INCREASING THE EFFICIENCY OF RADIATION SHIELDING CALCULATIONS BY USING ANTITHETIC VARIATES

This paper considers the passage of a parallel, uniform stream of part icles through a parallel-sided, homogeneous slab of material capable o f scattering and absorption. Particle histories are followed until the particle escapes from the near or far surface of the slab. Each parti cle carries a weight (initially 1, at the near surface of the slab) an d the total weight of particles escaping through the far surface is co mpared with the total number of particles initiated originally. To inc rease efficiency of the computation, (i) we disregard absorption, by m ultiplying the weight of each particle by its non-absorption probabili ty at each collision, and (ii) we select N parallel geometric surfaces inside the slab (parallel to the sides of the slab) and, as a particl e crosses any such surface - if it is crossing it in a backward direct ion - we play ''Russian roulette'' with probability l/m (multiplying i ts weight by m if it survives), while - if it is crossing the surface in a forward direction - we ''split'' the particle into m identical pa rticles tall initially moving with the same velocity vector), each wit h weight 1/m times that of the particle we split. In the case of split ting, the paper compares two alternative techniques. Either (1) we sel ect m independent random numbers with which to compute the m free path lengths to the next (scattering) collision, or (2) we select one rand om number and form m ''antithetically'' balanced values with which to compute the m free path lengths (with appropriate weight-adjustments). The results obtained are very promising. The use of ''antithetic spli tting'' increases the efficiency tin terms of the work required to obt ain a given variance in the resulting estimate of the transmission coe fficient) by a factor ranging from about 1 to about 30 (the improvemen t appears to be most marked for scattering probabilities around 0.5, r ather than near 1.0). (C) 1998 IMACS/Elsevier Science B.V.