Real-Space ab initio Calculations on the Basis of Spectral Element Method
Real-Space ab initio Calculations on the Basis of Spectral Element Method
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基于谱元法的实空间从头计算
DOI：
10.1299/jmmp.2.1288
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
N. Yoshikawa
中科院分区：
文献类型：
--
作者：
Y. Shiihara;Nobuyuki Ishizaki;O. Kuwazuru;N. Yoshikawa
本文在范数守恒赝势方法的基础上，研究了谱元方法在从头计算电子结构计算中的适用性。谱元法作为有限元法的一种变体，采用高斯-洛巴托-勒让德多项式作为形函数。使用高阶形函数，我们得到的总能量的误差相对于自由度的数量的快速收敛。当执行高精度计算时，该属性显著降低了计算成本。在谱元法中，通过选择求积点的位置，使某些矩阵成为对角矩阵和稀疏矩阵。这也减少了密度泛函计算中所需的计算任务。
We have investigated the usability of the spectral element method in ab-initio electron structure calculations on the basis of norm-conserving pseudopotential method. The spectral element method as a variant of the finite element method employs a Gauss-Lobatto-Legendre polynomial as a shape function. Using higher-order shape function, we obtain rapid convergence of the error in the total energy with respect to the number of degrees of freedom. This property significantly reduces the computational cost when one performs the highly accurate calculation. In the spectral element method positions of quadrature points are chosen so that some matrices turn to be diagonal matrix and sparse matrix. This also reduces the computational task required in the density functional calculation.