A Rayleigh quotient method for criticality eigenvalue problems in neutron transport
Not Available
Ortega, M. I.↗
Engineering topics
Bailey, T. S.
Publications and source records attributed to Bailey, T. S..
An Efficient Sweep-Based Solver for the S N Equations on High-Order Meshes
In this study, we propose a graph-based sweep algorithm for solving the steady-state, monoenergetic discrete ordinates on meshes of high-order (HO) curved mesh elements. Our spatial discretization consists of arbitrarily HO discontinuous Galerkin finite elements using upwinding at mesh element faces. To determine mesh element sweep ordering, we define a directed, weighted graph whose vertices correspond to mesh elements and whose edges correspond to mesh element upwind dependencies. This graph is made acyclic by removing select edges in a way that approximately minimizes the sum of removed edge weights. Once the set of removed edges is determined, transport sweeps are performed by lagging the upwind dependency associated with the removed edges. The proposed algorithm is tested on several two-dimensional and three-dimensional meshes composed of HO curved mesh elements.
97 MATHEMATICS AND COMPUTING↗
Preserving spherical symmetry in axisymmetric coordinates for diffusion problems
Persevering symmetric solutions, even in the under-converged limit, is important to the robustness of production simulation codes. We explore the symmetry preservation in both a continuous nodal and a mixed finite element method. In their standard formulation, neither method preserves spherical solution symmetry in axisymmetric (RZ) coordinates. We propose two methods, one for each family of finite elements, that recover spherical symmetry for low-order finite elements on linear or curvilinear meshes. This is a first step toward understanding achieving symmetry for higher-order elements. (authors)
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Thick diffusion limit boundary layer test problems
We develop two simple test problems that quantify the behavior of computational transport solutions in the presence of boundary layers that are not resolved by the spatial grid. In particular we study the quantitative effects of 'contamination' terms that, according to previous asymptotic analyses, may have a detrimental effect on the solutions obtained by both discontinuous finite element (DFEM) and characteristic-method (CM) spatial discretizations, at least for boundary layers caused by azimuthally asymmetric incident intensities. Few numerical results have illustrated the effects of this contamination, and none have quantified it to our knowledge. Our test problems use leading-order analytic solutions that should be equal to zero in the problem interior, which means the observed interior solution is the error introduced by the contamination terms. Results from DFEM solutions demonstrate that the contamination terms can cause error propagation into the problem interior for both orthogonal and non-orthogonal grids, and that this error is much worse for non-orthogonal grids. This behavior is consistent with the predictions of previous analyses. We conclude that these boundary layer test problems and their variants are useful tools for the study of errors that are introduced by unresolved boundary layers in diffusive transport problems. (authors)
97 MATHEMATICS AND COMPUTING↗
Provably optimal parallel transport sweeps on regular grids
We have found provably optimal algorithms for full-domain discrete-ordinate transport sweeps on regular grids in 3D Cartesian geometry. We describe these algorithms and sketch a 'proof that they always execute the full eight-octant sweep in the minimum possible number of stages for a given P{sub x} x P{sub y} x P{sub z} partitioning. Computational results demonstrate that our optimal scheduling algorithms execute sweeps in the minimum possible stage count. Observed parallel efficiencies agree well with our performance model. An older version of our PDT transport code achieves almost 80% parallel efficiency on 131,072 cores, on a weak-scaling problem with only one energy group, 80 directions, and 4096 cells/core. A newer version is less efficient at present-we are still improving its implementation - but achieves almost 60% parallel efficiency on 393,216 cores. These results conclusively demonstrate that sweeps can perform with high efficiency on core counts approaching 10{sup 6}. (authors)
97 MATHEMATICS AND COMPUTING↗