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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 1,477 records · Page 82
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DOE OSTI2018

The fully nonconforming virtual element method for biharmonic problems

Here in this paper, we address the numerical approximation of linear fourth-order elliptic problems on polygonal meshes. In particular, we present a novel nonconforming virtual element discretization of arbitrary order of accuracy for biharmonic problems. The approximation space is made of possibly discontinuous functions, thus giving rise to the fully nonconforming virtual element method. We derive optimal error estimates in a suitable (broken) energy norm and present numerical results to assess the validity of the theoretical estimates.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Improvements in the orbitalwise scaling down of Perdew–Zunger self-interaction correction in many-electron regions

The Perdew-Zunger (PZ) method offers a way to remove the self-interaction (SI) error from density functional approximations on an orbital by orbital basis. The PZ method provides significant improvements for the properties such as barrier heights or dissociation energies but results in over-correcting the properties well described by SI-uncorrected semi-local functional. One cure to rectify the over-correcting tendency is to scale down the magnitude of SI-correction of each orbital in the many electron region. We have implemented the orbitalwise scaled down SI-correction (OSIC) scheme of Vydrov et al. [J. Chem. Phys. 124, 094108 (2006)] using the Fermi-L owdin SI-correction method. After validating the OSIC implementation with previously reported OSICLSDA results, we examine its performance with the most successful non-empirical SCAN meta-GGA functional. Using different forms of scaling factors to identify one-electron regions, we assess the performance of OSIC-SCAN for a wide range of properties: total energies, ionization potentials and electron affinities for atoms, atomization energies, dissociation and reaction energies, and reaction barrier heights of molecules. Our results show that OSIC-SCAN provides superior results than the previously reported OSIC-LSDA, -PBE, and -TPSS results. Furthermore, we propose selective scaling of OSIC (SOSIC) to remove its major shortcoming that destroys the -1/r asymptotic behavior of the potentials. The SOSIC method gives the highest occupied orbital eigenvalues practically identical to those in PZSIC and unlike OSIC provides bound atomic anions even with larger powers of scaling factors. Furthermore, SOSIC compared to PZSIC or OSIC provides more balanced description of total energies and barrier heights.

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

Neural-adjoint method for the inverse design of all-dielectric metasurfaces

All-dielectric metasurfaces exhibit exotic electromagnetic responses, similar to those obtained with metal-based metamaterials. Research in all-dielectric metasurfaces currently uses relatively simple unit-cell designs, but increased geometrical complexity may yield even greater scattering states. Although machine learning has recently been applied to the design of metasurfaces with impressive results, the much more challenging task of finding a geometry that yields a desired spectra remains largely unsolved. We propose and demonstrate a method capable of finding accurate solutions to ill-posed inverse problems, where the conditions of existence and uniqueness are violated. A specific example of finding the metasurface geometry which yields a radiant exitance matching the external quantum efficiency of gallium antimonide is demonstrated. We also show how the neural-adjoint method can intelligently grow the design search space to include designs that increasingly and accurately approximate the desired scattering response. The neural-adjoint method is not restricted to the case demonstrated and may be applied to plasmonics, photonic crystal, and other artificial electromagnetic materials.

42 ENGINEERING↗
DOE OSTI2022

A mass conservative, well balanced, tangency preserving and energy decaying method for the shallow water equations on a sphere

Here a fully discrete surface finite element method is proposed for solving the viscous shallow water equations in a bounded Lipschitz domain on the sphere based on a general triangular mesh. The method consists of a modified Crank–Nicolson method in time and a Galerkin surface finite element method in space for the fluid thickness H and the fluid velocity u. A finite element space tangential to the sphere at all finite element nodes is proposed to approximate the fluid velocity u. The proposed method has second-order accuracy in time and first-order accuracy in space, and preserves mass conservation, well balancedness, tangency of velocity to the sphere, and energy decay. Numerical experiments are presented to illustrate the accuracy of the proposed method and the preservation of the physical properties, including mass conservation, well balancedness, and energy decay. A numerical simulation of ocean mesoscale activity on a circular basin with a continental shelf is provided.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Low-Rank Correction Methods for Algebraic Domain Decomposition Preconditioners

This study presents a parallel preconditioning method for distributed sparse linear systems, based on an approximate inverse of the original matrix, that adopts a general framework of distributed sparse matrices and exploits domain decomposition (DD) and low-rank corrections. The DD approach decouples the matrix and, once inverted, a low-rank approximation is applied by exploiting the Sherman--Morrison--Woodbury formula, which yields two variants of the preconditioning methods. The low-rank expansion is computed by the Lanczos procedure with reorthogonalizations. Numerical experiments indicate that, when combined with Krylov subspace accelerators, this preconditioner can be efficient and robust for solving symmetric sparse linear systems. Comparisons with pARMS, a DD-based parallel incomplete LU (ILU) preconditioning method, are presented for solving Poisson's equation and linear elasticity problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Real-space formulation of the stress tensor for O (N) density functional theory: Application to high temperature calculations

We present an accurate and efficient real-space formulation of the Hellmann–Feynman stress tensor for O (N) Kohn–Sham density functional theory (DFT). While applicable at any temperature, the formulation is most efficient at high temperature where the Fermi–Dirac distribution becomes smoother and the density matrix becomes correspondingly more localized. We first rewrite the orbital-dependent stress tensor for real-space DFT in terms of the density matrix, thereby making it amenable to O (N) methods. We then describe its evaluation within the O (N) infinite-cell Clenshaw–Curtis Spectral Quadrature (SQ) method, a technique that is applicable to metallic and insulating systems, is highly parallelizable, becomes increasingly efficient with increasing temperature, and provides results corresponding to the infinite crystal without the need of Brillouin zone integration. We demonstrate systematic convergence of the resulting formulation with respect to SQ parameters to exact diagonalization results and show convergence with respect to mesh size to the established plane wave results. Here, we employ the new formulation to compute the viscosity of hydrogen at 10 6 K from Kohn–Sham quantum molecular dynamics, where we find agreement with previous more approximate orbital-free density functional methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Efficient generalized boundary detection

Fast, efficient, and robust compression-based methods for detecting boundaries in arbitrary datasets, including sequences (1D datasets), are desired. The methods, each employing three simple algorithms, approximate the information distance between two adjacent sliding windows within a dataset. One of the algorithms calculates an initial ordered list of subsequences; while a second algorithm updates the ordered list of subsequences by dropping a first entry and appending a last entry rather than calculating completely new ordered lists with each iteration. Large values in the distance metric are indicative of boundary locations. A smoothed z-score or a wavelet-based algorithm may then be used to locate peaks in the distance metric, thereby identifying boundary locations. An adaptive version of the method employs a collection of window sizes and corresponding weighting functions, making it more amenable to real datasets with unknown, complex, and changing structures.

Ting, Christina↗
DOE OSTI2025

Analysis of the weighted shifted boundary method for the Poisson and Stokes problems

The Shifted Boundary Method (SBM) belongs to the class of unfitted (or immersed, or embedded) finite element methods, and relies on reformulating the original boundary value problem over a surrogate (approximate) computational domain. Accuracy is maintained by properly shifting the location and values of the boundary conditions. This avoids integration over cut cells and the associated implementation issues. Recently, the Weighted SBM (WSBM) was proposed for the Navier-Stokes equations with free surfaces and the Stokes flow with moving boundaries. The attribute “weighted” in the name WSBM stems from the fact that its variational form is weighted with the elemental volume fraction of active fluid. The motivation for the development of the WSBM was the preservation of the volume of active fluid to a higher degree of accuracy, which in turn resulted in improved stability and robustness characteristics in moving-boundary, time-dependent simulations. In this article, we present the numerical analysis of the WSBM formulations for the Poisson and Stokes problems. We give mathematical conditions under which the bilinear forms defining the discrete variational formulations are uniformly coercive (Poisson problem) or inf-sup stable (Stokes problem). By these results, stability and optimal convergence is proven in the natural norm; L2-error estimates can also be derived.

Approximate domain boundaries↗
DOE OSTI2020

Signatures of multiple charge excitations in resonant inelastic x-ray scattering spectra of metals

In this work, we study how multiple charge excitations appear in the resonant inelastic x-ray scattering (RIXS) spectra of metals. Typically, the focus is upon single excitations in the problem, the plasmons and electron-hole pairs, while the multiexcitation processes are neglected. However, at small momentum transfer the multiexcitation contributions may dominate the signal and one needs to understand how to interpret the data in such cases. In particular, we demonstrate how to “decode” the total multiexcitation intensity and extract the plasmon dispersion. Furthermore, while our calculations are based on the random phase approximation for jellium, which does not allow us to obtain quantitatively precise results in the entire region of parameters, we expect them to capture semiqualitatively all features expected for charged Fermi-liquid states, including universal and singular properties of the RIXS spectra.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

A Galerkin method with two-dimensional Haar basis functions for the computation of the Karhunen–Loève expansion

We study the numerical approximation of a homogeneous Fredholm integral equation of second kind associated with the Karhunen–Loève expansion of Gaussian random fields. We develop, validate, and discuss an algorithm based on the Galerkin method with two-dimensional Haar wavelets as basis functions. The shape functions are constructed from the orthogonal decomposition of tensor-product spaces of one-dimensional Haar functions, and a recursive algorithm is employed to compute the matrix of the discrete eigenvalue system without the explicit calculation of integrals, allowing the implementation of a fast and efficient algorithm that provides considerable reduction in CPU time, when compared with classical Galerkin methods. Numerical experiments confirm the convergence rate of the method and assess the approximation error and the sparsity of the eigenvalue system when the wavelet expansion is truncated. We illustrate the numerical solution of a diffusion problem with random input data with the present method. In this problem, accuracy was retained after dropping the coefficients below a threshold value that was numerically determined. A similar method with scaling functions rather than wavelet functions does not need a discrete wavelet transform and leads to eigenvalue systems with better conditioning but lower sparsity.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Hierarchical Particle Mesh: An FFT-accelerated Fast Multipole Method

I observe a modification to the original Fast Multipole Method (FMM) of Greengard & Rokhlin that approximates the gravitation field of an FMM cell as a small uniform grid (a “gridlet”) of effective masses. The effective masses on a gridlet are set from the requirement that the multipole moments of the FMM cells are reproduced exactly, thus preserving the accuracy of the gravitational field representation. The measurement of the gravitational field from a multipole expansion can then be computed for all multipole orders simultaneously, with a single Fast Fourier Transform, significantly reducing the computational cost at a given value of the required accuracy. The described approach belongs to the class of “kernel independent” variants of the FMM method and works with any Green function.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Polynomial chaos expansions for dependent random variables

Polynomial chaos expansions (PCE) are well-suited to quantifying uncertainty in models parameterized by independent random variables. The assumption of independence leads to simple strategies for building multivariate orthonormal bases and for sampling strategies to evaluate PCE coefficients. In contrast, the application of PCE to models of dependent variables is much more challenging. Three approaches can be used to construct PCE of models of dependent variables. The first approach uses mapping methods where measure transformations, such as the Nataf and Rosenblatt transformation, can be used to map dependent random variables to independent ones; however we show that this can significantly degrade performance since the Jacobian of the map must be approximated. A second strategy is the class of dominating support methods. In these approaches a PCE is built using independent random variables whose distributional support dominates the support of the true dependent joint density; we provide evidence that this approach appears to produce approximations with suboptimal accuracy. A third approach, the novel method proposed here, uses Gram-Schmidt orthogonalization (GSO) to numerically compute orthonormal polynomials for the dependent random variables. This approach has been used successfully when solving differential equations using the intrusive stochastic Galerkin method, and in this paper we use GSO to build PCE using a non-intrusive stochastic collocation method. The stochastic collocation method treats the model as a black box and builds approximations of the input-output map from a set of samples. Building PCE from samples can introduce ill-conditioning which does not plague stochastic Galerkin methods. To mitigate this ill-conditioning we generate weighted Leja sequences, which are nested sample sets, to build accurate polynomial interpolants. We show that our proposed approach, GSO with weighted Leja sequences, produces PCE which are orders of magnitude more accurate than PCE constructed using mapping or dominating support methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Progress Towards Synthesis of Uranium Chloride Fuel Salts Using Zinc Chloride

Reliable, scalable methods for producing high-purity actinide chloride salts are needed to support molten salt reactor fuel development and deployment. This report describes the continued development and demonstration of a bench-scale chlorination and purification apparatus using a zinc chloride-based method for synthesizing uranium chloride fuel salts. In this approach, uranium metal is chlorinated by ZnCl2 to produce LiCl-KCl-UCl3. Reaction with three aliquots of added uranium metal was used to generate a target uranium concentration of 30 wt %. While this concentration was chosen for initial testing of the apparatus and method, the final uranium concentration is not limited to 30 wt %. The zinc metal generated in the reaction forms an immiscible layer that was removed by volatilization at moderately high temperatures. Electrochemical measurements confirmed the removal of zinc and applied sensing methods indicated the uranium concentration to be approximately 25 wt %. These initial results demonstrate that the bench-scale chlorination apparatus is an effective platform for the synthesis and purification of uranium chloride salts using ZnCl2. This method shows promise for application to industry-relevant salt systems such as NaCl-UCl3. Further development is recommended to optimize reagent loading, zinc removal, and avoid possible U-Zn alloy formation.

Dulovic, Stephanie↗
DOE OSTI2015

Low-energy positron scattering by pyrimidine

This work reports elastic integral and differential cross sections for positron collisions with pyrimidine, for energies up to 20 eV. The cross sections were computed with the Schwinger multichannel method in the static plus polarization approximation. We also employed the Born closure procedure to account for the long range potential due to the permanent dipole moment of the molecule. Our results are compared with the experimental total cross section of Zecca et al. [J. Phys. B 43, 215204 (2010)], the experimental grand-total, quasi-elastic integral and differential cross section of Palihawadana et al. [Phys. Rev. A 88, 12717 (2013)]. We also compare our results with theoretical integral and differential cross sections obtained by Sanz et al. [Phys. Rev. A 88, 62704 (2013)] with the R-matrix and the independent atom model with screening-corrected additivity rule methods, and with the results computed by Franz and Gianturco [Phys. Rev. A 88, 042711 (2013)] using model correlation-polarization potentials. The agreement between the theory and the experiment is encouraging.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Integral approximations to classical diffusion and smoothed particle hydrodynamics

The contribution of the paper is the approximation of a classical diffusion operator by an integral equation with a volume constraint. A particular focus is on classical diffusion problems associated with Neumann boundary conditions. By exploiting this approximation, we can also approximate other quantities such as the flux out of a domain. Our analysis of the model equation on the continuum level is closely related to the recent work on nonlocal diffusion and peridynamic mechanics. In particular, we elucidate the role of a volumetric constraint as an approximation to a classical Neumann boundary condition in the presence of physical boundary. The volume-constrained integral equation then provides the basis for accurate and robust discretization methods. An immediate application is to the understanding and improvement of the Smoothed Particle Hydrodynamics (SPH) method.

boundary conditions, smoothed particle hydrodynami↗
DOE OSTI2013

Water dissociation on Ni(100) and Ni(111): Effect of surface temperature on reactivity

Water adsorption and dissociation on Ni(100) and Ni(111) surfaces are studied using density functional theory calculations. Water adsorbs on top site on both the surfaces, while H and OH adsorb on four fold hollow and three fold hollow (fcc) sites on Ni(100) and Ni(111), respectively. Transition states (TS) on both surfaces are identified using climbing image-nudged elastic band method. It is found that the barrier to dissociation on Ni(100) surface is slightly lower than that on Ni(111) surface. Dissociation on both the surfaces is exothermic, while the exothermicity on Ni(100) is large. To study the effect of lattice motion on the energy barrier, TS calculations are performed for various values of Q (lattice atom coordinate along the surface normal) and the change in the barrier height and position is determined. Calculations show that the energy barrier to reaction decreases with increasing Q and increases with decreasing Q on both the surfaces. Dissociation probability values at different surface temperatures are computed using semi-classical approximation. Results show that the influence of surface temperature on dissociation probability on the Ni(100) is significantly larger compared to that of Ni(111). Moreover, on Ni(100), a dramatic shift in energy barrier to lower incident energy values is observed with increasing surface temperature, while the shift is smaller in the case of Ni(111)

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

The molecular gradient using the divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation theory: The DEC-RI-MP2 gradient

We report an implementation of the molecular gradient using the divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation theory (DEC-RI-MP2). The new DEC-RI-MP2 gradient method combines the precision control as well as the linear-scaling and massively parallel features of the DEC scheme with efficient evaluations of the gradient contributions using the RI approximation. We further demonstrate that the DEC-RI-MP2 gradient method is capable of calculating molecular gradients for very large molecular systems. A test set of supramolecular complexes containing up to 158 atoms and 1960 contracted basis functions has been employed to demonstrate the general applicability of the DEC-RI-MP2 method and to analyze the errors of the DEC approximation. Moreover, the test set contains molecules of complicated electronic structures and is thus deliberately chosen to stress test the DEC-RI-MP2 gradient implementation. Additionally, as a showcase example the full molecular gradient for insulin (787 atoms and 7604 contracted basis functions) has been evaluated.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Analysis of the Spectral Stability of the Generalized Runge–Kutta Methods Applied to Initial-Boundary-Value Problems for Equations of the Parabolic Type. I. Explicit Methods

We develop a general algorithm for the analysis the spectral stability of generalized multistage Runge–Kutta methods of various orders of accuracy as applied to the numerical integration with respect to time of an initial-boundary-value problem for the second-order parabolic equation. The expression for the function of spectral stability is obtained in two alternative forms: on the basis of matrix relations and in the determinant form. We study specific realizations of various generalized explicit Runge–Kutta methods and their spectral stability. It is shown that all explicit generalized Runge–Kutta methods possess the property of conditional spectral stability and the property of conditional monotonicity of the numerical solution in time whose violation leads to the appearance of false oscillations of the approximate solution. The stability function for these methods is polynomial. It is shown that the application of two-stage generalized explicit Runge–Kutta methods leads to the appearance of predictor-corrector-type schemes. In the case of nonstationary one-dimensional heat-conduction problem, on the basis of a one-stage generalized Runge–Kutta method, we obtain the classical two-layer conditionally stable explicit finite-difference scheme on a four-point template. It is demonstrated that the five-stage generalized Runge–Kutta–Merson method is characterized by the weakest condition of spectral stability as compared with all investigated explicit generalized Runge–Kutta methods.

42 ENGINEERING↗