Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Iterative 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 163 records · Page 9

Implementation and application of the peak scaling method for temperature measurement in the laser heated diamond anvil cell

In this work, a new design for a double-sided high-pressure diamond anvil cell laser heating set-up is described. The prototype is deployed at beamline 12.2.2 of the Advanced Light Source at Lawrence Berkeley National Lab. Our compact design features shortened mechanical lever arms, which results in more stable imaging optics, and thus more user friendly and more reliable temperature measurements based on pyrometry. A modification of the peak scaling method was implemented for pyrometry, including an iterative method to determine the absolute peak temperature, thus allowing for quasi-real time temperature mapping of the actual hotspot within a laser-heated diamond anvil cell without any assumptions on shape, size, and symmetry of the hotspot and without any assumptions to the relationship between fitted temperature and peak temperature. This is important since we show that the relationship between peak temperature and temperature obtained by fitting the Planck function against the thermal emission spectrum averaged over the entire hotspot is not constant but depends on variable fitting parameters (in particular, the size and position of the fitting window). The accuracy of the method is confirmed through measuring melting points of metal wires at ambient pressure. Having absolute temperature maps in real time allows for more differentiated analyses of laser heating experiments. Finally, we present such an example of the pressure variations within a heated hotspot of AgI at a loaded base pressure of 3.8 GPa.

42 ENGINEERING↗

Copper Mountain Conference Series, 2015-2018 (Final Report)

This four-year project supports the annual conferences of the Copper Mountain Conference Series, held in late March or early April each year at Copper Mountain, Colorado. Begun in 1983, the Series represents an important forum for the exchange of ideas in these two closely related fields. The subject of the Copper Mountain Conference Series alternates between Multigrid Methods in odd-numbered years and Iterative Methods in even-numbered years. Funding for the conferences in this period was provided mainly by grants from the DOE, with some contributions from a variety of other sources. The DOE project budget includes basic organizational costs and support for participation by students, women, minorities, and disabled.

97 MATHEMATICS AND COMPUTING↗

Anderson acceleration stability in NDA-accelerated k-eigenvalue problems

Anderson acceleration (AA) has been used to improve the stability and convergence rate of multiphysics iterative methods for reactor analysis. Most applications studied assume a tightly converged solution for the different physics problems, and AA is usually applied to state variables like temperature, density, and heat generation rate. In this paper, we study the theoretical performance of AA in NDA-accelerated k-eigenvalue problems. The problems and algorithms studied are simplified from the coupled iteration scheme adopted by MPACT and many other high-fidelity whole-core reactor codes. Compared to previous analyses of AA for these iteration schemes, we study the case with a partially converged neutronics solution and possibly partially converged nonlinear diffusion acceleration (NDA)/coarse mesh finite difference (CMFD) solutions. We observe that the performance of the iteration scheme with AA is very sensitive to the initial guess and is affected by the partially converged CMFD solutions. When the NDA solution is fully converged, using AA cannot achieve the optimal convergence rate in large-sized problems. Conversely, if the NDA solution is partially converged, the iteration scheme with AA can diverge or converge extremely slowly. It is found that the loss of robustness for AA is due to the fact that it is applied to the iterative subspace of state variables rather than the fundamental unknowns of the governing equations. To improve the robustness, the scalar flux should also be considered in the implementation of AA. After considering the residuals of flux, we observe that the stability is regardless of the partial convergence of NDA solutions. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Speeding up N -body simulations of modified gravity: chameleon screening models

We describe and demonstrate the potential of a new and very efficient method for simulating certain classes of modified gravity theories, such as the widely studied f ( R ) gravity models. High resolution simulations for such models are currently very slow due to the highly nonlinear partial differential equation that needs to be solved exactly to predict the modified gravitational force. This nonlinearity is partly inherent, but is also exacerbated by the specific numerical algorithm used, which employs a variable redefinition to prevent numerical instabilities. The standard Newton-Gauss-Seidel iterative method used to tackle this problem has a poor convergence rate. Our new method not only avoids this, but also allows the discretised equation to be written in a form that is analytically solvable. We show that this new method greatly improves the performance and efficiency of f ( R ) simulations. For example, a test simulation with 512{sup 3} particles in a box of size 512 Mpc/ h is now 5 times faster than before, while a Millennium-resolution simulation for f ( R ) gravity is estimated to be more than 20 times faster than with the old method. Our new implementation will be particularly useful for running very high resolution, large-sized simulations which, to date, are only possible for the standard model, and also makes it feasible to run large numbers of lower resolution simulations for covariance analyses. We hope that the method will bring us to a new era for precision cosmological tests of gravity.

79 ASTRONOMY AND ASTROPHYSICS↗

Influence of refraction index strength on the light propagation in dielectrics material with periodic refraction index

This study investigated the influence of refraction index strength on the light propagation in refraction index-varied dielectric material. This dielectric material served as photonic lattice. The behavior of light propagation influenced by variation of refraction index in photonic lattice was investigated. Modes of the guiding light were determined numerically using squared-operator iteration method. It was found that the greater the strength of refraction index, the smaller the guiding modes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Langmuir probe analysis in electronegative plasmas

This paper compares two methods to analyze Langmuir probe data obtained in electronegative plasmas. The techniques are developed to allow investigations in plasmas, where the electronegativity α{sub 0} = n{sub –}/n{sub e} (the ratio between the negative ion and electron densities) varies strongly. The first technique uses an analytical model to express the Langmuir probe current-voltage (I-V) characteristic and its second derivative as a function of the electron and ion densities (n{sub e}, n{sub +}, n{sub –}), temperatures (T{sub e}, T{sub +}, T{sub –}), and masses (m{sub e}, m{sub +}, m{sub –}). The analytical curves are fitted to the experimental data by adjusting these variables and parameters. To reduce the number of fitted parameters, the ion masses are assumed constant within the source volume, and quasi-neutrality is assumed everywhere. In this theory, Maxwellian distributions are assumed for all charged species. We show that this data analysis can predict the various plasma parameters within 5–10%, including the ion temperatures when α{sub 0} > 100. However, the method is tedious, time consuming, and requires a precise measurement of the energy distribution function. A second technique is therefore developed for easier access to the electron and ion densities, but does not give access to the ion temperatures. Here, only the measured I-V characteristic is needed. The electron density, temperature, and ion saturation current for positive ions are determined by classical probe techniques. The electronegativity α{sub 0} and the ion densities are deduced via an iterative method since these variables are coupled via the modified Bohm velocity. For both techniques, a Child-Law sheath model for cylindrical probes has been developed and is presented to emphasize the importance of this model for small cylindrical Langmuir probes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Estimating Jupiter’s Gravity Field Using Juno Measurements, Trajectory Estimation Analysis, and a Flow Model Optimization

The upcoming Juno spacecraft measurements have the potential of improving our knowledge of Jupiter’s gravity field. The analysis of the Juno Doppler data will provide a very accurate reconstruction of spatial gravity variations, but these measurements will be very accurate only over a limited latitudinal range. In order to deduce the full gravity field of Jupiter, additional information needs to be incorporated into the analysis, especially regarding the Jovian flow structure and its depth, which can influence the measured gravity field. In this study we propose a new iterative method for the estimation of the Jupiter gravity field, using a simulated Juno trajectory, a trajectory estimation model, and an adjoint-based inverse model for the flow dynamics. We test this method both for zonal harmonics only and with a full gravity field including tesseral harmonics. The results show that this method can fit some of the gravitational harmonics better to the “measured” harmonics, mainly because of the added information from the dynamical model, which includes the flow structure. Thus, it is suggested that the method presented here has the potential of improving the accuracy of the expected gravity harmonics estimated from the Juno and Cassini radio science experiments.

79 ASTRONOMY AND ASTROPHYSICS↗

POLARIZED LINE FORMATION IN MULTI-DIMENSIONAL MEDIA. IV. A FOURIER DECOMPOSITION TECHNIQUE TO FORMULATE THE TRANSFER EQUATION WITH ANGLE-DEPENDENT PARTIAL FREQUENCY REDISTRIBUTION

To explain the linear polarization observed in spatially resolved structures in the solar atmosphere, the solution of polarized radiative transfer (RT) equation in multi-dimensional (multi-D) geometries is essential. For strong resonance lines, partial frequency redistribution (PRD) effects also become important. In a series of papers, we have been investigating the nature of Stokes profiles formed in multi-D media including PRD in line scattering. For numerical simplicity, so far we have restricted our attention to the particular case of PRD functions which are averaged over all the incident and scattered directions. In this paper, we formulate the polarized RT equation in multi-D media that takes into account the Hanle effect with angle-dependent PRD functions. We generalize here to the multi-D case the method for Fourier series expansion of angle-dependent PRD functions originally developed for RT in one-dimensional geometry. We show that the Stokes source vector S = (S{sub I} , S{sub Q} , S{sub U} ){sup T} and the Stokes vector I = (I, Q, U){sup T} can be expanded in terms of infinite sets of components S-tilde{sup (k)}, I-tilde{sup (k)}, respectively, k in [0, +{infinity}). We show that the components S-tilde{sup (k)} become independent of the azimuthal angle ({psi}) of the scattered ray, whereas the components I-tilde{sup (k)} remain dependent on {psi} due to the nature of RT in multi-D geometry. We also establish that S-tilde{sup (k)} and I-tilde{sup (k)} satisfy a simple transfer equation, which can be solved by any iterative method such as an approximate Lambda iteration or a Bi-Conjugate Gradient-type projection method provided we truncate the Fourier series to have a finite number of terms.

79 ASTRONOMY AND ASTROPHYSICS↗

LINE-INTERLOCKING EFFECTS ON POLARIZATION IN SPECTRAL LINES BY RAYLEIGH AND RAMAN SCATTERING

The polarized spectrum of the Sun and stars is formed from the scattering of anisotropic radiation on atoms. Interpretation of this spectrum requires the solution of polarized line transfer in multilevel atomic systems. While sophisticated quantum theories of polarized line formation in multilevel atomic systems exist, they are limited by the approximation of complete frequency redistribution in scattering. The partial frequency redistribution (PRD) in line scattering is a necessary component in modeling the polarized spectra of strong lines. The polarized PRD line scattering theories developed so far confine themselves to a two-level or a two-term atom model. In this paper, we present a heuristic approach to the problem of polarized line formation in multilevel atoms taking into account the effects of PRD and a weak magnetic field. Starting from the unpolarized PRD multilevel atom approach of Hubeny et al., we incorporate the polarization state of the radiation field. However, the lower level polarization is neglected. Two iterative methods of solving the polarized PRD line transfer in multilevel atoms are also presented. Taking the example of a five-level Ca II atom model, we present illustrative results for an isothermal one-dimensional model atmosphere.

79 ASTRONOMY AND ASTROPHYSICS↗

WE-G-207-04: Non-Local Total-Variation (NLTV) Combined with Reweighted L1-Norm for Compressed Sensing Based CT Reconstruction

Purpose: Compressed sensing (CS) has been used for CT (4DCT/CBCT) reconstruction with few projections to reduce dose of radiation. Total-variation (TV) in L1-minimization (min.) with local information is the prevalent technique in CS, while it can be prone to noise. To address the problem, this work proposes to apply a new image processing technique, called non-local TV (NLTV), to CS based CT reconstruction, and incorporate reweighted L1-norm into it for more precise reconstruction. Methods: TV minimizes intensity variations by considering two local neighboring voxels, which can be prone to noise, possibly damaging the reconstructed CT image. NLTV, contrarily, utilizes more global information by computing a weight function of current voxel relative to surrounding search area. In fact, it might be challenging to obtain an optimal solution due to difficulty in defining the weight function with appropriate parameters. Introducing reweighted L1-min., designed for approximation to ideal L0-min., can reduce the dependence on defining the weight function, therefore improving accuracy of the solution. This work implemented the NLTV combined with reweighted L1-min. by Split Bregman Iterative method. For evaluation, a noisy digital phantom and a pelvic CT images are employed to compare the quality of images reconstructed by TV, NLTV and reweighted NLTV. Results: In both cases, conventional and reweighted NLTV outperform TV min. in signal-to-noise ratio (SNR) and root-mean squared errors of the reconstructed images. Relative to conventional NLTV, NLTV with reweighted L1-norm was able to slightly improve SNR, while greatly increasing the contrast between tissues due to additional iterative reweighting process. Conclusion: NLTV min. can provide more precise compressed sensing based CT image reconstruction by incorporating the reweighted L1-norm, while maintaining greater robustness to the noise effect than TV min.

60 APPLIED LIFE SCIENCES↗

A special generalized HSS method for discrete ill-posed problems

In this paper, we use a new special generalized Hermitian and skew-Hermitian splitting (SGHSS) method for solving ill-posed inverse problems. Based on an augmented system formulation, we apply a new splitting for the Hermitian part of the coefficient matrix and discuss on the convergence of this iterative method. Moreover, the optimal parameter minimizing the spectral radius of iteration matrix is derived. Finally, we present some numerical examples to demonstrate the performance of the presented method.

97 MATHEMATICS AND COMPUTING↗

Seven open problems in applied combinatorics

We present and discuss seven different open problems in applied combinatorics. Additionally, the application areas relevant to this compilation include quantum computing, algorithmic differentiation, topological data analysis, iterative methods, hypergraph cut algorithms, and power systems.

97 MATHEMATICS AND COMPUTING↗

Performance evaluation of OpenFOAM on many-core architectures

In this article application of Open Source Field Operation and Manipulation (OpenFOAM) C++ libraries for solving engineering problems on many-core architectures is presented. Objective of this article is to present scalability of OpenFOAM on parallel platforms solving real engineering problems of fluid dynamics. Scalability test of OpenFOAM is performed using various hardware and different implementation of standard PCG and PBiCG Krylov iterative methods. Speed up of various implementations of linear solvers using GPU and MIC accelerators are presented in this paper. Numerical experiments of 3D lid-driven cavity flow for several cases with various number of cells are presented.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Final Report, DE-FG01-06ER25718 Domain Decomposition and Parallel Computing

The goal of this project is to develop and improve domain decomposition algorithms for a variety of partial differential equations such as those of linear elasticity and electro-magnetics.These iterative methods are designed for massively parallel computing systems and allow the fast solution of the very large systems of algebraic equations that arise in large scale and complicated simulations. A special emphasis is placed on problems arising from Maxwell's equation. The approximate solvers, the preconditioners, are combined with the conjugate gradient method and must always include a solver of a coarse model in order to have a performance which is independent of the number of processors used in the computer simulation. A recent development allows for an adaptive construction of this coarse component of the preconditioner.

97 MATHEMATICS AND COMPUTING↗

Absorption effects in electron-sulfur-dioxide collisions

A joint experimental-theoretical study on electron-SO{sub 2} collisions in the low and intermediate energy range is reported. More specifically, experimental elastic differential, integral, and momentum transfer cross sections in absolute scale are measured in the 100-1000 eV energy range using the relative-flow technique. Calculated elastic differential, integral, and momentum transfer cross sections as well as grand-total and total absorption cross sections are also presented in the 1-1000 eV energy range. A complex optical potential is used to represent the electron-molecule interaction dynamics, whereas the Schwinger variational iterative method combined with the distorted-wave approximation is used to solve the scattering equations. Comparison of the present results is made with the theoretical and experimental results available in the literature.

74 ATOMIC AND MOLECULAR PHYSICS↗

Thermophysical properties of nitrogen plasmas under thermal equilibrium and non-equilibrium conditions

Calculated thermophysical properties of nitrogen plasmas in and out of thermal equilibrium are presented. The cut-off of the partition functions due to the lowering of the ionization potential has been taken into account, together with the contributions from different core excited electronic states. The species composition and thermodynamic properties are determined numerically using the Newton-Raphson iterative method, taking into account the corrections due to Coulomb interactions. The transport properties including diffusion coefficient, viscosity, thermal conductivity, and electrical conductivity are calculated using the most recent collision interaction potentials by adopting Devoto's electron and heavy particle decoupling approach, expanded to the third-order approximation (second-order for viscosity) in the framework of Chapman-Enskog method. Results are presented in the pressure range of 0.1 atm-10 atm and in electron temperature range from 300 to 40 000 K, with the ratio of electron temperature to heavy-particle temperature varied from 1 to 20. Results are compared with those from previous works, and the influences of different definitions of the Debye length are discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Polymer/metal hybrid multilayers modified Schottky devices

Insulating, polymethylmethacrylate (PMMA), and semiconducting, poly(3-hexylthiophene) (P3HT), nanometer thick polymers/Au nanoparticles based hybrid multilayers (HyMLs) were fabricated on p-Si single-crystal substrate. An iterative method, which involves, respectively, spin-coating (PMMA and P3HT deposition) and sputtering (Au nanoparticles deposition) techniques to prepare Au/HyMLs/p-Si Schottky device, was used. The barrier height and the ideality factor of the Au/HyMLs/p-Si Schottky devices were investigated by current-voltage measurements in the thickness range of 1–5 bilayers. It was observed that the barrier height of such hybrid layered systems can be tuned as a function of bilayers number and its evolution was quantified and analyzed.

36 MATERIALS SCIENCE↗

TU-EF-204-04: Feasibility Study of a Novel Stationary Spectral CT Scanner

Purpose: To evaluate a cadmium zinc telluride (CZT) detector module and to develop a proof-of-concept bench-top system to examine the concept and feasibility of a stationary spectral scanner that would consist of a CZT detector ring and a distributed source for rotationless imaging. Methods: The bench-top system employs a double-rotation set-up with two concentric but independent rotating stages, one for turning the object at sparse angles to mimic the imaging from a sequentially activated source distributed on a ring, while the other for translating the detector module to simulate a projection arc along a virtual detector ring. A source of 30-degree fan is used in the set-up, and the ring is designed to be 85cm in diameter in order to provide a 22cm field-of-view that is large enough for an average human head. The CZT detector module has 16×16 0.5mm pixels and eight global energy thresholds, and is attached to an experimental data acquisition board from the same vendor (Nova R&D). Its pixel gain is first calibrated using radioisotope Tc-99m to align the photo-peaks. Count rate performance is assessed using the X-ray source. Air and offset corrections are done prior to each CT scan. A 10cm acrylic phantom with 5 different inserts is imaged at 100kVp, 2mA, with an effective exposure window of 150ms per projection. Reconstruction is done using a total variation-type iterative method. Results: The detector module exhibited large gain variations among pixels. Average count rate was over 1Mcps per pixel. Parallax effect was observed along the arcs but was corrected. Reconstructed images from two energy bins demonstrated good contrast, spatial resolution and image uniformity, with little artifacts. Conclusion: The CZT detector tested is suitable for imaging relatively small objects. A stationary spectral CT appears feasible should we have enough buttable modules and a distributed source. This work was supported by Ministry of Science and Technology of China through grants 11YQ040082 and 2012BAI13B04.

60 APPLIED LIFE SCIENCES↗