A Mesh-Input-Free On-The-Fly Source Convergence Indicator in Monte Carlo Power Method

Abstract

A mesh-input-free on-the-fly source convergence indicator is proposed for Monte Carlo source iterations by the power method. This indicator consists of two step computations of source particle centers. In the first step, the geometric center of all source particles is computed. The spatial domain is then divided into eight subdomains by the xy, yz, and zx planes that intersect at the geometric center. In the second step, a new geometric center is computed for the source particles in each of the eight subdomains. Therefore, nine centers are obtained at each cycle of source iterations and the distances to the corresponding centers at the initial cycle are computed, yielding the nine center-distances sum (NCDS). NCDS was compared against entropy indicators defined on a fixed mesh. Visual inspection reveals that the overall trend of NCDS is as sound as the entropy indicators. The feasibility of NCDS is shown by the step-refined on-thefly convergence diagnosis with Wilcoxon rank sum.

Fractal dimension analysis for run length diagnosis of Monte Carlo criticality calculation

“…Equations (2) and (4) reveal that the convergence implied in CLT is part of the convergence implied in FCLT. On the other hand, BM in Equations (2) and (5) is known to assume a unique value of a dimension indicator in fractal geometry [6].…”

“…Here, the largest value of t i and t j is unity as in Equations (2) and (3). Note that the "C" in C A indicates covariance while the "C" in C n (t) in Equation 2indicates the "central" in FCLT.…”

“…The initial generation starts with a guess of source distribution, and tallies are scored after some presumed beginning of the statistical equilibrium of source distribution. The diagnosis of the convergence toward such equilibrium has been well researched; discrete entropy diagnosis [1] is widely accepted as an effective ex post facto tool, and a mesh-input-free on-the-fly convergence indicator [2] is also available. On the other hand, the diagnosis of the number of generations is not yet established.…”

Brownian bridge and statistical error estimation in Monte Carlo reactor calculation

“…. ..; see elsewhere [17] for the run-time judgment of source convergence. The variance of the sample mean of y 1 , y 2 , .…”