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

2013 ◽  
Vol 690-693 ◽  
pp. 3199-3202
Author(s):  
Jia Yu Han ◽  
Yi Du Yang
Keyword(s):  
Electronic Structure ◽  
Eigenvalue Problem ◽  
Numerical Experiments ◽  
Spectral Element ◽  
Element Approximation ◽  
Hydrogen Atoms ◽  
Local Refinement ◽  
Spectral Element Methods ◽  
Highly Efficient ◽  
Refinement Algorithm

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.

The Spectral Element Method for the Steklov Eigenvalue Problem

2013 ◽  
Vol 853 ◽  
pp. 631-635 ◽  
Author(s):  
Yan Jun Li ◽  
Yi Du Yang ◽  
Hai Bi
Keyword(s):  
Eigenvalue Problem ◽  
Spectral Element Method ◽  
A Priori ◽  
Spectral Element ◽  
Element Approximation ◽  
Steklov Eigenvalue ◽  
Steklov Eigenvalue Problem ◽  
Priori Error Estimates ◽  
Shaped Domain ◽  
Element Method

This paper discusses the spectral element approximation with LGL node basis for the Steklov eigenvalue problem, and analyzes the a priori error estimates. Finally, numerical experi-ments on the square and the L-shaped domain are carried out to get very accurate approximations by the spectral element method.

scholarly journals Oscillating behaviour of the spectrum for a plasmonic problem in a domain with a rounded corner

2018 ◽  
Vol 52 (4) ◽  
pp. 1285-1313 ◽  
Author(s):  
Lucas Chesnel ◽  
Xavier Claeys ◽  
Sergei A. Nazarov
Keyword(s):  
Asymptotic Expansion ◽  
Eigenvalue Problem ◽  
Recent Work ◽  
Present Article ◽  
Error Estimates ◽  
Numerical Experiments ◽  
Source Term ◽  
Oscillatory Behaviour ◽  
Time Harmonic ◽  
Rounded Corner

We investigate the eigenvalue problem −div(σ∇u) = λu (P) in a 2D domain Ω divided into two regions Ω±. We are interested in situations where σ takes positive values on Ω+ and negative ones on Ω−. Such problems appear in time harmonic electromagnetics in the modeling of plasmonic technologies. In a recent work [L. Chesnel, X. Claeys and S.A. Nazarov, Asymp. Anal. 88 (2014) 43–74], we highlighted an unusual instability phenomenon for the source term problem associated with (P): for certain configurations, when the interface between the subdomains Ω± presents a rounded corner, the solution may depend critically on the value of the rounding parameter. In the present article, we explain this property studying the eigenvalue problem (P). We provide an asymptotic expansion of the eigenvalues and prove error estimates. We establish an oscillatory behaviour of the eigenvalues as the rounding parameter of the corner tends to zero. We end the paper illustrating this phenomenon with numerical experiments.

Highly efficient electrocatalytic oxidation of urea on a Mn-incorporated Ni(OH)2/carbon fiber cloth for energy-saving rechargeable Zn–air batteries

2017 ◽  
Vol 53 (77) ◽  
pp. 10711-10714 ◽  
Author(s):  
Xian Zhang ◽  
Guoqiang Liu ◽  
Cuijiao Zhao ◽  
Guozhong Wang ◽  
Yunxia Zhang ◽  
...  
Keyword(s):  
Electronic Structure ◽  
Carbon Fiber ◽  
Energy Saving ◽  
Electrocatalytic Oxidation ◽  
Oxidation Activity ◽  
Highly Efficient ◽  
Carbon Fiber Cloth ◽  
Potential Applications

The introduction of Mn can effectively regulate the electronic structure of Ni hydroxides on CFC, exhibiting superior electrocatalytic oxidation activity toward urea and potential applications in energy-saving rechargeable Zn–air batteries.

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