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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 883 records · Page 49
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Two-Level Transport Methods with Independent Discretization

In this proposal, we introduce two-level nonlinear iteration methods for the transport equation in 1D slab geometry approximated by means of the linear discontinuous finite element method (LDFEM). We develop transport schemes based on the quasidiffusion (QD) method in which the low-order QD (LOQD) equations are discretized by the linear continuous finite element method (LCFEM). This requires a mapping of the LCFEM low-order solution to the LDFEM high-order solution to define the scattering term. Several mappings are proposed and analyzed. Another suggested transport discretization scheme is based on the step characteristics for the transport equation and LCFEM for the LOQD equations. We also develop new nonlinear synthetic acceleration (NSA) methods based on the LCFEM discretization of the QD equation. To gain iterative stability, the NSA algorithms are combined with the nonlinear Krylov acceleration method. We present numerical results that demonstrate performance and basic properties of the proposed discretization schemes and iterative solution methods.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2017

A Continuous-Discontinuous Hybrid Finite Element Method for S{sub N} Transport

Particle transport phenomenon for neutral particles, such as neutrons and photons, is governed by the linear Boltzmann equation, which is a first-order partial differential equation (PDE). In order to solve the transport equation, discontinuous finite element method (DFEM) is heavily developed. However, the large memory consumption due to the extra degrees of freedom is problematic in multi-D calculations. Another path is to recast the transport equation to a second-order form, such as the well-known self-adjoint angular flux equation (SAAF) and the even parity equations, and spatially discretize the equation using continuous finite element method (CFEM). Yet, such forms generally have problems in void situation as the streaming operator contains a 1/σ{sub t} term and becomes singular in void, which draws numerous efforts on developing void-treatment methods. An intuition to mitigate the shortcomings of both methods is then to develop a method that utilizes DFEM in part of the problem where CFEM has issues while in the other part, CFEM is employed to avoid DFEM's high cost. In this work, we present a novel continuous-discontinuous finite element method (CDFEM) for solving the discrete-ordinates (S{sub N}) transport equations. We perform the hybridization between 1/σ{sub t}-weighted least-squares finite element methods (1/σ{sub t}-LSFEM), with continuous basis functions, and first-order solver. Different solvers are defined in different regions, or subdomains, of the problem. The resulting scheme is such that CFEM-SAAF is performed in subdomains with continuous basis functions while upwinding based DFEM solver is utilized in subdomains with discontinuous basis functions. The connection between subdomains is through an upwinding operation on the interface, which can be performed via the sweep procedure. A foreseeable benefit is such a scheme is compatible with void as first-order DFEM solver can be used in void. On the other hand, as DFEM is only used in part of the problem, CDFEM can effectively avoid the notorious memory consumption of DFEM in multi-D calculation for the future work.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

A mathematical assessment of the isolation random forest method for anomaly detection in big data

We present the mathematical analysis of the Isolation Random Forest Method (IRF Method) for anomaly detection, proposed by Liu F.T., Ting K.M. and Zhou Z. H. in their seminal work as a heuristic method for anomaly detection in Big Data. We prove that the IRF space can be endowed with a probability induced by the Isolation Tree algorithm (iTree). In this setting, the convergence of the IRF method is proved, using the Law of Large Numbers. Here, a couple of counterexamples are presented to show that the method is inconclusive and no certificate of quality can be given, when using it as a means to detect anomalies. Hence, an alternative version of the method is proposed whose mathematical foundation is fully justified. Furthermore, a criterion for choosing the number of sampled trees needed to guarantee confidence intervals of the numerical results is presented. Finally, numerical experiments are presented to compare the performance of the classic method with the proposed one.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Modern Monte Carlo methods for efficient uncertainty quantification and propagation: A survey

Uncertainty quantification (UQ) includes the characterization, integration, and propagation of uncertainties that result from stochastic variations and a lack of knowledge or data in the natural world. Monte Carlo (MC) method is a sampling-based approach that has widely used for quantification and propagation of uncertainties. However, the standard MC method is often time-consuming if the simulation-based model is computationally intensive. This article gives an overview of modern MC methods to address the existing challenges of the standard MC in the context of UQ. Specifically, multilevel Monte Carlo (MLMC) extending the concept of control variates achieves a significant reduction of the computational cost by performing most evaluations with low accuracy and corresponding low cost, and relatively few evaluations at high accuracy and corresponding high cost. Multifidelity Monte Carlo (MFMC) accelerates the convergence of standard Monte Carlo by generalizing the control variates with different models having varying fidelities and varying computational costs. Multimodel Monte Carlo method (MMMC), having a different setting of MLMC and MFMC, aims to address the issue of UQ and propagation when data for characterizing probability distributions are limited. Multimodel inference combined with importance sampling is proposed for quantifying and efficiently propagating the uncertainties resulting from small data sets. All of these three modern MC methods achieve a significant improvement of computational efficiency for probabilistic UQ, particularly uncertainty propagation. Finally, an algorithm summary and the corresponding code implementation are provided for each of the modern MC methods. The extension and application of these methods are discussed in detail.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Time-evolution methods for matrix-product states

Highlights: • Introductory review of time-evolution methods for matrix-product states. • Detailed description of five state-of-the-art algorithms. • Extended comparison of numerical examples. • Extended error analysis of each algorithm. • Pseudo-code examples towards an implementation where necessary. - Abstract: Matrix-product states have become the de facto standard for the representation of one-dimensional quantum many body states. During the last few years, numerous new methods have been introduced to evaluate the time evolution of a matrix-product state. Here, we will review and summarize the recent work on this topic as applied to finite quantum systems. We will explain and compare the different methods available to construct a time-evolved matrix-product state, namely the time-evolving block decimation, the MPO W{sup I,II} method, the global Krylov method, the local Krylov method and the one- and two-site time-dependent variational principle. We will also apply these methods to four different representative examples of current problem settings in condensed matter physics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Partitioned exponential methods for coupled multiphysics systems

Multiphysics problems involving two or more coupled physical phenomena are ubiquitous in science and engineering. This work develops a new partitioned exponential approach for the time integration of multiphysics problems. After a possible semi-discretization in space, the class of problems under consideration is modeled by a system of ordinary differential equations where the right-hand side is a summation of two component functions, each corresponding to a given set of physical processes. The partitioned-exponential methods proposed herein evolve each component of the system via an exponential integrator, and information between partitions is exchanged via coupling terms. Here, the traditional approach to constructing exponential methods, based on the variation-of-constants formula, is not directly applicable to partitioned systems. Rather, our approach to developing new partitioned-exponential families is based on a general-structure additive formulation of the schemes. Two method formulations are considered, one based on a linear-nonlinear splitting of the right hand component functions, and another based on approximate Jacobians. The paper develops classical (non-stiff) order conditions theory for partitioned exponential schemes based on particular families of T-trees and B-series theory. Several practical methods of third order are constructed that extend the Rosenbrock-type and EPIRK families of exponential integrators. Several implementation optimizations specific to the application of these methods to reaction-diffusion systems are also discussed. Numerical experiments reveal that the new partitioned-exponential methods can perform better than traditional unpartitioned exponential methods on some problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

A new method to compute periodic orbits in general symplectic maps

The search of high-order periodic orbits has been typically restricted to problems with symmetries that help to reduce the dimension of the search space. Well-known examples include reversible maps with symmetry lines. The present work proposes a new method to compute high-order periodic orbits in twist maps without the use of symmetries. The method is a combination of the parameterization method in Fourier space and a Newton–Gauss multiple shooting scheme. The parameterization method has been successfully used in the past to compute quasi-periodic invariant circles. However, this is the first time that this method is used in the context of periodic orbits. Numerical examples are presented showing the accuracy and efficiency of the proposed method. Furthermore, the method is also applied to verify the renormalization prediction of the residues’ convergence at criticality (extensively studied in reversible maps) in the relatively unexplored case of maps without symmetries.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2017

A moment projection method for population balance dynamics with a shrinkage term

A new method of moments for solving the population balance equation is developed and presented. The moment projection method (MPM) is numerically simple and easy to implement and attempts to address the challenge of particle shrinkage due to processes such as oxidation, evaporation or dissolution. It directly solves the moment transport equation for the moments and tracks the number of the smallest particles using the algorithm by Blumstein and Wheeler (1973) . The performance of the new method is measured against the method of moments (MOM) and the hybrid method of moments (HMOM). The results suggest that MPM performs much better than MOM and HMOM where shrinkage is dominant. The new method predicts mean quantities which are almost as accurate as a high-precision stochastic method calculated using the established direct simulation algorithm (DSA).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

A level-set immersed boundary method for reactive transport in complex topologies with moving interfaces

A simulation framework based on the level-set and the immersed boundary methods (LS-IBM) has been developed for reactive transport problems in porous media involving a moving solid-fluid interface. The interface movement due to surface reactions is tracked by the level-set method, while the immersed boundary method captures the momentum and mass transport at the interface. The proposed method is capable of accurately modeling transport near evolving boundaries in Cartesian grids. The framework formulation guarantees second order accuracy in space. Since the interface velocity is only defined at the moving boundary, an interface velocity propagation method is also proposed. The method can be applied to other moving interface problems of the “Stefan” type. Here, we validate the proposed LS-IBM both for flow and transport close to an immersed object with reactive boundaries as well as for crystal growth. Lastly, the proposed method provides a powerful tool to model more realistic problems involving moving reactive interfaces in complex domains.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Random Force Perturbations: A New Extension of the Cell Perturbation Method for Turbulence Generation in Multiscale Atmospheric Boundary Layer Simulations

Coupling between mesoscale and large eddy simulation (LES) is critically important for many atmospheric model applications, from predictions of wind energy to fire propagation. The grid-nesting technique enables bridging between vastly different scales without incurring prohibitive computational costs. Yet, the transition from coarser to finer resolutions often requires a large number of grid points from inflow boundaries for the development of fine-scale turbulence features in the LES domain. Recently, the cell perturbation method (CPM) was developed to reduce the turbulence development region with high computational efficiency. Herein, we explore a new method based on the CPM that uses force perturbations in both the horizontal and vertical directions (Force Cell Perturbation Method) instead of the potential temperature perturbations in the original CPM, as an attempt to further explore the performance of the random perturbation techniques. This method is tested for a neutral and a convective atmospheric boundary layer under idealized conditions. Overall, similar performance is found between the optimal configurations of the CPM and the Force Cell Perturbation Method pointing to the robustness of this family of perturbation methods in accelerating turbulence generation in nested domains. Vertical force perturbations performed better than horizontal force perturbations for both atmospheric stability conditions. The CPM performed best under convective stability conditions. The combination of the force and potential temperature perturbations is found to provide no additional performance improvement over the stand-alone application of the individual methods.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Self-consistent implementation of locally scaled self-interaction-correction method

Recently proposed local self-interaction correction (LSIC) method is a one-electron self-interaction-correction (SIC) method that uses an iso-orbital indicator to apply the SIC at each point in space by scaling the exchange–correlation and Coulomb energy densities. The LSIC method is exact for the one-electron densities, also recovers the uniform electron gas limit of the uncorrected density functional approximation, and reduces to the well-known Perdew–Zunger SIC (PZSIC) method as a special case. This article presents the self-consistent implementation of the LSIC method using the ratio of Weizsäcker and Kohn–Sham kinetic energy densities as an iso-orbital indicator. The atomic forces as well as the forces on the Fermi-Löwdin orbitals are also implemented for the LSIC energy functional. Results show that LSIC with the simplest local spin density functional predicts atomization energies of the AE6 dataset better than some of the most widely used generalized-gradient-approximation (GGA) functional and barrier heights of the BH6 database better than some of the most widely used hybrid functionals. The LSIC method [a mean absolute error (MAE) of 0.008 Å] predicts bond lengths of a small set of molecules better than the PZSIC-LSDA (MAE 0.042 Å) and LSDA (0.011 Å). Furthermore, this work shows that accurate results can be obtained from the simplest density functional by removing the self-interaction-errors using an appropriately designed SIC method.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Examination of Semi-Analytical Solution Methods in the Coarse Operator of Parareal Algorithm for Power System Simulation

With continuing advances in high-performance parallel computing platforms, parallel algorithms have become powerful tools for development of faster than real-time power system dynamic simulations. In particular, it has been demonstrated in recent years that parallel-in-time (Parareal) algorithms have the potential to achieve such an ambitious goal. Here, the selection of a fast and reasonably accurate coarse operator of the Parareal algorithm is crucial for its effective utilization and performance. This paper examines semi-analytical solution (SAS) methods as the coarse operators of the Parareal algorithm and explores performance of the SAS methods to the standard numerical time integration methods. Two promising time-power series-based SAS methods were considered; Adomian decomposition method and Homotopy analysis method with a windowing approach for improving the convergence. Numerical performance case studies on 10-generator 39-bus system and 327-generator 2383-bus system were performed for these coarse operators over different disturbances, evaluating the number of Parareal iterations, computational time, and stability of convergence. All the coarse operators tested with different scenarios have converged to the same corresponding true solution (if they are convergent) and the SAS methods provide comparable computational speed, while having more stable convergence to the true solution in many cases.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Nonlocal and Mixed-Locality Multiscale Finite Element Methods

In many applications the resolution of small-scale heterogeneities remains a significant hurdle to robust and reliable predictive simulations. In particular, while material variability at the mesoscale plays a fundamental role in processes such as material failure, the resolution required to capture mechanisms at this scale is often computationally intractable. Multiscale methods aim to overcome this difficulty through judicious choice of a subscale problem and a robust manner of passing information between scales. One promising approach is the multiscale finite element method, which increases the fidelity of macroscale simulations by solving lower-scale problems that produce enriched multiscale basis functions. Here, in this study, we present the first work toward application of the multiscale finite element method to the nonlocal peridynamic theory of solid mechanics. This is achieved within the context of a discontinuous Galerkin framework that facilitates the description of material discontinuities and does not assume the existence of spatial derivatives. Analysis of the resulting nonlocal multiscale finite element method is achieved using the ambulant Galerkin method, developed here with sufficient generality to allow for application to multiscale finite element methods for both local and nonlocal models that satisfy minimal assumptions. Finally, we conclude with preliminary results on a mixed-locality multiscale finite element method in which a nonlocal model is applied at the fine scale and a local model at the coarse scale.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Application of Electrochemical Methods to Molten Salt Reactors: Draft TLR Documenting Assessment of Electrochemical Monitoring

Nuclear Regulatory Commission (NRC) is developing the regulatory framework and technical expertise to support regulatory review of advanced non-water reactors, including molten salt reactors (MSRs). In an MSR, it is essential that the salt chemistry be maintained in a desired range in terms of redox potential for reliable operation and mitigation of corrosion to structural materials in the reactor, particularly the reactor vessel and heater exchanger. Measuring the redox potential of the salt in the reactor would also allow for the material lifetimes to be predicted more accurately, and chemical issues to be diagnosed more quickly. In addition to the chemical composition analysis by ICP-MS, electrochemical methods including potentiometry and linear wave scanning (LSC) were also used in molten salt reactor experiment (MSRE) for redox potential monitoring purposes. Electrochemcial methods offers unique advantages such as quick turnaround in results and unique capability of in-line monitoring of redox potential, and are considered popular electroanalytical techniques that can be used to monitor redox potentials and salt chemistry including impurities. The last two decades have seen significant advances in science and engineering of electrochemical methods for potential application to molten salts. The primary goal of this report is to assist NRC in understanding the monitoring of the salt chemistry by electrochemical methods and provide NRC reviewers with necessary information and tools to support regulatory review of MSR designs. This reports consists of two majors parts—Part 1, chemical potential of molten salts and effects by fission process in MSR; Part 2, assessment of electrochemical methods for application to MSRs. The TRLs of the typical relevant electrochemical methods for molten salts were evaluated based on the DOE TRL guidelines and upon a review of the current status of the electrochemical methods for two typical salt systems, fluoride and chloride, for MSRs.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Different methods of estimating riverbed sediment grain size diverge at the basin scale

Introduction: The distribution of sediment grain size in streams and rivers is often quantified by the median grain size (D50), a key metric for understanding and predicting hydrologic and biogeochemical function of streams and rivers. Manual D50 measurements are time-consuming and ignore larger grains, while approaches to model D50 based on catchment characteristics may over-generalize and miss site-scale heterogeneity. Machine learning-enabled object detection methods like You Only Look Once (YOLO) provides an alternative that enables estimation of D50 that is faster than manual measurements and more site-specific than predictions based on catchment characteristics. Methods: To understand the potential role of object detection methods for improving understanding of D50, we compared D50 estimates made manually, predicted from catchment characteristics, and using a YOLO-enabled approach across the Yakima River Basin. Results: We found distinct differences between methods for D50 averages and variability, and relationships between D50 estimates and basin characteristics. Discussion: We discuss the advantages and limitations of object detection methods versus current methods, and explore potential future directions to combine D50 methods to better estimate spatiotemporal variation of D50, and improve incorporation into basin-scale models.

grain size distribution↗
DOE OSTI2020

Subspace Methods in Multi-Parameter Seismic Full Waveform Inversion

In full waveform inversion (FWI) high-resolution subsurface model parameters are sought. FWI is normally treated as a nonlinear least-squares inverse problem, in which the minimum of the corresponding misfit function is found by updating the model parameters. When multiple elastic or acoustic properties are solved for, simple gradient methods tend to confuse parameter classes. This is referred to as parameter cross-talk; it leads to incorrect model solutions, poor convergence and strong dependence on the scaling of the different parameter types. Determining step lengths in a subspace domain, rather than directly in terms of gradients of different parameters, is a potentially valuable approach to address this problem. The particular subspace used can be defined over a span of different sets of data or different parameter classes, provided it involves a small number of vectors compared to those contained in the whole model space. Additionally, in a subspace method, the basis vectors are defined first, and a local minimum is found in the space spanned by these. We examine the application of the subspace method within acoustic FWI in determining simultaneously updates for velocity and density. We first discuss the choice of basis vectors to construct the spanned space, from linear updates by distinguishing only the contributions of different parameter classes towards nonlinear updates by adding the contributions of higher-order perturbations of each parameter class. The numerical character of FWI solutions generated via subspace methods involving different basis vectors is then analyzed and compared with traditional FWI methods. The subspace methods can provide better reconstructions of the model, especially for the velocity, as well as improved convergence rates, while the computational costs are still comparable with the traditional FWI methods.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Hyperspectral Image Classification Using Graph Clustering Methods

Hyperspectral imagery is a challenging modality due to the dimension of the pixels which can range from hundreds to over a thousand frequencies depending on the sensor. Most methods in the literature reduce the dimension of the data using a method such as principal component analysis, however this procedure can lose information. More recently methods have been developed to address classification of large datasets in high dimensions. This paper presents two classes of graph-based classification methods for hyperspectral imagery. Using the full dimensionality of the data, we consider a similarity graph based on pairwise comparisons of pixels. The graph is segmented using a pseudospectral algorithm for graph clustering that requires information about the eigenfunctions of the graph Laplacian but does not require computation of the full graph. We develop a parallel version of the Nyström extension method to randomly sample the graph to construct a low rank approximation of the graph Laplacian. With at most a few hundred eigenfunctions, we can implement the clustering method designed to solve a variational problem for a graph-cut-based semi-supervised or unsupervised classification problem. We implement OpenMP directive-based parallelism in our algorithms and show performance improvement and strong, almost ideal, scaling behavior. The method can handle very large datasets including a video sequence with over a million pixels, and the problem of segmenting a data set into a pre-determined number of classes.

47 OTHER INSTRUMENTATION↗
NASA NTRSDate not supplied

Discontinuous Galerkin and Related Methods for ODE

A defining feature of the discontinuous Galerkin (DG) method for ODE is that the piecewise polynomial solution can have a jump discontinuity at the beginning of each step. Starting from the standard integral formulation, the DG method is derived here in differential form. The key ingredient is a polynomial called the correction function, which helps ‘correct’ the discontinuous solution by approximating the jump and yields a continuous one. Under the right Radau quadrature, this continuous solution is identical to the solutions by the right Radau collocation and the continuous Galerkin (CG) methods. Next, the correction function facilitates the construction of the associated implicit Runge-Kutta schemes (IRK-DG). Different quadratures for DG result in different IRK-DG methods: left Radau quadrature in Radau IA, right Radau quadrature in Radau IIA or right Radau collocation, and Gauss quadrature in a method called DG-Gauss. The construction of IRK-DG clarifies the meaning and facilitates the proofs of various 𝐵(𝑝), 𝐶(𝜂), and 𝐷(𝜁) conditions for accuracy. The two consequences of these conditions are that all 𝑠-stage IRK-DG methods are accurate to order 2𝑠 − 1, and the IRK-DG methods of Radau type are unique. Numerical examples showing the behavior of the DG solutions are provided. In all, the correction function plays a key role and helps establish the relations among the DG, IRK-DG, collocation, and CG schemes.

numerical methods↗