Multilevel Iteration Method for Binary Stochastic Transport Problems
It addresses the computational challenge of solving transport problems in stochastic media, offering a potentially more efficient iterative approach for this domain-specific problem.
The paper develops a multilevel iteration method for solving linear particle transport problems in binary stochastic mixtures, achieving efficient convergence on numerical test problems.
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.