2019 journal article
Iteration Methods with Multigrid in Energy for Eigenvalue Neutron Diffusion Problems
NUCLEAR SCIENCE AND ENGINEERING, 193(8), 803–827.
author keywords: Neutron diffusion; eigenvalue problems; multigrid methods; multilevel iteration methods
TL;DR:
Nonlinear multilevel methods with multiple grids in energy for solving the k-eigenvalue problem for multigroup neutron diffusion equations and multigrid-in-energy algorithms based on a nonlinear projection operator and several advanced prolongation operators are presented.
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Added: August 5, 2019
Abstract In this paper we present nonlinear multilevel methods with multiple grids in energy for solving the k-eigenvalue problem for multigroup neutron diffusion equations. We develop multigrid-in-energy algorithms based on a nonlinear projection operator and several advanced prolongation operators. The evaluation of the eigenvalue is performed in the space with smallest dimensionality by solving the effective one-group diffusion problem. We consider two-dimensional Cartesian geometry. The multilevel methods are formulated in discrete form for the second-order finite volume discretization of the diffusion equation. The homogenization in energy is based on a spatially consistent discretization of the group diffusion equations on coarse grids in energy. We present numerical results of model reactor-physics problems with 44 energy groups. They demonstrate performance and main properties of the proposed iterative methods with multigrid in energy.