Accelerating spectral atomic and molecular collisions methods with graphics processing units

Abstract

We present a computation method to accelerate the calculation of the Hamiltonian of a three-body time independent Schr{"o}dinger equation for collisions. The Hamiltonian is constructed with one dimensional (basis overlaps) and two dimensional (interparticle interaction) integrals that are mapped into a computational grid in a Graphics Processing Unit (GPU). We illustrate the method for the case of an electron impact single ionization of a two electron atom. This proposal makes use of a Generalized Sturmian Basis set for each electron, which are obtained numerically on a quadrature grid that is used to compute the integrals in the GPU. The optimal computation is more than twenty times faster in the {GPU} than the calculation in CPU. The method can be easily scaled to computers with several Graphics Processing Units or clusters.