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At least 775 records · Page 43

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DOE OSTI2023

Deterministic-Monte Carlo Hybrid Methods for Eigenvalue Sensitivity Coefficient Calculations

The TSUNAMI suite within the SCALE code package includes several methods for generating sensitivity data, including multigroup (MG) and continuous-energy (CE) capabilities. For generating sensitivities with CE data, three methods are available in SCALE 6.3.0: (1) the iterated fission probability (IFP) method with the KENO Monte Carlo transport solver, (2) IFP with the Shift Monte Carlo transport solver, and (3) the Contributon-Linked eigenvalue sensitivity/Uncertainty estimation via Tracklength importance Characterization (CLUTCH) with the KENO Monte Carlo transport solver. Currently, it is difficult to generate accurate sensitivities with large reflectors when using the CLUTCH method, specifically with fissionable and hydrogenous materials. To address this issue, the work presented herein examines a methodology to calculate the adjoint flux externally with the 3D deterministic SN transport code DENOVO in SCALE; the result is then read directly into the CLUTCH-TSUNAMI sequence. This hybridization method replaces the Monte Carlo F*(r) calculation in CLUTCH while still utilizing the forward calculation. The critical benchmark HEU-MET-FAST-028-001 is used to generate sensitivities based on the inability of CLUTCH to generate accurate sensitivities. Results from the hybrid method appear to generate sensitivity values that are in excellent agreement with direct perturbations. Although further testing is needed, the method provides promising results for the development and utility of a hybrid method for use in TSUNAMI.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Inversion of dynamical Bragg intensities to complex structure factors by iterated projections. For Ultramic. 2020. ("Pico" Festschrift, May 2021)

We discuss a method for recovering complex structure factors from many simultaneously excited Bragg beam intensities is described. The method is applied to simulated transmission electron diffraction data over a wide range of crystal thickness and beam energies. The method is based on iterated projections between structure and scattering matrices, which are related by a matrix unitary transformation, exponential, which we invert. The algorithm removes multiple-scattering perturbations from diffraction data and might be extended to other fields, including X-ray and neutron diffraction and cryo-electron microscopy. Because coherent multiple scattering involves interference between Bragg beams, the method also solves the phase problem. Unlike dynamical inversion from electron microscope images or ptychography data, the method, which starts with Bragg beam intensities, provides complex structure factors unaffected by focusing errors or resolution limitations imposed by lenses. We provide inversions from simulated data with 441 simultaneously excited Bragg beams over a range of thickness and beam energy. We discuss the retrieval of chirality information from enantiomorphs, the efficient incorporation of symmetry information using the irreducible representation of the group of structure matrices, and the effect of HOLZ lines to provide three-dimensional information.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1981

Converting a digital filter to its analog equivalent

Two complementary methods for conversion are direct conversion method and inverse of Tustin's method. Required accuracy of filter is achieved using best-matched technique. Both require only direct computations and are simpler and more efficient than conventional iterative systems or methods requiring "ad hoc" filter parameter adjustment.

Lee, J. F. L.↗

NASA NTRS1990

Improved evaluation of optical depth components from Langley plot data

A simple, iterative procedure to determine the optical depth components of the extinction optical depth measured by a solar radiometer is presented. Simulated data show that the iterative procedure improves the determination of the exponent of a Junge law particle size distribution. The determination of the optical depth due to aerosol scattering is improved as compared to a method which uses only two points from the extinction data. The iterative method was used to determine spectral optical depth components for June 11-13, 1988 during the MAC III experiment.

Biggar, S. F.↗

NASA NTRS1985

Variation in efficiency of parallel algorithms

The present study has the objective to investigate some iterative parallel-processor linear equation solving algorithms with respect to efficiency for analyses of typical linear engineering systems. Attention is given to a set of n linear equations, Ku = p, where K = an n x n positive definite, sparsely populated, symmetric matrix, u = an n x 1 vector of unknown responses, and p = an n x 1 vector of prescribed constants. This study is concerned with a hybrid method in which iteration is used to solve the problem, while a direct method is used on the local processor level. Variations in the efficiency of parallel algorithms are explored. Measures of the efficiency are based on computer experiments regarding the algorithms. For all the algorithms, the wall clock time is found to decrease as the number of processors increases.

Hayashi, A.↗

NASA NTRS1983

Restoration of multichannel microwave radiometric images

Chin, R. T.↗

NASA NTRS1988

Calculations of transonic flows with shocks using Newton's method and direct solver. II - Solution of Euler equations

Transonic flows with shocks are simulated using steady Euler equations and by simultaneously solving the resulting nonlinear algebraic equations using Newton's method. At each iteration, a direct solver computes the corrections and the process is repeated until convergence is achieved. The corrections and errors are reduced quadratically with the present method, allowing solutions of machine accuracy to be obtained in a few steps. Nonunique inviscid solutions and nonunique solutions of the Navier Stokes equations for quasi-one-dimensional flows in nozzles are presented. Calculations are also presented for steady two-dimensional inviscid flows around a cylinder in the transonic regime.

Hafez, M.↗

DOE OSTI2023

An Incremental Gradient Method for Optimization Problems With Variational Inequality Constraints

We consider minimizing a sum of agent-specific nondifferentiable merely convex functions over the solution set of a variational inequality (VI) problem in that each agent is associated with a local monotone mapping. This problem finds an application in computation of the best equilibrium in nonlinear complementarity problems arising in transportation networks. We develop an iteratively regularized incremental gradient method where at each iteration, agents communicate over a directed cycle graph to update their solution iterates using their local information about the objective and the mapping. The proposed method is single-timescale in the sense that it does not involve any excessive hard-to-project computation per iteration. We derive nonasymptotic agent-wise convergence rates for the suboptimality of the global objective function and infeasibility of the VI constraints measured by a suitably defined dual gap function. Finally, the proposed method appears to be the first fully iterative scheme equipped with iteration complexity that can address distributed optimization problems with VI constraints over cycle graphs.

convergence↗

NASA NTRS1976

Accelerated iterative calculation of transonic nacelle flowfields

A method is presented for the calculation of inviscid, supercritical flowfields about axisymmetric inlet cowls. A finite-difference calculation is performed in a simple, rectangular domain obtained from the nacelle geometry by a nearly-conformal mapping procedure. Type-dependent finite-differences are constructed using a coordinate-independent, 'rotated' differencing scheme. Methods of accelerating convergence of the iterative solution are demonstrated including a hybrid fast-Poisson-solver/relaxation scheme and an extrapolated relaxation procedure. Calculated pressure distributions are compared with experimental data for a variety of Mach numbers and mass-flow ratios, and show generally good agreement.

Caughey, D. A.↗

NASA NTRS1979

Numerical computation of aeroelastically corrected transonic loads

A numerical scheme is presented for the computation of transonic aerodynamic loads on flexible wings. The method consists of iteratively applying the loads computed by a 3D transonic aerodynamics code to a structural model to obtain elastic twist, and then recomputing the loads. Because this iteration is performed concurrently with the iterations performed in computing the aerodynamics, flexible loads are obtained in roughly the same amount of computing time as required to obtain rigid loads. Applications of this method to a flexible supercritical transonic transport wing are presented and compared with model test data.

Chipman, R.↗

NASA NTRS1985

Restoration of multichannel microwave radiometric images

A constrained iterative image restoration method is applied to multichannel diffraction-limited imagery. This method is based on the Gerchberg-Papoulis algorithm utilizing incomplete information and partial constraints. The procedure is described using the orthogonal projection operators which project onto two prescribed subspaces iteratively. Its properties and limitations are presented. The effect of noise was investigated and a better understanding of the performance of the algorithm with noisy data has been achieved. The restoration scheme with the selection of appropriate constraints was applied to a practical problem. The 6.6, 10.7, 18, and 21 GHz satellite images obtained by the scanning multichannel microwave radiometer (SMMR), each having different spatial resolution, were restored to a common, high resolution (that of the 37 GHz channels) to demonstrate the effectiveness of the method. Both simulated data and real data were used in this study. The restored multichannel images may be utilized to retrieve rainfall distributions.

Chin, R. T.↗

NASA NTRS1995

Pseudo-time methods for constrained optimization problems governed by PDE

In this paper we present a novel method for solving optimization problems governed by partial differential equations. Existing methods are gradient information in marching toward the minimum, where the constrained PDE is solved once (sometimes only approximately) per each optimization step. Such methods can be viewed as a marching techniques on the intersection of the state and costate hypersurfaces while improving the residuals of the design equations per each iteration. In contrast, the method presented here march on the design hypersurface and at each iteration improve the residuals of the state and costate equations. The new method is usually much less expensive per iteration step since, in most problems of practical interest, the design equation involves much less unknowns that that of either the state or costate equations. Convergence is shown using energy estimates for the evolution equations governing the iterative process. Numerical tests show that the new method allows the solution of the optimization problem in a cost of solving the analysis problems just a few times, independent of the number of design parameters. The method can be applied using single grid iterations as well as with multigrid solvers.

Taasan, Shlomo↗

NASA NTRS2007

Investigation of a Parabolic Iterative Solver for Three-dimensional Configurations

A parabolic iterative solution procedure is investigated that seeks to extend the parabolic approximation used within the internal propagation module of the duct noise propagation and radiation code CDUCT-LaRC. The governing convected Helmholtz equation is split into a set of coupled equations governing propagation in the positive and negative directions. The proposed method utilizes an iterative procedure to solve the coupled equations in an attempt to account for possible reflections from internal bifurcations, impedance discontinuities, and duct terminations. A geometry consistent with the NASA Langley Curved Duct Test Rig is considered and the effects of acoustic treatment and non-anechoic termination are included. Two numerical implementations are studied and preliminary results indicate that improved accuracy in predicted amplitude and phase can be obtained for modes at a cut-off ratio of 1.7. Further predictions for modes at a cut-off ratio of 1.1 show improvement in predicted phase at the expense of increased amplitude error. Possible methods of improvement are suggested based on analytic and numerical analysis. It is hoped that coupling the parabolic iterative approach with less efficient, high fidelity finite element approaches will ultimately provide the capability to perform efficient, higher fidelity acoustic calculations within complex 3-D geometries for impedance eduction and noise propagation and radiation predictions.

Nark, Douglas M.↗

NASA NTRS2001

HITEMP Material and Structural Optimization Technology Transfer

The feasibility of adding viscoelasticity and the Generalized Method of Cells (GMC) for micromechanical viscoelastic behavior into the commercial HyperSizer structural analysis and optimization code was investigated. The viscoelasticity methodology was developed in four steps. First, a simplified algorithm was devised to test the iterative time stepping method for simple one-dimensional multiple ply structures. Second, GMC code was made into a callable subroutine and incorporated into the one-dimensional code to test the accuracy and usability of the code. Third, the viscoelastic time-stepping and iterative scheme was incorporated into HyperSizer for homogeneous, isotropic viscoelastic materials. Finally, the GMC was included in a version of HyperSizer. MS Windows executable files implementing each of these steps is delivered with this report, as well as source code. The findings of this research are that both viscoelasticity and GMC are feasible and valuable additions to HyperSizer and that the door is open for more advanced nonlinear capability, such as viscoplasticity.

Collier, Craig S.↗

DOE OSTI2021

Cross Section Generation Capability in Griffin

The Griffin code is a Multiphysics Object-Oriented Simulation Environment (MOOSE) based reactor multiphysics analysis application jointly developed by Idaho National Laboratory and Argonne National Laboratory. The code includes a variety of steady-state solvers for fixed-source, k-eigenvalue, adjoint, and subcritical multiplication, as well as transient solvers for point-kinetics, improved quasi-static, and spatial dynamics. The code reads multigroup cross sections in the ISOXML format generated from external deterministic or Monte Carlo cross section generation codes. The implementation of the cross section generation capability in Griffin was initiated last year by plugging in the cross section application programming interface (CSAPI) and reviewing the methodologies for treating particulate fuels. The focus this year was on improving the CSAPI integration and implementing advanced self-shielding methods for applications to advanced reactor problems with TRISO fuels. First, the process for cross section library generation was updated to accurately and rigorously produce isotopic cross section data. Second, the on-the-fly slowing down method for the resonance treatment was implemented in CSAPI to improve the accuracy of effective multigroup cross sections in the resonance energy range. Among various on-the-fly slowing down methods, the equivalent Dancoff factor cell method was employed. Third, the iterative local spatial self-shielding method was implemented under the calculation framework of the equivalent Dancoff factor cell method to accurately deal with the double heterogeneity effect of particulate fuel. The updated CSAPI with the advanced self-shielding methods, together with the cross section libraries generated based on the improved process, were tested for the very high temperature reactor (VHTR), high temperature test reactor (HTTR), and Empire benchmark problems with various resonance self-shielding conditions, indicating that the updated CSAPI in Griffin is able to produce multigroup cross sections accurately and efficiently. We also show that the methodology works well for pebble bed fuel from HTR-10, but the capability still needs to be fully integrated into CSAPI. In the future, further benchmark tests will be performed for various thermal reactor core problems, including particulate fuel-based pebble bed reactors.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

Stochastic average model methods

We consider the solution of finite-sum minimization problems, such as those appearing in nonlinear least-squares or general empirical risk minimization problems. We are motivated by problems in which the summand functions are computationally expensive and evaluating all summands on every iteration of an optimization method may be undesirable. Here we present the idea of stochastic average model (SAM) methods, inspired by stochastic average gradient methods. SAM methods sample component functions on each iteration of a trust-region method according to a discrete probability distribution on component functions; the distribution is designed to minimize an upper bound on the variance of the resulting stochastic model. We present promising numerical results concerning an implemented variant extending the derivative-free model-based trust-region solver POUNDERS, which we name SAM-POUNDERS.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Introducing the SLICE Method for estimating pebble-bed reactor inventories at equilibrium operation with SCALE

This paper introduces the SCALE Leap-In method for Cores at Equilibrium (SLICE) for estimating pebble-bed reactor equilibrium core isotopic inventories using capabilities in the SCALE code system, requiring only a small computational cluster and a few days of computation. This method uses an iterative approach that relies on (1) a surrogate spectrum model that captures spatial and time-dependent spectral conditions, (2) a multi-pass model that captures the pebble’s evolving nuclide inventory as a function of location and time in the core, and (3) a full-core model that captures the core’s spatial neutron flux distribution. The SLICE approach is applied to a generic fluoride salt–cooled high-temperature reactor, demonstrating fuel inventory convergence through nuclide concentration inspection across iterations and comparisons for core realizations with varying discretizations. Results agree within ~5% with another state-of-the-art code, with differences attributed to input parameter or modeling assumption variations in the equilibrium generation methods.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2022

Impact of Increased Latent Generations on Sensitivity Calculations with SCALE

Analyses of cross section sensitivity data from systems with fissile material allow analysts to associate an importance for each material, nuclide, reaction, and neutron energy by simulating real world criticality scenarios. Although criticality safety validation efforts can be guided by the cross-section sensitivity and uncertainty data generated for a particular system, these calculations can often be computationally expensive and sometimes cumbersome without proper guidance. The TSUNAMI suite within the SCALE code package has several methods for generating sensitivity data, including multigroup and continuous energy (CE) capabilities. The release of SCALE 6.3 has three different CE methods for generating cross section sensitivity data: (1) the Iterated Fission Probability (IFP) method with the KENO Monte Carlo transport solver, (2) the IFP method with the Shift Monte Carlo transport solver, and (3) the Contributon-Linked eigenvalue sensitivity/Uncertainty estimation via Tracklength importance CHaracterization (CLUTCH) method with the KENO Monte Carlo transport solver. Although the CLUTCH method has additional parameters for generating sensitivity data files relative to the IFP method, all three methods use latent generations, which are the generations between an event (i.e., fission) and the assessment of importance based on the asymptotic population of progeny neutrons. Increasing the number of latent generations in a calculation leads to increased discrimination of the sensitivity coefficients but at the cost of the increased uncertainty associated with those generated values. Analysts must balance the accuracy of the sensitivity calculations and its uncertainty with the associated computational cost involved in generating the values. This paper discusses the impact of adjusting the latent generation parameter for a range of sensitivity values and how these changes compare with the direct perturbation values obtained from a change of ±0.5% Δ k in both benchmark and safety application models. Two benchmarks from the International Handbook of Evaluated Criticality Safety Benchmark Experiments and the MPC-32 dual purpose canister for spent nuclear fuel are used for analysis.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗