[en] The Adjacent-cell Preconditioner (AP) is derived for accelerating generic fixed-weight, Weighted Diamond Difference (WDD) neutron transport methods in multidimensional Cartesian geometry. The AP is determined by requiring: (a) the eigenvalue of the combined mesh sweep-AP iterations to vanish in the vicinity of the origin in Fourier space; and (b) the diagonal and off-diagonal elements of the preconditioner to satisfy a diffusion-like condition. The spectra of the resulting iterations for a wide range of problem parameters exhibit a spectral radius smaller than .25, that vanishes implying immediate convergence for very large computational cells. More importantly, unlike other unconditionally stable acceleration schemes, the AP is cell-centered and its spectral radius remains small when the cell aspect ratio approaches 0 or ∞. Testing of the AP and comparison of its rate of convergence to the standard Source Iterations (SI) for Burre's Suite of Test Problems (BSTeP) demonstrates its high efficiency in reducing the number of iterations required to achieve convergence, especially for optically thick cells where acceleration is most needed

[en] The effect of three communication schemes for solving Arbitrarily High Order Transport (AHOT) methods of the Nodal type on parallel performance is examined via direct measurements and performance models. The target architecture in this study is Oak Ridge National Laboratory's 128 node Paragon XP/S 5 computer and the parallelization is based on the Parallel Virtual Machine (PVM) library. However, the conclusions reached can be easily generalized to a large class of message passing platforms and communication software. The three schemes considered here are: (1) PVM's global operations (broadcast and reduce) which utilizes the Paragon's native corresponding operations based on a spanning tree routing; (2) the Bucket algorithm wherein the angular domain decomposition of the mesh sweep is complemented with a spatial domain decomposition of the accumulation process of the scalar flux from the angular flux and the convergence test; (3) a distributed memory version of the Bucket algorithm that pushes the spatial domain decomposition one step farther by actually distributing the fixed source and flux iterates over the memories of the participating processes. Their conclusion is that the Bucket algorithm is the most efficient of the three if all participating processes have sufficient memories to hold the entire problem arrays. Otherwise, the third scheme becomes necessary at an additional cost to speedup and parallel efficiency that is quantifiable via the parallel performance model

No abstract available

[en] Coarse-grained angular domain decomposition of the mesh sweep algorithm has been implemented in ORNL's three dimensional transport code TORT for Cray's macrotasking environment on platforms running the UNICOS operating system. A performance model constructed earlier is reviewed and its main result, namely the identification of the sources of parallelization overhead, is used to motivate the present work. The sources of overhead treated here are: redundant operations in the angular loop across participating tasks; repetitive task creation; lock utilization to prevent overwriting the flux moment arrays accumulated by the participating tasks. Substantial reduction in the parallelization overhead is demonstrated via sample runs with fixed tunning, i.e. zero CPU hold time. Up to 50% improvement in the wall clock speedup over the previous implementation with autotunning is observed in some test problems

[en] A new high-accuracy, coarse-mesh, nodal integral approach is developed for the efficient numerical solution of linear partial differential equations. It is shown that various special cases of this general nodal integral approach correspond to several high efficiency nodal methods developed recently for the numerical solution of neutron diffusion and neutron transport problems. The new approach is extended to the nonlinear Navier-Stokes equations of fluid mechanics; its extension to these equations leads to a new computational method, the nodal integral method which is implemented for the numerical solution of these equations. Application to several test problems demonstrates the superior computational efficiency of this new method over previously developed methods. The solutions obtained for several driven cavity problems are compared with the available experimental data and are shown to be in very good agreement with experiment. Additional comparisons also show that the coarse-mesh, nodal integral method results agree very well with the results of definitive ultra-fine-mesh, finite-difference calculations for the driven cavity problem up to fairly high Reynolds numbers

[en] A coarse-grained, static-scheduling parallelization of the standard iterative scheme used for solving the discrete-ordinates approximation of the neutron transport equation is described. The parallel algorithm is based on a decomposition of the angular domain along the discrete ordinates, thus naturally producing a set of completely uncoupled systems of equations in each iteration. Implementation of the parallel code on Intcl's iPSC/2 hypercube, and solutions to test problems are presented as evidence of the high speedup and efficiency of the parallel code. The performance of the parallel code on the iPSC/2 is analyzed, and a model for the CPU time as a function of the problem size (order of angular quadrature) and the number of participating processors is developed and validated against measured CPU times. The performance model is used to speculate on the potential of massively parallel computers for significantly speeding up real-life transport calculations at acceptable efficiencies. We conclude that parallel computers with a few hundred processors are capable of producing large speedups at very high efficiencies in very large three-dimensional problems. 10 refs., 8 figs

[en] An overview of ORNL's three-dimensional neutral particle transport code, TORT, is presented. Special features of the code that make it invaluable for large applications are summarized for the prospective user. Advanced capabilities currently under development and installation in the production release of TORT are discussed; they include: multitasking on Cray platforms running the UNICOS operating system; Adjacent cell Preconditioning acceleration scheme; and graphics codes for displaying computed quantities such as the flux. Further developments for TORT and its companion codes to enhance its present capabilities, as well as expand its range of applications are disucssed. Speculation on the next generation of neutron particle transport codes at ORNL, especially regarding unstructured grids and high order spatial approximations, are also mentioned

[en] Most optimization studies of cold neutron sources have concentrated on the numerical prediction or experimental measurement of the cold moderator optimum thickness which produces the largest cold neutron leakage for a given thermal neutron source. Optimizing the geometrical shape of the cold source, however, is a more difficult problem because the optimized quantity, the cold neutron leakage, is an implicit function of the shape which is the unknown in such a study. We draw an analogy between this problem and a state space search, then we use a simple Artificial Intelligence (AI) search technique to determine the optimum cold source shape based on a two-group, r-z diffusion model. We implemented this AI design concept in the computer program AID which consists of two modules, a physical model module and a search module, which can be independently modified, improved, or made more sophisticated. 7 refs., 1 fig

[en] A computer program that solves two-dimensional transport problems using the LN (linear nodal), LL (linear linear), or the BL (bi-linear) method was written and was used to solve two simple test problems. The results are used here to confirm our algebraic manipulations of the nodal equations and also to compare the performance of the three methods from the computational, as well as the theoretical, point of view. The three methods are found to have comparable accuracies, especially on meshes that are sufficiently fine. It is apparent that a given method will be more appropriate to use for solving certain problems than the other two methods, depending on the specifications of the problem

[en] Nodal Methods have been derived, implemented and numerically tested for several problems in physics and engineering. In the field of nuclear engineering, many nodal formalisms have been used for the neutron diffusion equation, all yielding results which were far more computationally efficient than conventional Finite Difference (FD) and Finite Element (FE) methods. However, not much effort has been devoted to theoretically comparing nodal and FD methods in order to explain the very high accuracy of the former. In this summary we outline the derivation of a simple five-point form for the lowest order nodal method and compare it to the traditional five-point, edge-centered FD scheme. The effect of the observed differences on the accuracy of the respective methods is established by considering a simple test problem. It must be emphasized that the nodal five-point scheme derived here is mathematically equivalent to previously derived lowest order nodal methods. 7 refs., 1 tab