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NASA NTRS1992

Improved method for solving the viscous shock layer equations

An improved method for solving the viscous shock layer equations for supersonic/hypersonic flows past blunt-nosed bodies is presented. The method is capable of handling slender to thick bodies. The solution is obtained by solving a coupled set of five equations, built of the four basic viscous shock layer equations and an additional equation for the standoff distance. The coupling of the equations prevents the local iterations divergence problems encountered by previous methods of solution far downstream on slender bodies. It also eliminates the need for local iterations, which were required by previous methods of solution, for a first-order scheme in the streamwise direction. A new global iteration procedure is employed to impose the shock boundary conditions. The procedure prevents the global iteration instability encountered by the basic method of solution and improves the convergence rate of the global iteration procedure of later methods devised to overcome this difficulty. The new technique reduces the computation time by 65-95 percent as compared to previous methods of solution. The method can efficiently be implemented in vector/parallel computers.

Gordon, Rachel↗
DOE OSTI2016

A FLEXIBLE NONLINEAR DIFFUSION ACCELERATION METHOD FOR THE FIRST ORDER EIGENVALUE SN EQUATIONS DISCRETIZED WITH DISCONTINUOUS FEM

This work describes a Nonlinear Diffusion Acceleration (NDA) method for the first order SN equations that discretizes both the transport equation and the associated diffusion system using discontinuous finite elements; the diffusion system is solved on a potentially coarser mesh and with a coarser energy group structure than the SN equations. The developed method differs from current methods by allowing the SN and diffusion system to be discretized with arbitrary FEM bases and by using an additive update of the SN system. The benefit of this capability is extension of the stability region to optically thicker mesh cells and stability without the necessity to underrelax the iterative algorithm. The presented method introduces the notion of consistency of the SN and diffusion solutions and derives suitable definitions of the cross sections, drift vectors, and element face closures. The NDA equations are solved using a Picard iteration scheme. Numerical results are presented for the C5G7 benchmark problem highlighting the effectiveness of the methods when deployed with the diffusion system discretized on the same mesh as the SN system. Additional results are presented for cases where the diffusion system features a coarser mesh, coarser energy group structure, or both, demonstrating its stability and effectiveness in these cases. It is observed that the effectiveness of the NDA method reduces when reducing the resolution of the associated diffusion system.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Implementation of Material and Geometry Criticality Search in RMC Code

RMC is a continuous-energy Reactor Monte Carlo neutron and photon transport code being developed by Department of Engineering Physics at Tsinghua University, Beijing. For the use of simulation of reactor control or design of reactor with unknown material and geometry parameters, an accurate and efficient method of eigenvalue search is implemented in RMC code. The eigenvalue search focuses on two types of parameters. One is nuclide atom density, called material search, which includes the fuel density, enrichment or boron concentration. Perturbation theory of Monte Carlo Code, like differential operator method and adjoint-weighted perturbation method has been widely researched in sensitivity and uncertainty study. For material search, the perturbation algorithm needs to coupled with flexible material control block and optimized strategy. The other type of parameter is surface position, called geometry search, which includes fuel rod diameter, pitch and control rod position. MC21 iterated on surface position based on bisection method or regula-falsi method, and directly recalculated k-eff until it converged to target error interval. In this paper, the differential operator method, improved Newton-Raphson method is introduced. Based on these methods, the global material search is implemented. Then based on material search and finite method, global geometry search is implement. Finally, fuel enrichment, boron concentration and control rod position in normal PWR assembly are searched. The results show that RMC can search material and geometry parameters accurately and efficiently. In this paper, global eigenvalue search of material and geometry parameters have been implemented in RMC code. They are based on the differential operator method in Monte Carlo perturbation theory. The differential operator method samples δk/δρ{sub r}, δ{sup 2}k/δρ{sub r}{sup 2} along with k-eff estimator. Therefore it won't take up too much additional computational resource. For homogeneous material search, fission source effect has little effect of accuracy and can be ignored. The results of fuel enrichment and boron concentration searches in assembly show that improved Newton-Raphson method can iterate efficiently until k-eff is in the error interval. Based on material search and finite difference formula, the geometry parameter, like control rod axial position, can iterate until k-eff is in the error interval. However, the tiny perturbed region may not contain enough tracks to simulate. Besides, the large number density's relative change up to -1 may cause underestimation of Δk-eff, and then slope of k-x curve. This will cause non-convergence for Newton- Raphson method. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Uniform-in-phase-space data selection with iterative normalizing flows

Improvements in computational and experimental capabilities are rapidly increasing the amount of scientific data that are routinely generated. In applications that are constrained by memory and computational intensity, excessively large datasets may hinder scientific discovery, making data reduction a critical component of data-driven methods. Datasets are growing in two directions: the number of data points and their dimensionality. Whereas dimension reduction typically aims at describing each data sample on lower-dimensional space, the focus here is on reducing the number of data points. A strategy is proposed to select data points such that they uniformly span the phase-space of the data. The algorithm proposed relies on estimating the probability map of the data and using it to construct an acceptance probability. An iterative method is used to accurately estimate the probability of the rare data points when only a small subset of the dataset is used to construct the probability map. Instead of binning the phase-space to estimate the probability map, its functional form is approximated with a normalizing flow. Therefore, the method naturally extends to high-dimensional datasets. The proposed framework is demonstrated as a viable pathway to enable data-efficient machine learning when abundant data are available.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1989

Stress analysis method for clearance-fit joints with bearing-bypass loads

Within a multi-fastener joint, fastener holes may be subjected to the combined effects of bearing loads and loads that bypass the hole to be reacted elsewhere in the joint. The analysis of a joint subjected to search combined bearing and bypass loads is complicated by the usual clearance between the hole and the fastener. A simple analysis method for such clearance-fit joints subjected to bearing-bypass loading has been developed in the present study. It uses an inverse formulation with a linear elastic finite-element analysis. Conditions along the bolt-hole contact arc are specified by displacement constraint equations. The present method is simple to apply and can be implemented with most general purpose finite-element programs since it does not use complicated iterative-incremental procedures. The method was used to study the effects of bearing-bypass loading on bolt-hole contact angles and local stresses. In this study, a rigid, frictionless bolt was used with a plate having the properties of a quasi-isotropic graphite/epoxy laminate. Results showed that the contact angle as well as the peak stresses around the hole and their locations were strongly influenced by the ratio of bearing and bypass loads. For single contact, tension and compression bearing-bypass loading had opposite effects on the contact angle. For some compressive bearing-bypass loads, the hole tended to close on the fastener leading to dual contact. It was shown that dual contact reduces the stress concentration at the fastener and would, therefore, increase joint strength in compression. The results illustrate the general importance of accounting for bolt-hole clearance and contact to accurately compute local bolt-hole stresses for combined bearings and bypass loading.

Naik, R. A.↗
DOE OSTI2013

Breast density quantification using magnetic resonance imaging (MRI) with bias field correction: A postmortem study

Purpose: Quantification of breast density based on three-dimensional breast MRI may provide useful information for the early detection of breast cancer. However, the field inhomogeneity can severely challenge the computerized image segmentation process. In this work, the effect of the bias field in breast density quantification has been investigated with a postmortem study. Methods: T1-weighted images of 20 pairs of postmortem breasts were acquired on a 1.5 T breast MRI scanner. Two computer-assisted algorithms were used to quantify the volumetric breast density. First, standard fuzzy c-means (FCM) clustering was used on raw images with the bias field present. Then, the coherent local intensity clustering (CLIC) method estimated and corrected the bias field during the iterative tissue segmentation process. Finally, FCM clustering was performed on the bias-field-corrected images produced by CLIC method. The left–right correlation for breasts in the same pair was studied for both segmentation algorithms to evaluate the precision of the tissue classification. Finally, the breast densities measured with the three methods were compared to the gold standard tissue compositions obtained from chemical analysis. The linear correlation coefficient, Pearson'sr, was used to evaluate the two image segmentation algorithms and the effect of bias field. Results: The CLIC method successfully corrected the intensity inhomogeneity induced by the bias field. In left–right comparisons, the CLIC method significantly improved the slope and the correlation coefficient of the linear fitting for the glandular volume estimation. The left–right breast density correlation was also increased from 0.93 to 0.98. When compared with the percent fibroglandular volume (%FGV) from chemical analysis, results after bias field correction from both the CLIC the FCM algorithms showed improved linear correlation. As a result, the Pearson'sr increased from 0.86 to 0.92 with the bias field correction. Conclusions: The investigated CLIC method significantly increased the precision and accuracy of breast density quantification using breast MRI images by effectively correcting the bias field. It is expected that a fully automated computerized algorithm for breast density quantification may have great potential in clinical MRI applications.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
NASA NTRS2018

Regression Analysis and Calibration Recommendations for the Characterization of Balance Temperature Effects

Analysis and use of temperature-dependent wind tunnel strain-gage balance calibration data are discussed in the paper. First, three different methods are presented and compared that may be used to process temperature-dependent strain-gage balance data. The first method uses an extended set of independent variables in order to process the data and predict balance loads. The second method applies an extended load iteration equation during the analysis of balance calibration data. The third method uses temperature-dependent sensitivities for the data analysis. Physical interpretations of the most important temperature-dependent regression model terms are provided that relate temperature compensation imperfections and the temperature-dependent nature of the gage factor to sets of regression model terms. Finally, balance calibration recommendations are listed so that temperature-dependent calibration data can be obtained and successfully processed using the reviewed analysis methods.

wind tunnel test↗
DOE OSTI2022

Improvements to the Griffin Transport Solvers

Griffin 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. This document summarizes the transport solver development efforts pursued during Fiscal Year 2022. We added the multiphysics transient capability for the coarse-mesh finite difference accelerated Richardson iteration for discontinuous finite element method discrete ordinates (DFEM-SN) scheme to support high-order heterogeneous transport simulations. HFEM (hybrid finite element method) - PN (spherical harmonics expansion) was completed and red-black iteration was added for solving the HFEM-PN system with both preconditioned Jacobian-free Newton Krylov and Richardson iteration solvers. The HFEM-PN scheme, as one of the low-order transport schemes, is expected for supporting routine design simulations. Pin power reconstruction capability was also designed and implemented with the Griffin ISOXML module to enhance all the low-order transport solvers for more accurate multiphysics simulations. Numerical results are presented for demonstrating the capabilities and verifying their performance, and future works are discussed.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2016

A Numerical Theory for Impedance Education in Three-Dimensional Normal Incidence Tubes

A method for educing the locally-reacting acoustic impedance of a test sample mounted in a 3-D normal incidence impedance tube is presented and validated. The unique feature of the method is that the excitation frequency (or duct geometry) may be such that high-order duct modes may exist. The method educes the impedance, iteratively, by minimizing an objective function consisting of the difference between the measured and numerically computed acoustic pressure at preselected measurement points in the duct. The method is validated on planar and high-order mode sources with data synthesized from exact mode theory. These data are then subjected to random jitter to simulate the effects of measurement uncertainties on the educed impedance spectrum. The primary conclusions of the study are 1) Without random jitter the method is in excellent agreement with that for known impedance samples, and 2) Random jitter that is compatible to that found in a typical experiment has minimal impact on the accuracy of the educed impedance.

Watson, Willie R.↗
DOE OSTI2013

The spectral green's function nodal method for multigroup slab-geometry fixed-source S{sub N} problems with anisotropic scattering

A generalization of the spectral Green's function (SGF) method is developed for multigroup, fixed-source, slab-geometry discrete ordinates (S{sub N}) problems with anisotropic scattering. The offered SGF method with the one-node block inversion (NBI) iterative scheme converges numerical solutions that are completely free from spatial truncation errors for multigroup slab-geometry S{sub N} problems with scattering anisotropy of order L, provided L < N. As a coarse-mesh numerical method, the SGF method generates numerical solutions that generally do not give detailed information on the problem solution profile, as the grid points can be located considerably away from each other. Therefore, presented here is a technique for the spatial reconstruction of the coarse-mesh solution generated by the multigroup SGF method. Numerical results are given to illustrate the method's accuracy. (authors)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

Optimal control with accelerated convergence: Combining the Krotov and quasi-Newton methods

One of the most popular methods for solving numerical optimal control problems is the Krotov method, adapted for quantum control by Tannor and coworkers. The Krotov method has the following three appealing properties: (1) monotonic increase of the objective with iteration number, (2) no requirement for a line search, leading to a significant savings over gradient (first-order) methods, and (3) macrosteps at each iteration, resulting in significantly faster growth of the objective at early iterations than in gradient methods where small steps are required. The principal drawback of the Krotov method is slow convergence at later iterations, which is particularly problematic when high fidelity is desired. We show here that, near convergence, the Krotov method degenerates to a first-order gradient method. We then present a variation on the Krotov method that has all the advantages of the original Krotov method but with significantly enhanced convergence (second-order or quasi-Newton) as the optimal solution is approached. We illustrate the method by controlling the three-dimensional dynamics of the valence electron in the Na atom.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Establishing Outcrop Time Series at Various Depths in a Nonlinear Soil Column: An Iterative Approach

Seismic soil-structure interaction (SSI) analysis of nuclear facilities is an important consideration during design and retrofit. SSI tools used in the nuclear industry are currently based on an equivalent linear approach. Procedures for developing input ground motion for equivalent linear approaches are well established. However, the procedures for establishing input ground motion for Nonlinear Soil-Structure Interaction (NLSSI) analysis of nuclear facilities is not well established. A collaborative research group at Idaho National Laboratory (INL) has recently developed analytical methods and numerical tools for using NLSSI analysis for nuclear facility seismic calculations. NLSSI analysis for a nuclear facility allows for calculation of seismic wave motion through a near field soil domain using either, (1) vertically propagating shear and compressive waves, which is the current industry practice, or (2) a three-dimensional non-vertical wave field. This paper presents an iterative procedure for establishing outcrop motion at a depth in the soil column for NLSSI analysis that uses vertically propagating shear waves. The approach presented in this paper starts with a known ground motion at the surface, deconvolves to a depth, and then convolves the obtained motion up to a different desired location of input for the NLSSI model. To demonstrate the validity of the approach a finite element soil column, that is representative of a nuclear facility site in the US, is used to produce compatible outcrop seismic time series for reduced nonlinear soil mesh depths. The developed approach for reducing the nonlinear soil column model depth is a two-step iterative method; 1) the first step is establishing an outcrop time series at the lowest depth considered that produces the top-of-soil response spectrum of an actual recorded ground motion, and 2) the second step is providing compatible outcrop time series at a shallower depth based on the information from the first step. The comparison of the 5% damped response spectrum from the resulting acceleration time series based on the iterated outcrop motions and the original acceleration time series are conducted. The study showed that the proposed iterative approach produced comparable results within 1% range of the original recorded time series results when sufficient iterations were performed.

58 GEOSCIENCES↗
DOE OSTI2019

An Efficient Parallel-in-Time Method for Optimization with Parabolic PDEs

To solve optimization problems with parabolic PDE constraints, often methods working on the reduced objective functional are used. They are computationally expensive due to the necessity of solving both the state equation and a backward-in-time adjoint equation to evaluate the reduced gradient in each iteration of the optimization method. In this study, we investigate the use of the parallel-in-time method PFASST in the setting of PDE-constrained optimization. In order to develop an efficient fully time-parallel algorithm, we discuss different options for applying PFASST to adjoint gradient computation, including the possibility of doing PFASST iterations on both the state and the adjoint equations simultaneously. Here, we also explore the additional gains in efficiency from reusing information from previous optimization iterations when solving each equation. Numerical results for both a linear and a nonlinear reaction-diffusion optimal control problem demonstrate the parallel speedup and efficiency of different approaches.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Electrostatics of proteins in dielectric solvent continua. II. Hamiltonian reaction field dynamics

In Paper I of this work [S. Bauer, G. Mathias, and P. Tavan, J. Chem. Phys. 140, 104102 (2014)] we have presented a reaction field (RF) method, which accurately solves the Poisson equation for proteins embedded in dielectric solvent continua at a computational effort comparable to that of polarizable molecular mechanics (MM) force fields. Building upon these results, here we suggest a method for linearly scaling Hamiltonian RF/MM molecular dynamics (MD) simulations, which we call “Hamiltonian dielectric solvent” (HADES). First, we derive analytical expressions for the RF forces acting on the solute atoms. These forces properly account for all those conditions, which have to be self-consistently fulfilled by RF quantities introduced in Paper I. Next we provide details on the implementation, i.e., we show how our RF approach is combined with a fast multipole method and how the self-consistency iterations are accelerated by the use of the so-called direct inversion in the iterative subspace. Finally we demonstrate that the method and its implementation enable Hamiltonian, i.e., energy and momentum conserving HADES-MD, and compare in a sample application on Ac-Ala-NHMe the HADES-MD free energy landscape at 300 K with that obtained in Paper I by scanning of configurations and with one obtained from an explicit solvent simulation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Optimal Run Strategies in Monte Carlo Iterated Fission Source Simulations

The method of successive generations used in Monte Carlo simulations of nuclear reactor models is known to suffer from intergenerational correlation between the spatial locations of fission sites. One consequence of the spatial correlation is that the convergence rate of the variance of the mean for a tally becomes worse than O(N–1). In this work, we consider how the true variance can be minimized given a total amount of work available as a function of the number of source particles per generation, the number of active/discarded generations, and the number of independent simulations. We demonstrate through both analysis and simulation that under certain conditions the solution time for highly correlated reactor problems may be significantly reduced either by running an ensemble of multiple independent simulations or simply by increasing the generation size to the extent that it is practical. However, if too many simulations or too large a generation size is used, the large fraction of source particles discarded can result in an increase in variance. We also show that there is a strong incentive to reduce the number of generations discarded through some source convergence acceleration technique. Furthermore, we discuss the efficient execution of large simulations on a parallel computer; we argue that several practical considerations favor using an ensemble of independent simulations over a single simulation with very large generation size.

correlation↗
NASA NTRS1992

Mesh generation/refinement using fractal concepts and iterated function systems

A novel method of mesh generation is proposed which is based on the use of fractal concepts to derive contractive, affine transformations. The transformations are constructed in such a manner that the attractors of the resulting maps are a union of the points, lines and surfaces in the domain. In particular, the mesh nodes may be generated recursively as a sequence of points which are obtained by applying the transformations to a coarse background mesh constructed from the given boundary data. A Delaunay triangulation or similar edge connection approach can then be performed on the resulting set of nodes in order to generate the mesh. Local refinement of an existing mesh can also be performed using the procedure. The method is easily extended to three dimensions, in which case the Delaunay triangulation is replaced by an analogous 3D tesselation.

Bova, S. W.↗
DOE OSTI2016

C–IBI: Targeting cumulative coordination within an iterative protocol to derive coarse-grained models of (multi-component) complex fluids

We present a coarse-graining strategy that we test for aqueous mixtures. The method uses pair-wise cumulative coordination as a target function within an iterative Boltzmann inversion (IBI) like protocol. We name this method coordination iterative Boltzmann inversion (C–IBI). While the underlying coarse-grained model is still structure based and, thus, preserves pair-wise solution structure, our method also reproduces solvation thermodynamics of binary and/or ternary mixtures. In addition, we observe much faster convergence within C–IBI compared to IBI. To validate the robustness, we apply C–IBI to study test cases of solvation thermodynamics of aqueous urea and a triglycine solvation in aqueous urea.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2017

Projected Commutator DIIS Method for Accelerating Hybrid Functional Electronic Structure Calculations

The commutator direct inversion of the iterative subspace (commutator DIIS or C-DIIS) method developed by Pulay is an efficient and the most widely used scheme in quantum chemistry to accelerate the convergence of self-consistent field (SCF) iterations in Hartree–Fock theory and Kohn–Sham density functional theory. The C-DIIS method requires the explicit storage of the density matrix, the Fock matrix, and the commutator matrix. Hence, the method can only be used for systems with a relatively small basis set, such as the Gaussian basis set. We develop a new method that enables the C-DIIS method to be efficiently employed in electronic structure calculations with a large basis set such as planewaves for the first time. The key ingredient is the projection of both the density matrix and the commutator matrix to an auxiliary matrix called the gauge-fixing matrix. The resulting projected commutator-DIIS method (PC-DIIS) only operates on matrices of the same dimension as that consists of Kohn–Sham orbitals. The cost of the method is comparable to that of standard charge mixing schemes used in large basis set calculations. The PC-DIIS method is gauge-invariant, which guarantees that its performance is invariant with respect to any unitary transformation of the Kohn–Sham orbitals. We demonstrate that the PC-DIIS method can be viewed as an extension of an iterative eigensolver for nonlinear problems. We use the PC-DIIS method for accelerating Kohn–Sham density functional theory calculations with hybrid exchange–correlation functionals, and demonstrate its superior performance compared to the commonly used nested two-level SCF iteration procedure. Furthermore, we demonstrate that in the context of ab initio molecular dynamics (MD) simulation with hybrid functionals one can extrapolate the gauge-fixing matrix to achieve the goal of extrapolating the entire density matrix implicitly along the MD trajectory. Here, numerical results indicate that the new method significantly reduces the number of SCF iterations per MD step, compared to the commonly used strategy of extrapolating the electron density.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗