  We present a new deterministic approach for the solution of the Boltzmann
kinetic equation based on nodal discontinuous Galerkin (DG) discretizations in
velocity space. In the new approach the collision operator has the form of a
bilinear operator with pre-computed kernel; its evaluation requires $O(n^5)$
operations at every point of the phase space where $n$ is the number of degrees
of freedom in one velocity dimension. The method is generalized to any
molecular potential. Results of numerical simulations are presented for the
problem of spatially homogeneous relaxation for the hard spheres potential.
Comparison with the method of Direct Simulation Monte Carlo (DSMC) showed
excellent agreement.
