@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{anistratov_jones_2015, title={Space-Angle Homogenization of the Step Characteristic Scheme}, volume={44}, ISSN={["2332-4325"]}, DOI={10.1080/23324309.2015.1076848}, abstractNote={We present a new homogenized discretization scheme for solving k-eigenvalue neutron transport problems on coarse grids in space and angle. The developed scheme for 1D slab geometry is based on the step characteristic (SC) method. It is algebraically consistent with fine-mesh SC equations. We analyze the sensitivity of the homogenized transport scheme to perturbations in homogenized cross-sections and other coefficients of the scheme. The obtained results demonstrate that the proposed scheme is stable to small perturbations in its parameters.}, number={4-5}, journal={JOURNAL OF COMPUTATIONAL AND THEORETICAL TRANSPORT}, author={Anistratov, Dmitriy Y. and Jones, Jesse P.}, year={2015}, pages={215–228} }
 @article{anistratov_jones_2014, title={Spatial Homogenization of Transport Discretization Schemes}, volume={43}, ISSN={["2332-4325"]}, DOI={10.1080/00411450.2014.914040}, abstractNote={Neutron transport problems for whole reactor core calculations result in a very large amount of unknowns. Some difficulties related to dimensionality of this kind of problem can be resolved by solving a well-posed homogenized transport problem on a coarse grid. We apply homogenization methodology to develop discretization schemes for solving k-eigenvalue problems on coarse meshes in 1D slab geometry. The step characteristic (SC) method is used for fine-mesh transport calculations. We develop spatially homogenized transport schemes on a basis of two different transport discretization methods: SC and linear discontinuous schemes. The basic approach is to formulate a discretization that is spatially consistent with the given fine-mesh transport discretization. The presented numerical results demonstrate features of the developed methods in preserving grid functions of the angular flux computed with the SC method on fine spatial meshes. We study sensitivity of the proposed schemes to various types of perturbations in spatially averaged cross sections and other homogenization parameters.}, number={1-7}, journal={JOURNAL OF COMPUTATIONAL AND THEORETICAL TRANSPORT}, author={Anistratov, Dmitriy and Jones, Jesse}, year={2014}, pages={262–288} }