Fast and Accurate Scheme for Green Functions and Eigenvectors : Regulated Polynomial Expansion without Gibbs Oscillation
Fast and Accurate Scheme for Green Functions and Eigenvectors : Regulated Polynomial Expansion without Gibbs Oscillation
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快速准确的格林函数和特征向量方案：无吉布斯振荡的调节多项式展开
DOI：
10.1143/jpsj.76.054004
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发表时间：
2007
影响因子：
1.7
通讯作者：
M. Itoh
中科院分区：
文献类型：
--
作者：
S. Sota;M. Itoh
提出了一种无振荡的傅立叶展开式，并将其应用于预解算子的多项式展开式，作为Voter等人对核多项式方法(KPM)Gibbs现象的替代处理。[物理。修订本B 53(1996年)12733]。采用调节勒让德多项式作为基函数，在完全消除非物理振荡的同时，基本保留了KPM的递推算法。分辨率在频域内是均匀的，并通过扩大展开式的截断范围来无限制地提高。该方法还可以用来计算高精度的特征向量。它被进一步扩展到时间域，能够在相同的算法中处理量子演化。对193个原子的晶格动力学以及计算机生成的1000个原子的Lennard-Jones玻璃进行了数值计算。它不仅是一种最有效的散货模拟方案，而且证实了其计算量是最大的。
An oscillation-free Fourier expansion is proposed and applied to the polynomial expansion of resolvent operator, as an alternative treatment for Gibbs phenomenon to the kernel polynomial method (KPM) by Voter et al. [Phys. Rev. B 53 (1996) 12733]. Adopting regulated Legendre polynomial as basis functions, the recurrence algorithm underlying the KPM is practically preserved, while it eliminates unphysical oscillations entirely. The resolution is uniform in the frequency domain, and improved without limitation by extending the truncation range of the expansion. The method can also be used to calculate the eigenvector with remarkably high precision. It is further extended to the time domain, being able to deal with the quantum evolution in the same algorithm. A numerical test was performed against a lattice dynamics of 19 3 atoms, as well as of a computer generated Lennard–Jones glass of 1000 atoms. Not only it serves as a most efficient simulation scheme for a bulk, confirmed was also that the calculation c...