New general approach in few-body scattering calculations: Solving   discretized Faddeev equations on a graphics processing unit
  Background: The numerical solution of few-body scattering   problems with realistic interactions is a difficult problem that   normally must be solved on powerful supercomputers, taking a lot   of computer time. This strongly limits the possibility of accurate   treatments for many important few-particle problems in different   branches of quantum physics.   Purpose: To develop a new general highly effective approach   for the practical solution of few-body scattering equations that   can be implemented on a graphics processing unit.   Methods: The general approach is realized in three steps: (i)   the reformulation of the scattering equations using a convenient   analytical form for the channel resolvent operator; (ii) a complete   few-body continuum discretization and projection of all operators   and wave functions onto a $L_2$ basis constructed from   stationary wave packets and (iii) the ultra-fast solution of the   resulting matrix equations using graphics processor.   Results: The whole approach is illustrated by a calculation of   the neutron-deuteron elastic scattering cross section below and   above the three-body breakup threshold with a realistic $NN$   potential which is performed on a standard PC using a graphics   processor with an extremely short runtime.   Conclusions: The general technique proposed in this paper opens a   new way for a fast practical solution of quantum few-body scattering   problems both in non-relativistic and relativistic formulations in   hadronic, nuclear and atomic physics. 
V.N. Pomerantsev, V.I. Kukulin, O.A. Rubtsova
nucl-th