A QUASI-MONTE CARLO SCHEME USING NETS FOR A LINEAR BOLTZMANN-EQUATION

A quasi-Monte Carlo particle simulation for solving a linear Boltzmann equation is constructed and a convergence proof is given. The analysi s is restricted to the three-dimensional equation in the space homogen eous case and the velocity domain is normalized to be I-3 = [0;1)(3). A particle simulation is described. It combines a Euler scheme in time with quasi-Monte Carlo integration in velocity space. The quadratures use (0,m,s)-nets, which are sets with a very regular distribution beh avior. The particles are reordered according to the components of thei r velocity at each time step. A deterministic error bound is obtained. Finally, numerical experiments are presented for some test problems w here an exact solution is known. The accuracy of the quasi-Monte Carlo scheme is compared with a standard Monte Carlo algorithm. The results show an improvement in both magnitude of error and convergence rate o f quasi-Monte Carlo over Monte Carlo approach.