Quasi-random Simulation of Linear Kinetic Equations

We study the improvement achieved by using quasi-random sequences in place of pseudo-random numbers for solving linear spatially homogeneous kinetic equations. Particles are sampled from the initial distribution. Time is discretized and quasi-random numbers are used to move the particles in the velocity space. Quasi-random points are not blindly used in place of pseudo-random numbers: at each time step, the number order of the particles is scrambled according to their velocities. Convergence of the method is proved. Numerical results are presented for a sample problem in dimensions 1, 2 and 3. We show that by using quasi-random sequences in place of pseudo-random points, we are able to obtain reduced errors for the same number of particles.