Search NASA⌕ Search

SEARCH · Search NASA

Results for “Approximation methods”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 505 records · Page 28
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

A NEW APPROACH TO DETERMINE OPTICALLY THICK H{sub 2} COOLING AND ITS EFFECT ON PRIMORDIAL STAR FORMATION

We present a new method for estimating the H{sub 2} cooling rate in the optically thick regime in simulations of primordial star formation. Our new approach is based on the TreeCol algorithm, which projects matter distributions onto a spherical grid to create maps of column densities for each fluid element in the computational domain. We have improved this algorithm by using the relative gas velocities to weight the individual matter contributions with the relative spectral line overlaps, in order to properly account for the Doppler effect. We compare our new method to the widely used Sobolev approximation, which yields an estimate for the column density based on the local velocity gradient and the thermal velocity. This approach generally underestimates the photon escape probability because it neglects the density gradient and the actual shape of the cloud. We present a correction factor for the true line overlap in the Sobolev approximation and a new method based on local quantities, which fits the exact results reasonably well during the collapse of the cloud, with the error in the cooling rates always being less than 10%. Analytical fitting formulae fail at determining the photon escape probability after formation of the first protostar (error of ∼40%) because they are based on the assumption of spherical symmetry and therefore break down once a protostellar accretion disk has formed. Our method yields lower temperatures and hence promotes fragmentation for densities above ∼10{sup 10} cm{sup –3} at a distance of ∼200 AU from the first protostar. Since the overall accretion rates are hardly affected by the cooling implementation, we expect Pop III stars to have lower masses in our simulations, compared to the results of previous simulations that used the Sobolev approximation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Recommended Nuclear Data for the Production of Selected Therapeutic Radionuclides

Increasing interest in the treatment of human disease by means of targeted radionuclide-based therapies requires an accurate understanding of achievable yields and quantification of realisable degrees of purity. Important studies within a more extensive Coordinated Research Project of the International Atomic Energy Agency (IAEA CRP) have included in-depth assessments and evaluations of all available measured cross-section data for ten nuclear reactions leading to the formation of 131 Cs, 131 Ba, 225 Ac, 225 Ra, 227 Th, 227 Ac, 230 U and 230 Pa for various on-going and proposed therapeutic applications in nuclear medicine. Equivalent studies were also undertaken of possible reactions to produce the 178W /low-spin 178m Ta generator system that has been clinically applied in diagnosis by means of SPECT - these particular cross-section studies and recommendations are included in this paper for completeness. All available measured data have been critically reviewed and assessed to produce statistically consistent datasets. Selected datasets have been fitted by a least-squares method with Padé approximations of variable order to evaluate the production cross sections and corresponding uncertainties. New measurements have been made in some instances, and reported data have been adjusted to accommodate new nuclear decay or monitor reaction data which altered the original reported quantities adversely. Insufficient measured data are available in many cases to permit a reliable evaluation of cross sections, and these instances are discussed. Finally, recommended therapeutic radionuclide production reaction data and their uncertainties are available on the Web page of the IAEA Nuclear Data Section at www-nds.iaea.org/radionuclides/ and also at the IAEA medical portal www-nds.iaea.org/medportal/.

63 RADIATION, THERMAL, AND OTHER ENVIRON. POLLUTAN↗
DOE OSTI2017

Efficient Scalable Parallel Higher Order Direct MoM-SIE Method With Hierarchically Semiseparable Structures for 3-D Scattering

A novel fast scalable parallel algorithm is proposed for the solution of large 3-D scattering problems based on: 1) the double (geometrical and current-approximation) higher order (DHO) method of moments (MoM) in the surface integral equation (SIE) formulation and 2) a direct solver for dense linear systems utilizing hierarchically semiseparable (HSS) structures. Namely, an HSS matrix representation is used for compression, factorization, and solution of the system matrix. In addition, a rank-revealing QR decomposition for memory compression is used, with a stopping criterion in terms of the relative rank tolerance value. One method for geometrical preprocessing of the scatterers based on the cobblestone distance sorting technique is employed in order to enhance the HSS algorithm accuracy and parallelization. Numerical examples show how the accuracy of the DHO HSS-MoM-SIE method is easily controllable by using the relative tolerance for the matrix compression. Furthermore, the examples demonstrate low memory consumption, as well as much faster simulation time, when compared to the direct LU decomposition. The method enables dramatically faster monostatic scattering computations than iterative solvers and reduced number of unknowns when compared to low-order discretizations. Finally, great scalability of the algorithm is demonstrated on more than one thousand processes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Efficient linear-scaling second-order Møller-Plesset perturbation theory: The divide–expand–consolidate RI-MP2 model

The Resolution of the Identity second-order Møller-Plesset perturbation theory (RI-MP2) method is implemented within the linear-scaling Divide-Expand-Consolidate (DEC) framework. In a DEC calculation, the full molecular correlated calculation is replaced by a set of independent fragment calculations each using a subset of the total orbital space. The number of independent fragment calculations scales linearly with the system size, rendering the method linear-scaling and massively parallel. The DEC-RI-MP2 method can be viewed as an approximation to the DEC-MP2 method where the RI approximation is utilized in each fragment calculation. The individual fragment calculations scale with the fifth power of the fragment size for both methods. However, the DEC-RI-MP2 method has a reduced prefactor compared to DEC-MP2 and is well-suited for implementation on massively parallel supercomputers, as demonstrated by test calculations on a set of medium-sized molecules. The DEC error control ensures that the standard RI-MP2 energy can be obtained to the predefined precision. The errors associated with the RI and DEC approximations are compared, and it is shown that the DEC-RI-MP2 method can be applied to systems far beyond the ones that can be treated with a conventional RI-MP2 implementation.

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

L-BFGS Class Implementation in C++

This report presents a header-only C++ class implementation of the Limited-memory BroydenFletcher-Goldfarb-Shanno (L-BFGS) algorithm. The L-BFGS method is a general purpose quasi-Netwon optimization method that builds an approximation of the descent direction from consecutive iterate and gradient vectors. The limited-memory aspect stems from the replacement of the N × N approximation matrix of the original BFGS method with M vectors of length N. An example usage of the class is included along with the reference source code.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Systems and methods for convex relaxations and linear approximations for optimal power flow in multiphase radial networks

Centralized node controllers in accordance with embodiments of the invention enable linear approximation of optimal power flow. One embodiment includes a centralized node controller including: a network interface, a processor, and a memory containing: a centralized power control application a network topology, where the network is multiphase unbalanced and comprises a plurality of connected nodes; wherein the processor is configured by the centralized controller application to: request node operating parameters from the plurality of connected nodes; calculate network operating parameters using a linear approximation of optimal power flow and the node operating parameters from the plurality of connected nodes; send network operating parameters to the plurality of connected nodes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Scaling Symmetries in Elastic-Plastic Dynamic Cavity Expansion Equations Using the Isovector Method

Cavity-expansion approximations are widely-used in the study of penetration mechanics and indentation phenomena. We apply the isovector method to a well-established model in the literature for elastic-plastic cavity-expansion to systematically demonstrate the existence of Lie symmetries corresponding to scale-invariant solutions. Here we use the symmetries obtained from the equations of motion to determine compatible auxiliary conditions describing the cavity wall trajectory and the elastic-plastic material interface. The admissible conditions are then compared with specific similarity solutions in the literature.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Direct discrete simulation of the kinetic Landau-Fokker-Planck equation with an alternating external electromagnetic field

A stochastic method of simulation of Coulomb interaction is considered. The main idea of the method is to approximate the nonlinear Landau kinetic collision integral by the Boltzmann integral. In its realization, the method can be attributed to a wide class of Monte Carlo-type methods. It is easily combined with the existing particle methods used to simulate collisionless plasmas. This is important for simulation of the dynamics of both laboratory and space plasmas when the mean free path of plasma particles is comparable with the plasma inhomogeneity scale length. Illustrative examples of relaxation of two-temperature plasma being subject to a high-frequency alternating electric field are given, and differences from their classical description are considered. The method satisfies the conservation laws for the number of particles, momentum, and energy and is simple and efficient in implementation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Improved tomographic reconstruction of large-scale real-world data by filter optimization

In advanced tomographic experiments, large detector sizes and large numbers of acquired datasets can make it difficult to process the data in a reasonable time. At the same time, the acquired projections are often limited in some way, for example having a low number of projections or a low signal-to-noise ratio. Direct analytical reconstruction methods are able to produce reconstructions in very little time, even for large-scale data, but the quality of these reconstructions can be insufficient for further analysis in cases with limited data. Iterative reconstruction methods typically produce more accurate reconstructions, but take significantly more time to compute, which limits their usefulness in practice. In this paper, we present the application of the SIRT-FBP method to large-scale real-world tomographic data. The SIRT-FBP method is able to accurately approximate the simultaneous iterative reconstruction technique (SIRT) method by the computationally efficient filtered backprojection (FBP) method, using precomputed experiment-specific filters. We specifically focus on the many implementation details that are important for application on large-scale real-world data, and give solutions to common problems that occur with experimental data. We show that SIRT-FBP filters can be computed in reasonable time, even for large problem sizes, and that precomputed filters can be reused for future experiments. Reconstruction results are given for three different experiments, and are compared with results of popular existing methods. The results show that the SIRT-FBP method is able to accurately approximate iterative reconstructions of experimental data. Furthermore, they show that, in practice, the SIRT-FBP method can produce more accurate reconstructions than standard direct analytical reconstructions with popular filters, without increasing the required computation time.

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

On a fully-implicit VMS-stabilized FE formulation for low Mach number compressible resistive MHD with application to MCF

This study presents the development and evaluation of a fully-implicit variational multiscale (VMS) stabilized unstructured finite element (FE) formulation for compressible magnetohydrodynamics (MHD) model, at low Mach number regime. The model describes the dynamics of a compressible conducting fluid in the low Mach number limit in the presence of electromagnetic fields and can be used to study aspects of astrophysical phenomena, important science and technology applications, and basic plasma physics phenomena. The specific applications that motivate this study are macroscopic simulations of the longer time-scale stability and disruptions of magnetic confinement fusion (MCF) devices, specifically the ITER tokamak. The discussion considers the development of the VMS FE representation, the structure of the stabilizing terms that deal with significant convective flows, the stabilization of the nearly incompressible response of the fluid flow, and the stabilization of the constraint that enforces the solenoidal involution on the magnetic field. The nonlinear discretized system is solved with scalable preconditioned Newton–Krylov iterative methods, which employs a multiphysics block preconditioning method based on approximate block factorizations and Schur complements. The study presents an evaluation of the VMS method on a 2D cartesian tearing mode instability, and illustrates the scalability of the solvers on MCF relevant problems. A set of results are also presented for longer time-scale stability and disruptions for the ITER tokamak. These include a vertical displacement event (VDE), and a (1,1) internal kink mode. Here, the formulation is demonstrated to be scalable and also reasonably robust with respect to the Lundquist number scaling.

42 ENGINEERING↗
DOE OSTI2018

The use of Jacobi wavelets for constrained approximation of rational Bézier curves

This paper presents an efficient method to solve the approximation problem of the rational Bézier curve by continuous piecewise polynomial curve in L{sub 2}-norm. For this purpose, extended Jacobi wavelets together with the Gauss–Jacobi quadrature rules are employed. The proposed technique has some advantages such as: simplicity, high accuracy and fast computation. Also, the method in the paper performs multi-degree reduction at one time and does not need the stepwise computing. Several examples are given to illustrate the effectiveness of the algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Embedded random phase approximation for magnetic systems: H 2 dissociative adsorption on Fe(110)

The random phase approximation (RPA), a method for treating electron correlation, has been shown to be superior to standard density functional theory (DFT) approximations in numerous cases. However, the RPA’s computational cost is substantially higher than that of DFT, particularly restricting its application to extended surfaces. The recently introduced embedded RPA (emb-RPA) approach [Wei et al., J. Chem. Phys. 159(19), 194108 (2023)] reduces this computational cost by approximately two orders of magnitude. While previous applications of emb-RPA focused on non-spin-polarized systems, here we extend the approach to ferromagnetic ones. Unlike other embedded correlated wavefunction methods, such as embedded complete active space self-consistent field theory, emb-RPA is advantageous for spin-polarized systems because the RPA is compatible with unrestricted DFT solutions, which are eigenfunctions of the spin angular momentum operator S z but not the total spin-squared operator S 2 . By applying emb-RPA with specific magnetization constraints, we achieved a speedup of two to three orders of magnitude (one order when accounting for the one-time embedding potential optimization cost) with only small errors (∼50 meV) compared to full periodic RPA. Moreover, emb-RPA significantly reduces the over-binding errors of DFT approximations. In conclusion, we anticipate that the acceleration enabled by the spin-polarized emb-RPA approach will broaden the applicability of RPA to magnetic materials.

Density functional theory↗
DOE OSTI2019

Approximate Bayesian Model Inversion for PDEs with Heterogeneous and State-Dependent Coefficients

We present two approximate Bayesian inference methods for parameter estimation in partial differential equation (PDE) models with space-dependent and state-dependent parameters. We demonstrate that these methods provide accurate and cost-effective alternatives to Markov Chain Monte Carlo simulation. We assume a parameterized Gaussian prior on the unknown functions, and approximate the posterior density by a parameterized multivariate Gaussian density. The parameters of the prior and posterior are estimated from sparse observations of the PDE model's states and the unknown functions themselves by maximizing the evidence lower bound (ELBO), a lower bound on the log marginal likelihood of the observations. The first method, Laplace-EM, employs the expectation maximization algorithm to maximize the ELBO, with a Laplace approximation of the posterior on the E-step, and minimization of a Kullback-Leibler divergence on the M-step. The second method, DSVI-EB, employs the doubly stochastic variational inference (DSVI) algorithm, in which the ELBO is maximized via gradient-based stochastic optimization, with nosiy gradients computed via simple Monte Carlo sampling and Gaussian backpropagation. We apply these methods to identifying diffusion coefficients in linear and nonlinear diffusion equations, and we find that both methods provide accurate estimates of posterior densities and the hyperparameters of Gaussian priors. While the Laplace-EM method is more accurate, it requires computing Hessians of the physics model. The DSVI-EB method is found to be less accurate but only requires gradients of the physics model.

approximate Bayesian inference, model inversion, v↗
DOE OSTI2016

Structural and Electronic Effects on the Properties of Fe 2 (dobdc) upon Oxidation with N 2 O

Here, we report electronic, vibrational, and magnetic properties, together with their structural dependences, for the metal–organic framework Fe 2 (dobdc) (dobdc 4 – = 2,5-dioxido-1,4-benzenedicarboxylate) and its derivatives, Fe 2 (O) 2 (dobdc) and Fe 2 (OH) 2 (dobdc)—species arising in the previously proposed mechanism for the oxidation of ethane to ethanol using N 2 O as an oxidant. Magnetic susceptibility measurements reported for Fe 2 (dobdc) in an earlier study and reported in the current study for Fe II 0.26 [Fe III (OH)] 1.74 (dobdc)(DMF) 0.15 (THF) 0.22 , which is more simply referred to as Fe 2 (OH) 2 (dobdc), were used to confirm the computational results. Theory was also compared to experiment for infrared spectra and X-ray powder diffraction structures. Structural and magnetic properties were computed by using Kohn-Sham density functional theory both with periodic boundary conditions and with cluster models. In addition, we studied the effects of different treatments of the exchange interactions on the magnetic coupling parameters by comparing several approaches to the exchange-correlation functional: generalized gradient approximation (GGA), GGA with empirical Coulomb and exchange integrals for 3d electrons (the GGA+U method), nonseparable gradient approximation with empirical Coulomb and exchange integrals for 3d electrons (GAM+U), hybrid GGA, meta-GGA, and hybrid meta- GGA. We found the coupling between the metal centers to be ferromagnetic in the case of Fe 2 (dobdc) and antiferromagnetic in the cases of Fe 2 (O) 2 (dobdc) and Fe 2 (OH) 2 (dobdc). The shift in magnetic coupling behavior correlates with the changing electronic structure of the framework, which derives from both structural and electronic changes that occur upon metal oxidation and addition of the charge-balancing oxo and hydroxo ligands.

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

Evaluating marginal likelihood with thermodynamic integration method and comparison with several other numerical methods

Evaluating marginal likelihood is the most critical and computationally expensive task, when conducting Bayesian model averaging to quantify parametric and model uncertainties. The evaluation is commonly done by using Laplace approximations to evaluate semianalytical expressions of the marginal likelihood or by using Monte Carlo (MC) methods to evaluate arithmetic or harmonic mean of a joint likelihood function. This study introduces a new MC method, i.e., thermodynamic integration, which has not been attempted in environmental modeling. Instead of using samples only from prior parameter space (as in arithmetic mean evaluation) or posterior parameter space (as in harmonic mean evaluation), the thermodynamic integration method uses samples generated gradually from the prior to posterior parameter space. This is done through a path sampling that conducts Markov chain Monte Carlo simulation with different power coefficient values applied to the joint likelihood function. The thermodynamic integration method is evaluated using three analytical functions by comparing the method with two variants of the Laplace approximation method and three MC methods, including the nested sampling method that is recently introduced into environmental modeling. The thermodynamic integration method outperforms the other methods in terms of their accuracy, convergence, and consistency. The thermodynamic integration method is also applied to a synthetic case of groundwater modeling with four alternative models. The application shows that model probabilities obtained using the thermodynamic integration method improves predictive performance of Bayesian model averaging. As a result, the thermodynamic integration method is mathematically rigorous, and its MC implementation is computationally general for a wide range of environmental problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Similarity-transformed equation-of-motion vibrational coupled-cluster theory

A similarity-transformed equation-of-motion vibrational coupled-cluster (STEOM-XVCC) method is introduced as a one-mode theory with an effective vibrational Hamiltonian, which is similarity transformed twice so that its lower-order operators are dressed with higher-order anharmonic effects. The first transformation uses an exponential excitation operator, defining the equation-of-motion vibrational coupled-cluster (EOM-XVCC) method, and the second uses an exponential excitation-deexcitation operator. From diagonalization of this doubly similarity-transformed Hamiltonian in the small one-mode excitation space, the method simultaneously computes accurate anharmonic vibrational frequencies of all fundamentals, which have unique significance in vibrational analyses. We establish a diagrammatic method of deriving the working equations of STEOM-XVCC and prove their connectedness and thus size-consistency as well as the exact equality of its frequencies with the corresponding roots of EOM-XVCC. We furthermore elucidate the similarities and differences between electronic and vibrational STEOM methods and between STEOM-XVCC and vibrational many-body Green’s function theory based on the Dyson equation, which is also an anharmonic one-mode theory. The latter comparison inspires three approximate STEOM-XVCC methods utilizing the common approximations made in the Dyson equation: the diagonal approximation, a perturbative expansion of the Dyson self-energy, and the frequency-independent approximation. The STEOM-XVCC method including up to the simultaneous four-mode excitation operator in a quartic force field and its three approximate variants are formulated and implemented in computer codes with the aid of computer algebra, and they are applied to small test cases with varied degrees of anharmonicit

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Accelerating the solution of the S N equations with highly anisotropic scattering using the Fokker-Planck approximation

The discrete ordinates method can model forward-peaked transport problems accurately. However, convergence of discrete ordinates solution can become arbitrarily slow upon use of standard iterative procedures like source iteration. Standard zeroth and first moment-based acceleration methods like nonlinear diffusion acceleration and diffusion synthetic acceleration are ineffective in accelerating such problems because these methods do not correct higher order Legendre-moments of angular flux. In this paper, we explore the idea of using the Fokker-Planck approximation as a preconditioner to accelerate the convergence of solution of forward-peaked transport problems. Finally, we observe that such preconditioning can successfully reduce the iteration count by up to four orders of magnitude, and solver runtime by up to three orders of magnitude when compared to diffusion synthetic acceleration.

42 ENGINEERING↗