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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

The Iterated Fission Matrix Method

The fission matrix (FM) method has been successfully demonstrated for different applications. One of the interesting features of this method, which is not possible via standard criticality source Monte Carlo calculations, is the capability to calculate higher forward and adjoint Eigenmodes; however, the accuracy of the estimates for higher eigenvalues strongly depends on the spatial discretization adopted for the fission matrix. A fine mesh ensures accurate results but requires matrices of large size. This is considered a limitation to the applicability of the FM method due to the memory requirements for storage of large full matrices. The adoption of sparse matrix storage (e.g., in MCNP) partially overcomes this problem; nonetheless, the sparse matrix indexing increases the complexity of the implementation of the FM algorithm and introduces the additional task of sparsifying the fission matrix. This summary presents a new method, named the iterated fission matrix (IFM), that allows to estimate higher eigenvalues of multiplying systems on much smaller meshes, but with the same level of accuracy in terms of spatial discretization errors, as compared to the FM method. The following Sections describe this new approach and provide a demonstration using two case studies: a PWR fuel assembly, and a 2D PWR core. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2016

Iterative algorithms for processing experimental data

The need to solve linear and nonlinear integral equations arise, e.g., in recovering plasma parameters from the data of multichannel diagnostics. The paper presents an iterative method for solving integral equations with a singularity at the upper limit of integration. The method consists in constructing successive approximations and calculating the integral by quadrature formulas in each integration interval. An example of application of the iterative algorithm to numerically solve an integral equation similar to those arising in recovering the plasma density profile from reflectometry data is presented.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Considering nonlocality in the optical potentials within eikonal models

Background: For its simplicity, the eikonal method is the tool of choice to analyze nuclear reactions at high energies (E > 100 MeV/nucleon), including knockout reactions. However, so far, the effective interactions used in this method are assumed to be fully local. Purpose: Given the recent studies on nonlocal optical potentials, in this work we assess whether nonlocality in the optical potentials is expected to impact reactions at high energies and then explore different avenues for extending the eikonal method to include nonlocal interactions. Method: We compare angular distributions obtained for nonlocal interactions (using the exact R-matrix approach for elastic scattering and the adiabatic distorted wave approximation for transfer) with those obtained using their local-equivalent interactions. Results: Our results show that transfer observables are significantly impacted by nonlocality in the high-energy regime. Because knockout reactions are dominated by stripping (transfer to inelastic channels), nonlocality is expected to have a large effect on knockout observables too. Three approaches are explored for extending the eikonal method to nonlocal interactions, including an iterative method and a perturbation theory. Conclusions: None of the derived extensions of the eikonal model provide a good description of elastic scattering. Here, this paper suggests that nonlocality removes the formal simplicity associated with the eikonal model.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
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.↗
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↗
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↗
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↗
DOE OSTI2016

Alignment and position visualization methods for the biomedical imaging and therapy (BMIT) MRT lift

The Microbeam Radiation Therapy (MRT) Lift is an eight stage positioning and scanning system at the Canadian Light Source’s BMIT Facility. Alignment of the sample with the beam using the MRT Lift is a time consuming and challenging task. The BMIT Group has developed a Python-based MRT Lift positioning and control program that uses a combination of computational and iterative methods to independently adjust the sample’s X, Y, Z, pitch and roll positions. The program offers “1-Click” alignment of the sample to the beam. Use of a wireframe visualization technique enables even minute movements to be illustrated. Proposed movements and the resulting MRT Lift position can be manually verified before being applied. Optional integration with the SolidWorks modelling platform allows high quality renderings of the MRT Lift in its current or proposed position to be displayed in real time. Human factors principles are incorporated into the program with the objective of delivering easy to use controls for this complex device.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2017

Continuation of probability density functions using a generalized Lyapunov approach

Techniques from numerical bifurcation theory are very useful to study transitions between steady fluid flow patterns and the instabilities involved. Here, we provide computational methodology to use parameter continuation in determining probability density functions of systems of stochastic partial differential equations near fixed points, under a small noise approximation. Key innovation is the efficient solution of a generalized Lyapunov equation using an iterative method involving low-rank approximations. We apply and illustrate the capabilities of the method using a problem in physical oceanography, i.e. the occurrence of multiple steady states of the Atlantic Ocean circulation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

A preconditioning technique for Schur complement systems arising in stochastic optimization

Deterministic sample average approximations of stochastic programming problems with recourse are suitable for a scenario-based parallelization. In this paper the parallelization is obtained by using an interior-point method and a Schur complement mechanism for the interior-point linear systems. However, the direct linear solves involving the dense Schur complement matrix are expensive, and adversely affect the scalability of this approach. We address this issue by proposing a stochastic preconditioner for the Schur complement matrix and by using Krylov iterative methods for the solution of the dense linear systems. The stochastic preconditioner is built based on a subset of existing scenarios and can be assembled and factorized on a separate process before the computation of the Schur complement matrix finishes on the remaining processes. The expensive factorization of the Schur complement is removed from the parallel execution flow and the scaling of the optimization solver is considerably improved with this approach. The spectral analysis indicates an exponentially fast convergence in probability to 1 of the eigenvalues of the preconditioned matrix with the number of scenarios incorporated in the preconditioner. Numerical experiments performed on the relaxation of a unit commitment problem show good performance, in terms of both the accuracy of the solution and the execution time.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2012

Automated convergence detection in Monte Carlo criticality calculations using student's bridge statistics based on K{sub eff} or Shannon entropy

Monte Carlo (MC) criticality calculations are based on an iterative method. It requires a converged fission source distribution before beginning tallying the effective multiplication factor (K{sub eff}) or other quantities of interest. However, it is pretty difficult to locate on the run, the end of the source convergence and scores may be biased by an initial transient. This paper deals with a method that locates and suppresses the transient due to the initialization in an output series, applied here to K{sub eff} and Shannon entropy. It relies on modeling stationary series by an order 1 auto regressive process and applying statistical tests based on a Student Bridge statistics. It should be noticed that the initial transient suppression only aims at obtaining stationary output series and cannot guarantee any kind of convergence. The truncation method is applied on both K{sub eff} and Shannon entropy on three test cases. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Accelerating eigenvalue computation for nuclear structure calculations via perturbative corrections

Subspace projection methods utilizing perturbative corrections have been proposed for computing the lowest few eigenvalues and corresponding eigenvectors of large Hamiltonian matrices. In this paper, we build upon these methods and introduce the term Subspace Projection with Perturbative Corrections (SPPC) method to refer to this approach. We tailor the SPPC for nuclear many-body Hamiltonians represented in a truncated configuration interaction subspace, i.e., the no-core shell model (NCSM). We use the hierarchical structure of the NCSM Hamiltonian to partition the Hamiltonian as the sum of two matrices. The first matrix corresponds to the Hamiltonian represented in a small configuration space, whereas the second is viewed as the perturbation to the first matrix. Eigenvalues and eigenvectors of the first matrix can be computed efficiently. Because of the split, perturbative corrections to the eigenvectors of the first matrix can be obtained efficiently from the solutions of a sequence of linear systems of equations defined in the small configuration space. These correction vectors can be combined with the approximate eigenvectors of the first matrix to construct a subspace from which more accurate approximations of the desired eigenpairs can be obtained. We show by numerical examples that the SPPC method can be more efficient than conventional iterative methods for solving large-scale eigenvalue problems such as the Lanczos, block Lanczos and the locally optimal block preconditioned conjugate gradient (LOBPCG) method. The method can also be combined with other methods to avoid convergence stagnation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗