Spectral Element Approximation for the Eigenvalue Problem of Hydrogen Atoms Electronic Structure

Jia Yu Han; Yi Du Yang

doi:10.4028/www.scientific.net/AMR.690-693.3199

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HomeAdvanced Materials ResearchAdvanced Materials Research Vols. 690-693Spectral Element Approximation for the Eigenvalue...

Spectral Element Approximation for the Eigenvalue Problem of Hydrogen Atoms Electronic Structure

Abstract:

In this paper, the spectral element methods are adopted to solve the eigenvalue problem of hydrogen atoms electronic structure. A local refinement algorithm based on spectral element approximation is constructed to solve the problem on different domains. Numerical experiments indicate this algorithm is highly efficient.

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Periodical:

Advanced Materials Research (Volumes 690-693)

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3199-3202

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.690-693.3199

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Online since:

May 2013

Authors:

Jia Yu Han, Yi Du Yang

Keywords:

Eigenvalue Problem, Hydrogen Atoms Electronic Structure, Spectral Element Method

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References

[1] I. Babuska, J. Osborn, Eigenvalue Problems, in: P. G. Ciarlet, J. L. Lions, (Ed.), Finite Element Methods(Part 1), Handbook of Numerical Analysis, vol. 2, Elsevier Science Publishers, North-Holand, pp.640-787, 1991.

DOI: 10.1016/s1570-8659(05)80042-0

Google Scholar

[2] T. L. Beck, Real-space mesh techniques in density-function theory, Rev. Mod. Phys., 72, pp.1041-1080, 2000.

DOI: 10.1103/revmodphys.72.1041

Google Scholar

[3] C. Canuto, A. Quarteroni, M. Y. Hussaini, T. A. Zang, Spectral Methods Evolution to Complex Geometries and Applications to Fluid Dynamics, Springer, Heidelberg, 2007.

DOI: 10.1007/978-3-540-30728-0

Google Scholar

[4] X. Dai, J. Xu, A. Zhou, Convergence and optimal complexity of adaptive finite element eigenvalue computations, Numer. Math., 110, pp.313-355, 2008.

DOI: 10.1007/s00211-008-0169-3

Google Scholar

[5] X. Dai, A. Zhou, Three-scale finite element discretizations for quantum eigenvalue problems, SIAM J. Numer. Anal., 46(1), pp.295-324, 2008.

DOI: 10.1137/06067780x

Google Scholar

[6] X. Gong, L. Shen, D. Zhang, A. Zhou, Finite element approximations for Schrödinger equations with applications to electronic structure computations, Comp. Math., 26(3), pp.1-14, 2008.

Google Scholar

[7] R. M. Martin, Electronic Structure: Basic Theory and Practical Methods, Cambridge University Press, London, 2004.

Google Scholar

[8] J. Shen, T. Tang, L. L. Wang, Spectral Methods, springer, Heidelberg, 2011.

Google Scholar

[9] Y. Yang, Finite Element Methods for Eigenvalue Problems (in Chinese), Science Press, Beijing, China, 2012.

Google Scholar

[10] Y. Yang, H. Bi, A two-grid discretization scheme based on shifted-inverse power method, SIAM J. Numer. Anal., 49 , pp.1602-1624, 2011.

DOI: 10.1137/100810241

Google Scholar