  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.
