We propose the algorithm to evaluate the Coulomb potential in the ab initio density functional calculation on the graphics processor unit (GPU). The numerical accuracy required for the algorithm is investigated in detail. It is shown that GPU, which supports only the single-precision floating number natively, can take part in the major computational tasks. Because of the limited size of the wor...

In this paper, anti-Gaussian quadrature rules for trigonometric polynomials are introduced. Special attention is paid to an even weight function on [-?, ?). The main properties of such proved and a numerical method their construction presented. That based relations between nodes weights the rule algebraic polynomials. Some examples included. Also, we compare our with other available methods.

This paper presents a generalized Gaussian quadrature method for numerical integration over two-dimensional bounded regions with a curved exponential edge. A general formulae for numerical integration over the regions R1 = {(x,y)|a ≤ x ≤ b, c ≤ y ≤ e} and R2 = {(x,y)|a ≤ y ≤ b, c ≤ x ≤ e} are derived, which can be directly used for integrating any type of functions over such regions. In order t...