Upon first inspection, calculation of the neutron distribution in a commercial-scale nuclear reactor appears to be intractable. However, clever people over the course of several decades have created computational methods that produce highly accurate neutron distributions for very low computational cost. Here we describe the reactor-analysis problem and point out some of its daunting challenges. We introduce today's state-of-the-art methods and describe how and why they work so well for the problems they are designed to solve. The overall approach is "divide and conquer" -- solving the problem in stages, with each stage building on the previous one. Another key approach is tailoring the approximations to take advantage of the physics of the problem, which yields efficiency at the expense of general applicability. We show that decades of development using these approaches have produced a methodology for today's commercial light-water reactors that provides incredibly accurate solutions for incredibly low computational effort.
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