核心库】
关键词	Laplacian eigen-decomposition ; Regular hexagon domain ; Dirichlet boundary conditions
地址	Parallel Computing Division, Institute of Software, Chinese Academy of Sciences, 北京, 100080
语种	英文
文献类型	研究性论文
ISSN	0254-9409
学科	数学
基金	国家自然科学基金 ; 国家自然科学基金
文献收藏号	CSCD:1848257

参考文献共 6 共1页

	1. Mark A Pinsky. SIAM J. Math. Anal.,1985,16:848-851	被引 4 次
	2. Milan Prager. Applications of mathematics,1998,43:311-320	被引 5 次
	3. Sun Jiachang. ORTHOGONAL PIECE-WISE POLYNOMIALS BASIS ON AN ARBITRARY TRIANGULAR DOMAIN AND ITS APPLICATIONS. Journal of Computational Mathematics,2001,19:55-66	被引 8 次
	4. Sun Jiachang. MULTIVARIATE FOURIER SERIES OVER A CLASS OF NON TENSOR-PRODUCT PARTITION DOMAINS. Journal of Computational Mathematics,2003,21:53-62	被引 14 次
	5. Sun Jiachang. Advances in Computational Mathematics	被引 1 次
	6. Yang Zhijie. Mathematica Numerica Sinica,2003,25(2):219-230	被引 1 次

引证文献 1 篇

1 Lee Daniel Analysis of Hexagonal Grid Finite Difference Methods for Anisotropic Laplacian Related Equations Numerical Mathematics Theory, Methods and Applications,2017,10(3):562-596
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