AUTOMATIC VARIANCE REDUCTION FOR 3-DIMENSIONAL MONTE-CARLO SIMULATIONS BY THE LOCAL IMPORTANCE FUNCTION TRANSFORM .1. ANALYSIS

A new automated variance reduction method for the Monte Carlo simulati on of multigroup neutron transport source-detector problems is describ ed. The method is based on a modified transport problem that can be so lved by analog Monte Carlo with zero variance. The implementation of t his modified problem is impractical, in part because it requires the e xact solution of an adjoint transport problem. The new local importanc e function transform (LIFT) method is developed to overcome this diffi culty by approximating the exact adjoint solution with a piecewise-con tinuous function containing parameters that are obtained from a determ inistic adjoint calculation. The transport and collision processes of the transformed Monte Carlo problem bias source distribution, distance to collision, and selection of postcollision energy groups and direct ions. A companion paper provides numerical results that demonstrate th e efficiency of the LIFT method.