@article{cornejo_anistratov_smith_2019, title={Iteration Methods with Multigrid in Energy for Eigenvalue Neutron Diffusion Problems}, volume={193}, ISSN={["1943-748X"]}, DOI={10.1080/00295639.2019.1573601}, abstractNote={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.}, number={8}, journal={NUCLEAR SCIENCE AND ENGINEERING}, author={Cornejo, Luke R. and Anistratov, Dmitriy Y. and Smith, Kord}, year={2019}, pages={803–827} }
 @article{anistratov_cornejo_jones_2017, title={Stability analysis of nonlinear two-grid method for multigroup neutron diffusion problems}, volume={346}, ISSN={["1090-2716"]}, DOI={10.1016/j.jcp.2017.06.014}, abstractNote={We present theoretical analysis of a nonlinear acceleration method for solving multigroup neutron diffusion problems. This method is formulated with two energy grids that are defined by (i) fine-energy groups structure and (ii) coarse grid with just a single energy group. The coarse-grid equations are derived by averaging of the multigroup diffusion equations over energy. The method uses a nonlinear prolongation operator. We perform stability analysis of iteration algorithms for inhomogeneous (fixed-source) and eigenvalue neutron diffusion problems. To apply Fourier analysis the equations of the method are linearized about solutions of infinite-medium problems. The developed analysis enables us to predict convergence properties of this two-grid method in different types of problems. Numerical results of problems in 2D Cartesian geometry are presented to confirm theoretical predictions.}, journal={JOURNAL OF COMPUTATIONAL PHYSICS}, author={Anistratov, Dmitriy Y. and Cornejo, Luke R. and Jones, Jesse P.}, year={2017}, month={Oct}, pages={278–294} }
 @article{cornejo_anistratov_2016, title={Nonlinear Diffusion Acceleration Method with Multigrid in Energy for k-Eigenvalue Neutron Transport Problems}, volume={184}, ISSN={["1943-748X"]}, DOI={10.13182/nse16-78}, abstractNote={Abstract We present a multilevel method for solving multigroup neutron transport k-eigenvalue problems in two-dimensional Cartesian geometry. It is based on the nonlinear diffusion acceleration (NDA) method. The multigroup low-order NDA (LONDA) equations are formulated on a sequence of energy grids. Various multigrid cycles are applied to solve the hierarchy of multigrid LONDA equations. The algorithms developed accelerate transport iterations and are effective in solving the multigroup NDA low-order equations. We present numerical results for model reactor-physics problems with a large number of groups to demonstrate the performance of different iterative schemes.}, number={4}, journal={NUCLEAR SCIENCE AND ENGINEERING}, author={Cornejo, Luke R. and Anistratov, Dmitriy Y.}, year={2016}, month={Dec}, pages={514–526} }