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 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

AMPS: An Augmented Matrix Formulation for Principal Submatrix Updates with Application to Power Grids

We present an augmented matrix approach to update the solution to a linear system of equations when the coefficient matrix is modified by a few elements within a principal submatrix. This problem arises in the dynamic security analysis of a power grid, where operators need to perform $N-x$ contingency analysis, i.e., determine the state of the system when up to $x$ links from $N$ fail. Our algorithms augment the coefficient matrix to account for the changes in it, and then compute the solution to the augmented system without refactoring the modified matrix. We provide two algorithms, a direct method, and a hybrid direct-iterative method for solving the augmented system. We also exploit the sparsity of the matrices and vectors to accelerate the overall computation. Our algorithms are compared on three power grids with PARDISO, a parallel direct solver, and CHOLMOD, a direct solver with the ability to modify the Cholesky factors of the coefficient matrix. We show that our augmented algorithms outperform PARDISO (by two orders of magnitude), and CHOLMOD (by a factor of up to 5). Further, our algorithms scale better than CHOLMOD as the number of elements updated increases. The solutions are computed with high accuracy. Our algorithms are capable of computing $N-x$ contingency analysis on a $778K$ bus grid, updating a solution with $x=20$ elements in $1.6 \times 10^{-2}$ seconds on an Intel Xeon processor.

Yeung, Yu-Hong↗
DOE OSTI2012

COYOTE

COYOTE is designed for the analysis of steady and transient, multi-dimensional, nonlinear heat conduction problems. The spatial discretization technique is based on the Galerkin finite element method. The code contains a library of linear and quadratic elements and incudes bars and shells. COYOTE Implicit and explicit time integration methods, with adaptive time step control, are available for transient problems and fixed-point methods are used for Conjugate gradient iterative methods are used for the matrix solution. Coupled enclosure radiation with efficient view factor computation is included. Simulation capabilities include material motion, dynamic radiation enclosures, contact boundary conditions, multipoint constraints, material (element) addition, and deletion, bulk nodes, chemically reactive materials, and coupling with other mechanics codes. The code is designed for single or multi-processor computing

Gartling, DavidK.↗
NASA NTRS1983

Numerical simulation of two-dimensional heat transfer in composite bodies with application to de-icing of aircraft components

Transient, numerical simulations of the de-icing of composite aircraft components by electrothermal heating were performed for a two dimensional rectangular geometry. The implicit Crank-Nicolson formulation was used to insure stability of the finite-difference heat conduction equations and the phase change in the ice layer was simulated using the Enthalpy method. The Gauss-Seidel point iterative method was used to solve the system of difference equations. Numerical solutions illustrating de-icer performance for various composite aircraft structures and environmental conditions are presented. Comparisons are made with previous studies. The simulation can also be used to solve a variety of other heat conduction problems involving composite bodies.

Chao, D. F. K.↗
NASA NTRS1991

Inverse problems in diffraction

A two-dimensional problem of diffraction of a plane electromagnetic wave on a smooth 2 pi-periodic surface is considered. A numerical algorithm solving this problem is developed. An inverse problem of determination of the shape of 2 pi-periodic surface using the performance data of reverse scattering is considered. The inverse problem was solved by means of minimization of the residual functional with the help of the gradient descent method. The initial data were calculated with the help of the numerical method. On each step of the iterative method of minimization, the residual functional was calculated approximately with the help of the small slope method. The examples of the shape determination are considered.

Mikheev, Andrew G.↗
NASA NTRS1992

On the melting temperatures of low-temperature phases of polymorphic metals

An improved analytical formula for determining the melting temperatures of the low-temperature phases of polymorphic metals is proposed which uses the specific heat differences at the equilibrium transition temperatures. The formula is solved by an iterative method, with no more than one iteration necessary to converge. The results obtained using the formula proposed here are generally in good agreement with the analytical solution.

Ohsaka, K.↗
NASA NTRS2021

Skin Friction Extracted from Surface Pressure in Incident Shock-Wave/Boundary-Layer Interaction

High-resolution skin-friction fields are extracted from pressure-sensitive paint (PSP) data obtained in shock-wave/boundary-layer interaction (SWBLI). The method of extracting skin friction from surface pressure is described, including the fundamental relation between skin friction and surface pressure, the variational method, error analysis, and an approximate iterative method. The proposed method is based on a coupling relation between skin friction and surface pressure, where the boundary enstrophy flux is suitably modeled or approximated. This method is applied to unsteady PSP data obtained in incident SWBLIs at Mach 2.5 for different Reynolds numbers, revealing the skin-friction structures of the flows: particularly, the separation bubble induced by the incident shock wave. The extracted results are in good agreement with the data obtained by the surface-stress-sensitive film.

skin friction↗
DOE OSTI2014

Solving security constrained optimal power flow problems by a structure exploiting interior point method

In this paper we present a new approach to solve the DC (n - 1) security constrained optimal power flow (SCOPF) problem by a structure exploiting interior point solver. Our approach is based on a reformulation of the linearised SCOPF model, in which most matrices that need to be factorized are constant. Hence, most factorizations and a large number of back-solve operations only need to be performed once. However, assembling the Schur complement matrix remains expensive in this scheme. To reduce the effort, we suggest using a preconditioned iterative method to solve the corresponding linear system. We suggest two main schemes to pick a good and robust preconditioner based on combining different “active” contingency scenarios of the SCOPF model. These new schemes are implemented within the object-oriented parallel solver (OOPS), a structure-exploiting primal-dual interior-point implementation. We give results on several SCOPF test problems. The largest example contains 500 buses. We compare the results from the original interior point method (IPM) implementation in OOPS and our new reformulation.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2015

First and second order operator splitting methods for the phase field crystal equation

In this paper, we present operator splitting methods for solving the phase field crystal equation which is a model for the microstructural evolution of two-phase systems on atomic length and diffusive time scales. A core idea of the methods is to decompose the original equation into linear and nonlinear subequations, in which the linear subequation has a closed-form solution in the Fourier space. We apply a nonlinear Newton-type iterative method to solve the nonlinear subequation at the implicit time level and thus a considerably large time step can be used. By combining these subequations, we achieve the first- and second-order accuracy in time. We present numerical experiments to show the accuracy and efficiency of the proposed methods.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1984

Development of MCAERO wing design panel method with interactive graphics module

A reliable and efficient iterative method has been developed for designing wing section contours corresponding to a prescribed subcritical pressure distribution. The design process is initialized by using MCAERO (MCAIR 3-D Subsonic Potential Flow Analysis Code) to analyze a baseline configuration. A second program DMCAERO is then used to calculate a matrix containing the partial derivative of potential at each control point with respect to each unknown geometry parameter by applying a first-order expansion to the baseline equations in MCAERO. This matrix is calculated only once but is used in each iteration cycle to calculate the geometry perturbation and to analyze the perturbed geometry. The potential on the new geometry is calculated by linear extrapolation from the baseline solution. This extrapolated potential is converted to velocity by numerical differentiation, and velocity is converted to pressure by using Bernoulli's equation. There is an interactive graphics option which allows the user to graphically display the results of the design process and to interactively change either the geometry or the prescribed pressure distribution.

Hawk, J. D.↗
NASA NTRS2017

Accuracy/Computation Performance of a New Trilateration Scheme for GPS-Style Localization

We recently introduced a new geometric trilateration (GT) method for GPS-style positioning. Preliminary singlepoint analysis using simplistic error assumptions indicates that the new scheme delivers almost indistinguishable localization accuracy as the traditional Newton-Raphson (NR) approach. Also, the same computation procedure can be used to perform high-accuracy relative positioning between a reference vehicle and an arbitrary number of target vehicles. This scheme has the potential to enable a) new mission concepts in collaborative science, b) in-situ navigation services for human Mars missions, and c) lower cost and faster acquisition of GPS signals for consumer-grade GPS products. The new GT scheme differs from the NR scheme as follows: 1. The new scheme is derived from Pythagoras Theorem, whereas the NR method is based on the principle of linear regression. 2. The NR method uses the absolute locations (xi, yi, zi)’s of the GPS satellites as input to each step of the localization computation. The GT method uses the Directional Cosines Ui’s from Earth’s center to the GPS satellite Si. 3. Both the NR method and the GT method iterate to converge to a localized solution. In each iteration step, multiple matrix operations are performed. The NR method constructs a different matrix in each iterative step, thus requires performing a new set of matrix operations in each step. The GT scheme uses the same matrix in each iteration, thus requiring computing the matrix operations only once for all subsequent iterations. In this paper, we perform an in-depth comparison between the GT scheme and the NR method in terms of a) GPS localization accuracy in the GPS operation environment, b) its sensitivity with respect to systematic errors and random errors, and c) computation load required to converge to a localization solution.

Lee, Charles↗
DOE OSTI2014

Effect of time-of-flight and point spread function modeling on detectability of myocardial defects in PET

Purpose: A study was designed to investigate the impact of time-of-flight (TOF) and point spread function (PSF) modeling on the detectability of myocardial defects. Methods: Clinical FDG-PET data were used to generate populations of defect-present and defect-absent images. Defects were incorporated at three contrast levels, and images were reconstructed by ordered subset expectation maximization (OSEM) iterative methods including ordinary Poisson, alone and with PSF, TOF, and PSF+TOF. Channelized Hotelling observer signal-to-noise ratio (SNR) was the surrogate for human observer performance. Results: For three iterations, 12 subsets, and no postreconstruction smoothing, TOF improved overall defect detection SNR by 8.6% as compared to its non-TOF counterpart for all the defect contrasts. Due to the slow convergence of PSF reconstruction, PSF yielded 4.4% less SNR than non-PSF. For reconstruction parameters (iteration number and postreconstruction smoothing kernel size) optimizing observer SNR, PSF showed larger improvement for faint defects. The combination of TOF and PSF improved mean detection SNR as compared to non-TOF and non-PSF counterparts by 3.0% and 3.2%, respectively. Conclusions: For typical reconstruction protocol used in clinical practice, i.e., less than five iterations, TOF improved defect detectability. In contrast, PSF generally yielded less detectability. For large number of iterations, TOF+PSF yields the best observer performance.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
NASA NTRS1988

Domain decomposition methods for the parallel computation of reacting flows

Domain decomposition is a natural route to parallel computing for partial differential equation solvers. Subdomains of which the original domain of definition is comprised are assigned to independent processors at the price of periodic coordination between processors to compute global parameters and maintain the requisite degree of continuity of the solution at the subdomain interfaces. In the domain-decomposed solution of steady multidimensional systems of PDEs by finite difference methods using a pseudo-transient version of Newton iteration, the only portion of the computation which generally stands in the way of efficient parallelization is the solution of the large, sparse linear systems arising at each Newton step. For some Jacobian matrices drawn from an actual two-dimensional reacting flow problem, comparisons are made between relaxation-based linear solvers and also preconditioned iterative methods of Conjugate Gradient and Chebyshev type, focusing attention on both iteration count and global inner product count. The generalized minimum residual method with block-ILU preconditioning is judged the best serial method among those considered, and parallel numerical experiments on the Encore Multimax demonstrate for it approximately 10-fold speedup on 16 processors.

Keyes, David E.↗
DOE OSTI2015

MO-FG-204-01: Improved Noise Suppression for Dual-Energy CT Through Entropy Minimization

Purpose: In dual energy CT (DECT), noise amplification during signal decomposition significantly limits the utility of basis material images. Since clinically relevant objects contain a limited number of materials, we propose to suppress noise for DECT based on image entropy minimization. An adaptive weighting scheme is employed during noise suppression to improve decomposition accuracy with limited effect on spatial resolution and image texture preservation. Methods: From decomposed images, we first generate a 2D plot of scattered data points, using basis material densities as coordinates. Data points representing the same material generate a highly asymmetric cluster. We orient an axis by minimizing the entropy in a 1D histogram of these points projected onto the axis. To suppress noise, we replace pixel values of decomposed images with center-of-mass values in the direction perpendicular to the optimal axis. To limit errors due to cluster overlap, we weight each data point’s contribution based on its high and low energy CT values and location within the image. The proposed method’s performance is assessed on physical phantom studies. Electron density is used as the quality metric for decomposition accuracy. Our results are compared to those without noise suppression and with a recently developed iterative method. Results: The proposed method reduces noise standard deviations of the decomposed images by at least one order of magnitude. On the Catphan phantom, this method greatly preserves the spatial resolution and texture of the CT images and limits induced error in measured electron density to below 1.2%. In the head phantom study, the proposed method performs the best in retaining fine, intricate structures. Conclusion: The entropy minimization based algorithm with adaptive weighting substantially reduces DECT noise while preserving image spatial resolution and texture. Future investigations will include extensive investigations on material decomposition accuracy that go beyond the current electron density calculations. This work was supported in part by the National Institutes of Health (NIH) under Grant Number R21 EB012700.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

Recent progress in 3-D imaging of sea freight containers

The inspection of very large objects like sea freight containers with X-ray Computed Tomography (CT) is an emerging technology. A complete 3-D CT scan of a see-freight container takes several hours. Of course, this is too slow to apply it to a large number of containers. However, the benefits of a 3-D CT for sealed freight are obvious: detection of potential threats or illicit cargo without being confronted with legal complications or high time consumption and risks for the security personnel during a manual inspection. Recently distinct progress was made in the field of reconstruction of projections with only a relatively low number of angular positions. Instead of today’s 500 to 1000 rotational steps, as needed for conventional CT reconstruction techniques, this new class of algorithms provides the potential to reduce the number of projection angles approximately by a factor of 10. The main drawback of these advanced iterative methods is the high consumption for numerical processing. But as computational power is getting steadily cheaper, there will be practical applications of these complex algorithms in a foreseeable future. In this paper, we discuss the properties of iterative image reconstruction algorithms and show results of their application to CT of extremely large objects scanning a sea-freight container. A specific test specimen is used to quantitatively evaluate the image quality in terms of spatial and contrast resolution and depending on different number of projections.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

TH-EF-207A-05: Feasibility of Applying SMEIR Method On Small Animal 4D Cone Beam CT Imaging

Purpose: Small animal cone beam CT imaging has been widely used in preclinical research. Due to the higher respiratory rate and heat beats of small animals, motion blurring is inevitable and needs to be corrected in the reconstruction. Simultaneous motion estimation and image reconstruction (SMEIR) method, which uses projection images of all phases, proved to be effective in motion model estimation and able to reconstruct motion-compensated images. We demonstrate the application of SMEIR for small animal 4D cone beam CT imaging by computer simulations on a digital rat model. Methods: The small animal CBCT imaging system was simulated with the source-to-detector distance of 300 mm and the source-to-object distance of 200 mm. A sequence of rat phantom were generated with 0.4 mm{sup 3} voxel size. The respiratory cycle was taken as 1.0 second and the motions were simulated with a diaphragm motion of 2.4mm and an anterior-posterior expansion of 1.6 mm. The projection images were calculated using a ray-tracing method, and 4D-CBCT were reconstructed using SMEIR and FDK methods. The SMEIR method iterates over two alternating steps: 1) motion-compensated iterative image reconstruction by using projections from all respiration phases and 2) motion model estimation from projections directly through a 2D-3D deformable registration of the image obtained in the first step to projection images of other phases. Results: The images reconstructed using SMEIR method reproduced the features in the original phantom. Projections from the same phase were also reconstructed using FDK method. Compared with the FDK results, the images from SMEIR method substantially improve the image quality with minimum artifacts. Conclusion: We demonstrate that it is viable to apply SMEIR method to reconstruct small animal 4D-CBCT images.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2018

AdS spacetime in Lorentz covariant gauges

We show how to generate the AdS spacetime metric in general Lorentz covariant gauges. In particular we propose an iterative method for solving the Lorentz gauge.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Detailed Characterization of CZT Detector Response for Improved Coded-Aperture Imaging Performance

Gamma-ray imaging is a powerful method for locating and quantifying sources of radiation. The coded-aperture technique demonstrates superior angular resolution in comparison to other methods (e.g., Compton reconstruction). In this method, a mask constructed of highly attenuating material encodes the scene as a shadow pattern on a position-sensitive detector; this pattern can then be used to recreate the origin(s) of incident radiation. This is typically done through convolution of the mask and shadow patterns. Iterative methods which attempt to reconstruct the observed shadow pattern using a weighted combination of simulated patterns may also be employed. In either case, errors in event position reconstruction due to detector imperfections alter the shadow pattern and will therefore degrade system performance and may introduce imaging artifacts. These effects can be mitigated with a detailed understanding of such errors – allowing for the generation of representative simulations that include the errors and/or correction of raw imager data to remove the errors. We present a calibration process for a commercially available cadmium zinc telluride (CZT) gamma imager which provides a comprehensive characterization of the spatial and energy dependence of event reconstruction. By illuminating a mask featuring a regular grid of pinholes with a calibration source, the localized response of the detector can be measured with fine granularity. These local responses are combined to generate a full detector response map which can be used to distort simulations in a manner that is representative of the observed detector data. Details of the calibration procedure and an assessment of the impact of its end products on the performance of iterative imaging methods will be presented.

Ziock, Klaus-Peter↗