VARIANCE REDUCTION IN MONTE-CARLO RADIATION TRANSPORT USING ANTITHETIC VARIATES

The use of antithetic variates in conjunction with geometrical surface splitting/Russian roulette is numerically studied for one-group Monte-Carlo radiation transport problems in slab geometry. Numerical solutions of the coupled set of integral equations for the first and second moments around the scores, and thereby estimates of variances are obtained. Derivations of the equations for the score accumulation probability and the moments around the score are presented. Two types of antithetic transformations are considered. The results indicate that antithetic transformations always lead to the reduction of variance. A substantial reduction in variance is obtained when antithetic transformations are used with the rule of thumb splitting. The reduction in variance is attractively large for thick slabs (approximately 20 m.f.p.) and low scattering probability.