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Volume 22, Issue 2
On Approximation of Laplacian Eigenproblem over a Regular Hexagon with Zero Boundary Conditions

Jiachang Sun

J. Comp. Math., 22 (2004), pp. 275-286.

Published online: 2004-04

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  • Abstract

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 particular, we obtain an approximate value of the smallest eigenvalue $\lambda_1$~$\frac{29}{40} \pi^2=7.1555$, the absolute error is less than 0.0001.

  • Keywords

Laplacian eigen-decomposition, Regular hexagon domain, Dirichlet boundary conditions.

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COPYRIGHT: © Global Science Press

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@Article{JCM-22-275, author = {Sun , Jiachang}, title = {On Approximation of Laplacian Eigenproblem over a Regular Hexagon with Zero Boundary Conditions}, journal = {Journal of Computational Mathematics}, year = {2004}, volume = {22}, number = {2}, pages = {275--286}, abstract = {

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 particular, we obtain an approximate value of the smallest eigenvalue $\lambda_1$~$\frac{29}{40} \pi^2=7.1555$, the absolute error is less than 0.0001.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/10328.html} }
TY - JOUR T1 - On Approximation of Laplacian Eigenproblem over a Regular Hexagon with Zero Boundary Conditions AU - Sun , Jiachang JO - Journal of Computational Mathematics VL - 2 SP - 275 EP - 286 PY - 2004 DA - 2004/04 SN - 22 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/10328.html KW - Laplacian eigen-decomposition, Regular hexagon domain, Dirichlet boundary conditions. AB -

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 particular, we obtain an approximate value of the smallest eigenvalue $\lambda_1$~$\frac{29}{40} \pi^2=7.1555$, the absolute error is less than 0.0001.

Jiachang Sun. (1970). On Approximation of Laplacian Eigenproblem over a Regular Hexagon with Zero Boundary Conditions. Journal of Computational Mathematics. 22 (2). 275-286. doi:
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