Multilevel Iteration Method for Binary Stochastic Transport Problems

TL;DR

This paper introduces a multilevel iterative method based on nonlinear projection for efficiently solving linear particle transport problems in binary stochastic mixtures, combining high- and low-order equations.

Contribution

It develops a novel multilevel iteration scheme integrating high-order and low-order equations for stochastic transport problems, analyzed through numerical tests.

Findings

Effective convergence demonstrated on test problems

Combines high-order transport with low-order quasidiffusion equations

Provides a framework for solving stochastic particle transport efficiently

Abstract

This paper presents an iteration method for solving linear particle transport problems in binary stochastic mixtures. It is based on nonlinear projection approach. The method is defined by a hierarchy of equations consisting of the high-order transport equation for materials, low-order Yvon-Mertens equations for conditional ensemble average of the material partial scalar fluxes, and low-order quasidiffusion equations for the ensemble average of the scalar flux and current. The multilevel system of equations is solved by means of an iterative algorithm with the $V$-cycle. The iteration method is analyzed on a set of numerical test problems.