Real-Space Ab-Initio Calculations on the Basis of Spectral Element Method

Abstract

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.