A three-dimensional Fourier analysis of fine mesh rebalance acceleration of linear discontinuous sub-cell balance method for diffusion equation on tetrahedral meshes

Abstract

This paper presents a three-dimensional Fourier analysis of the fine mesh rebalance (FMR) acceleration of the Linear Discontinuous Expansion Method with Subcell Balance (LDEM-SCB) discretization method for solving the neutron diffusion equation on three-dimensional unstructured tetrahedral meshes in order to theoretically understand the convergence characteristics. The three-dimensional Fourier analysis is performed on one and two cubes called the basic elements in which each element is divided into six tetrahedral meshes for translation and reflective boundary conditions on the external boundaries. The Fourier analysis shows that the FMR method significantly accelerates the Gauss-Seidel (GS)-like iteration to solve the LDEM-SCB discretized diffusion equation. The analytical results of the homogeneous test problem taking different aspect ratios show that the convergence of FMR with the translation boundary conditions is less sensitive on the aspect ratio than the one with the reflective boundary conditions. In addition, we identified the convergence characteristics of the GS-like iteration and its FMR acceleration of the heterogeneous problem.