Caleb A. Shaw | Searcharxiv

arXiv2026

Hybrid Two-Level Transport Method with Solution Decomposition in Macro and Micro Components

This paper presents a new hybrid MC/deterministic method for solving the one-group steady-state Boltzmann transport equation based on decomposition of solution in macro and micro components. The macro component captures the large-scale structure of the solution. It is represented by angular moments of the high-order transport solution. The $P_1$ approximation is applied to define the macro component. The first two angular moments are obtained as a solution of hybrid low-order moment equations with exact closures. The equation for the micro component is solved using a MC simulation. The hybrid two-level system of equations for macro and micro components is solved by fixed-point iteration scheme. Numerical results are presented to demonstrate variance reduction of stochastic numerical solution and improvement in computational efficiency.

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arXiv2025

Hybrid Weight Window Method for Global Time-Dependent Monte Carlo Particle Transport Calculations

This paper presents a new Monte Carlo (MC) algorithm for time-dependent particle transport problems with global variance reduction based on automatic weight windows (WWs). The centers of WWs at a time step are defined by the solution of an auxiliary hybrid MC / deterministic problem formed by the low-order second-moment (LOSM) equations. The closures for the hybrid LOSM equations are calculated by the MC method. The LOSM equations are discretized by a scheme of the second-order accuracy in time and space. Filtering techniques are applied to reduce noise effects in the LOSM closures. The WWs defined with the auxiliary solution give rise to sufficiently uniform MC particle distribution in space on each time step. The algorithm is analyzed by means of an analytic transport benchmark. We study performance of the MC algorithm depending on a set parameters of WWs. Figure of merit and relative error results are presented, demonstrating the performance of the hybrid MC method and quantifying its computational efficiency.

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