AN IMPROVED DETERMINISTIC METHOD FOR THE SOLUTION OF STOCHASTIC MEDIA TRANSPORT PROBLEMS

摘要

We present an improved deterministic method for analyzing transport problems in random media. In the original method realizations were generated by means of a product quadrature rule; transport calculations were performed on each realization and the results combined to produce ensemble averages. In the present work we recognize that many of these realizations yield identical transport problems. We describe a method to generate only unique transport problems with the proper weighting to produce identical ensemble-averaged results at reduced computational cost. We also describe a method to ignore relatively unimportant realizations in order to obtain nearly identical results with further reduction in costs. Our results demonstrate that these changes allow for the analysis of problems of greater complexity than was practical for the original algorithm.