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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 577 records · Page 32

Massive Asynchronous Parallelization of Sparse Matrix Factorizations

Solving sparse problems is at the core of many DOE computational science applications. We focus on the challenge of developing sparse algorithms that can fully exploit the parallelism in extreme-scale computing systems, in particular systems with massive numbers of cores per node. Our approach is to express a sparse matrix factorization as a large number of bilinear constraint equations, and then solving these equations via an asynchronous iterative method. The unknowns in these equations are the matrix entries of the factorization that is desired.

97 MATHEMATICS AND COMPUTING↗

Asymptotic Expansion of the Impedance Per Unit Length for Rectangular Conductors

An iteration method is introduced to obtain the asymptotic form of the impedance per unit length of a rectangular conductor when the half side lengths are large compared to the skin depth. The first terms of the asymptotic expansion are extracted in closed form. The manner in which the corner corrections fit into the expansion are illustrated. The asymptotic results are compared to a numerical solution in the square limit. The odd corner correction for a right angle edge is also discussed.

42 ENGINEERING↗

Impact of Time-Dependent Reactor and Sensor Physics on Core Power Synthesis (Rev.1)

Online synthesis of power distribution is critical in the operation and control of nuclear power reactors to ensure that the core is operating within safety margins and to provide essential knowledge associated with the burnup of the fuel. In light-water reactors, power synthesis is achieved by using some a priori knowledge of the state of the reactor core and updating based on the signals coming from in-core sensors—namely, self-powered neutron detectors (SPNDs). This report examines the effects of fuel burnup and sensor degradation on the ability to accurately synthesize the power distribution in a pressurized water reactor (PWR), considering the typical low-enriched uranium (LEU, 3%-5% enrichment) fuel cycle as well as the higher enrichment LEU+ (5%-8% enrichment) fuel cycle. Several modeling tools were used to simulate power synthesis based on the responses of SPNDs, with emitters made out of Rh or V. A representative PWR LEU core was modeled using the Polaris/Purdue Advanced Reactor Core Simulator (PARCS) approach. The Monte Carlo N-Particle Transport 6 (MCNP6) code was used as well to calculate response functions between different segments of fuel to individual SPNDs; this is a crucial parameter for power synthesis. The Oak Ridge Isotope GENeration (ORIGEN) package in the Standardized Computer Analyses for Licensing Evaluation (SCALE) code was used to model the time-dependent isotopic transmutation in the SPND emitters. All these data were fed into a custom code that enacted the point-based iterative method to simulate power synthesis. Developmental work was also performed on high-fidelity SPND models in the GEometry ANd Tracking 4 (Geant4) code, which enables higher-accuracy modeling of the current responses from SPNDs. In this work, five sets of time-dependent power synthesis test cases were conducted. In these test cases, systematic changes in the input conditions enabled an analysis of the effect of (1) slightly inaccurate a priori power distribution assumptions with respect to fuel burnup, (2) highly inaccurate a priori power distribution assumptions with respect to fuel burnup (such that burnup is not included in the a priori assumed distribution), and (3) differences between Rh and V SPNDs in terms of downstream consequences of the transmutation in the emitters and the extended nature of the LEU+ fuel cycle in comparison with LEU. The authors discovered that one may permissibly have slightly inaccurate a priori assumptions of the fuel burnup (such that the level of burnup may be slightly underapproximated or overapproximated by the accumulated burnup in approximately 9.3 full power days), but to not account for burnup at all in the a priori assumptions leads to severe levels of error, approaching 25% at maximum (for LEU). The authors also discovered that V SPNDs are extraordinarily robust in both the LEU and LEU+ fuel cycles considered in this modeling work, whereas Rh SPNDs undergo significant transmutation that can result in large errors in the synthesized power distribution.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

A new multi-energy neutrino radiation-hydrodynamics code in full general relativity and its application to the gravitational collapse of massive stars

We present a new multi-dimensional radiation-hydrodynamics code for massive stellar core-collapse in full general relativity (GR). Employing an M1 analytical closure scheme, we solve spectral neutrino transport of the radiation energy and momentum based on a truncated moment formalism. Regarding neutrino opacities, we take into account a baseline set in state-of-the-art simulations, in which inelastic neutrino–electron scattering, thermal neutrino production via pair annihilation, and nucleon–nucleon bremsstrahlung are included. While the Einstein field equations and the spatial advection terms in the radiation-hydrodynamics equations are evolved explicitly, the source terms due to neutrino–matter interactions and energy shift in the radiation moment equations are integrated implicitly by an iteration method. To verify our code, we first perform a series of standard radiation tests with analytical solutions that include the check of gravitational redshift and Doppler shift. A good agreement in these tests supports the reliability of the GR multi-energy neutrino transport scheme. We then conduct several test simulations of core-collapse, bounce, and shock stall of a 15M{sub ⊙} star in the Cartesian coordinates and make a detailed comparison with published results. Our code performs quite well to reproduce the results of full Boltzmann neutrino transport especially before bounce. In the postbounce phase, our code basically performs well, however, there are several differences that are most likely to come from the insufficient spatial resolution in our current 3D-GR models. For clarifying the resolution dependence and extending the code comparison in the late postbounce phase, we discuss that next-generation Exaflops class supercomputers are needed at least.

79 ASTRONOMY AND ASTROPHYSICS↗

POLARIZED LINE FORMATION IN NON-MONOTONIC VELOCITY FIELDS

For a correct interpretation of the observed spectro-polarimetric data from astrophysical objects such as the Sun, it is necessary to solve the polarized line transfer problems taking into account a realistic temperature structure, the dynamical state of the atmosphere, a realistic scattering mechanism (namely, the partial frequency redistribution—PRD), and the magnetic fields. In a recent paper, we studied the effects of monotonic vertical velocity fields on linearly polarized line profiles formed in isothermal atmospheres with and without magnetic fields. However, in general the velocity fields that prevail in dynamical atmospheres of astrophysical objects are non-monotonic. Stellar atmospheres with shocks, multi-component supernova atmospheres, and various kinds of wave motions in solar and stellar atmospheres are examples of non-monotonic velocity fields. Here we present studies on the effect of non-relativistic non-monotonic vertical velocity fields on the linearly polarized line profiles formed in semi-empirical atmospheres. We consider a two-level atom model and PRD scattering mechanism. We solve the polarized transfer equation in the comoving frame (CMF) of the fluid using a polarized accelerated lambda iteration method that has been appropriately modified for the problem at hand. We present numerical tests to validate the CMF method and also discuss the accuracy and numerical instabilities associated with it.

79 ASTRONOMY AND ASTROPHYSICS↗

Mathematical and Numerical Aspects of the Adaptive Fast Multipole Poisson-Boltzmann Solver

This paper summarizes the mathematical and numerical theories and computational elements of the adaptive fast multipole Poisson-Boltzmann (AFMPB) solver. We introduce and discuss the following components in order: the Poisson-Boltzmann model, boundary integral equation reformulation, surface mesh generation, the nodepatch discretization approach, Krylov iterative methods, the new version of fast multipole methods (FMMs), and a dynamic prioritization technique for scheduling parallel operations. For each component, we also remark on feasible approaches for further improvements in efficiency, accuracy and applicability of the AFMPB solver to large-scale long-time molecular dynamics simulations. Lastly, the potential of the solver is demonstrated with preliminary numerical results.

97 MATHEMATICS AND COMPUTING↗

Shock and vibration response of multistage structure

Study of the shock and vibration response of a multistage structure employed analytically, lumped-mass, continuous-beam, multimode, and matrix-iteration methods. The study was made on the load paths, transmissibility, and attenuation properties along a longitudinal axis of a long, slender structure with increasing degree of complexity.

Lee, S. Y.↗

Inward pumping in mechanical face seals.

Hydrodynamic characteristics producing inward pumping in mechanical face seals, solving Reynolds equation for hydrodynamic lubrication with short-bearing approximation and numerical iterative methods

Findlay, J. A.↗

The potential calculation and some applications

Potential calculation from given source distribution, including direct and iterative methods, error analysis, convergence, computer programs and applications in plasma physics

Hockney, R. W.↗

Multiple zeros of polynomials

Analysis of four iterative methods for approximating zeros of polynomial expressions using digital computer

Wood, C. A.↗

Aerodynamic parameters of the Navion airplane extracted from flight

An iterative method, which is characterized as a maximum-likelihood minimum-variance technique, was used to extract the aerodynamic parameters of a Navion airplane from flight data. The purposes were to compare the results with parameters obtained from wind-tunnel tests and with results obtained by analog matching the same data, and to develop techniques for application of the parameter extraction program. Results from the study showed that the parameter-extraction program can produce aerodynamic parameters which will permit close estimation of the aircraft time histories used in the extraction process. The program determined an estimate of the standard deviations of the states and parameters. These estimates were used to indicate how well the calculated states fit the flight data and the confidence in the values of the estimated parameters. The study also showed that the values of the parameters were affected by the data and mathematical model used during the extraction process. Because of the lack of confidence in the parameters extracted by use of some of the sets of data, several parameters were estimated by other methods. By using a combination of methods, a set of parameters which gave a fit to the data was obtained.

Suit, W. T.↗

Iterative computation of generalized inverses, with an application to CMG steering laws

A cubically convergent iterative method for computing the generalized inverse of an arbitrary M X N matrix A is developed and a FORTRAN subroutine by which the method was implemented for real matrices on a CDC 3200 is given, with a numerical example to illustrate accuracy. Application to a redundant single-gimbal CMG assembly steering law is discussed.

Steincamp, J. W.↗

Differential correction schemes in nonlinear regression

Classical iterative methods in nonlinear regression are reviewed and improved upon. This is accomplished by discussion of the geometrical and theoretical motivation for introducing modifications using generalized matrix inversion. Examples having inherent pitfalls are presented and compared in terms of results obtained using classical and modified techniques. The modification is shown to be useful alone or in conjunction with other modifications appearing in the literature.

Decell, H. P., Jr.↗