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All sourcesNASA NTRSDOE OSTI
DOE OSTI2012

X-ray phase laminography with a grating interferometer using iterative reconstruction

X-ray phase computed laminography is performed using a Talbot interferometer and synchrotron radiation. An iterative reconstruction algorithm which includes prior information about limited support, range of values and sparsity of the imaged object has been developped. It allows the reconstruction of objects with an improved resolution of the unsampled frequencies, compared to the classical filtered backprojection. The imaging method, demonstrated for a nylon mesh sample and a leaf sample, shows promising results for the imaging of flat, laterally extended objects made of low absorbing elements.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2013

Improving IMRT delivery efficiency with reweighted L1-minimization for inverse planning

Purpose: This study presents an improved technique to further simplify the fluence-map in intensity modulated radiation therapy (IMRT) inverse planning, thereby reducing plan complexity and improving delivery efficiency, while maintaining the plan quality.Methods: First-order total-variation (TV) minimization (min.) based on L1-norm has been proposed to reduce the complexity of fluence-map in IMRT by generating sparse fluence-map variations. However, with stronger dose sparing to the critical structures, the inevitable increase in the fluence-map complexity can lead to inefficient dose delivery. Theoretically, L0-min. is the ideal solution for the sparse signal recovery problem, yet practically intractable due to its nonconvexity of the objective function. As an alternative, the authors use the iteratively reweighted L1-min. technique to incorporate the benefits of the L0-norm into the tractability of L1-min. The weight multiplied to each element is inversely related to the magnitude of the corresponding element, which is iteratively updated by the reweighting process. The proposed penalizing process combined with TV min. further improves sparsity in the fluence-map variations, hence ultimately enhancing the delivery efficiency. To validate the proposed method, this work compares three treatment plans obtained from quadratic min. (generally used in clinic IMRT), conventional TV min., and our proposed reweighted TV min. techniques, implemented by a large-scale L1-solver (template for first-order conic solver), for five patient clinical data. Criteria such as conformation number (CN), modulation index (MI), and estimated treatment time are employed to assess the relationship between the plan quality and delivery efficiency.Results: The proposed method yields simpler fluence-maps than the quadratic and conventional TV based techniques. To attain a given CN and dose sparing to the critical organs for 5 clinical cases, the proposed method reduces the number of segments by 10-15 and 30-35, relative to TV min. and quadratic min. based plans, while MIs decreases by about 20%-30% and 40%-60% over the plans by two existing techniques, respectively. With such conditions, the total treatment time of the plans obtained from our proposed method can be reduced by 12-30 s and 30-80 s mainly due to greatly shorter multileaf collimator (MLC) traveling time in IMRT step-and-shoot delivery.Conclusions: The reweighted L1-minimization technique provides a promising solution to simplify the fluence-map variations in IMRT inverse planning. It improves the delivery efficiency by reducing the entire segments and treatment time, while maintaining the plan quality in terms of target conformity and critical structure sparing.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2016

A robust real-time surface reconstruction method on point clouds captured from a 3D surface photogrammetry system

Purpose: To develop a robust and real-time surface reconstruction method on point clouds captured from a 3D surface photogrammetry system. Methods: The authors have developed a robust and fast surface reconstruction method on point clouds acquired by the photogrammetry system, without explicitly solving the partial differential equation required by a typical variational approach. Taking advantage of the overcomplete nature of the acquired point clouds, their method solves and propagates a sparse linear relationship from the point cloud manifold to the surface manifold, assuming both manifolds share similar local geometry. With relatively consistent point cloud acquisitions, the authors propose a sparse regression (SR) model to directly approximate the target point cloud as a sparse linear combination from the training set, assuming that the point correspondences built by the iterative closest point (ICP) is reasonably accurate and have residual errors following a Gaussian distribution. To accommodate changing noise levels and/or presence of inconsistent occlusions during the acquisition, the authors further propose a modified sparse regression (MSR) model to model the potentially large and sparse error built by ICP with a Laplacian prior. The authors evaluated the proposed method on both clinical point clouds acquired under consistent acquisition conditions and on point clouds with inconsistent occlusions. The authors quantitatively evaluated the reconstruction performance with respect to root-mean-squared-error, by comparing its reconstruction results against that from the variational method. Results: On clinical point clouds, both the SR and MSR models have achieved sub-millimeter reconstruction accuracy and reduced the reconstruction time by two orders of magnitude to a subsecond reconstruction time. On point clouds with inconsistent occlusions, the MSR model has demonstrated its advantage in achieving consistent and robust performance despite the introduced occlusions. Conclusions: The authors have developed a fast and robust surface reconstruction method on point clouds captured from a 3D surface photogrammetry system, with demonstrated sub-millimeter reconstruction accuracy and subsecond reconstruction time. It is suitable for real-time motion tracking in radiotherapy, with clear surface structures for better quantifications.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2014

Improved spectral data unfolding for radiochromic film imaging spectroscopy of laser-accelerated proton beams

An improved method to unfold the space-resolved proton energy distribution function of laser-accelerated proton beams using a layered, radiochromic film (RCF) detector stack has been developed. The method takes into account the reduced RCF response near the Bragg peak due to a high linear energy transfer (LET). This LET dependence of the active RCF layer has been measured, and published data have been re-interpreted to find a nonlinear saturation scaling of the RCF response with stopping power. Accounting for the LET effect increased the integrated particle yield by 25% after data unfolding. An iterative, analytical, space-resolved deconvolution of the RCF response functions from the measured dose was developed that does not rely on fitting. After the particle number unfold, three-dimensional interpolation is performed to determine the spatial proton beam distribution for proton energies in-between the RCF data points. Here, image morphing has been implemented as a novel interpolation method that takes into account the energy-dependent, changing beam topology.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2015

TU-EF-204-03: Task-Based KV and MAs Optimization for Radiation Dose Reduction in CT: From FBP to Statistical Model-Based Iterative Reconstruction (MBIR)

Purpose: The introduction of the highly nonlinear MBIR algorithm to clinical CT systems has made CNR an invalid metric for kV optimization. The purpose of this work was to develop a task-based framework to unify kV and mAs optimization for both FBP- and MBIR-based CT systems. Methods: The kV-mAs optimization was formulated as a constrained minimization problem: to select kV and mAs to minimize dose under the constraint of maintaining the detection performance as clinically prescribed. To experimentally solve this optimization problem, exhaustive measurements of detectability index (d’) for a hepatic lesion detection task were performed at 15 different mA levels and 4 kV levels using an anthropomorphic phantom. The measured d’ values were used to generate an iso-detectability map; similarly, dose levels recorded at different kV-mAs combinations were used to generate an iso-dose map. The iso-detectability map was overlaid on top of the iso-dose map so that for a prescribed detectability level d’, the optimal kV-mA can be determined from the crossing between the d’ contour and the dose contour that corresponds to the minimum dose. Results: Taking d’=16 as an example: the kV-mAs combinations on the measured iso-d’ line of MBIR are 80–150 (3.8), 100–140 (6.6), 120–150 (11.3), and 140–160 (17.2), where values in the parentheses are measured dose values. As a Result, the optimal kV was 80 and optimal mA was 150. In comparison, the optimal kV and mA for FBP were 100 and 500, which corresponded to a dose level of 24 mGy. Results of in vivo animal experiments were consistent with the phantom results. Conclusion: A new method to optimize kV and mAs selection has been developed. This method is applicable to both linear and nonlinear CT systems such as those using MBIR. Additional dose savings can be achieved by combining MBIR with this method. This work was partially supported by an NIH grant R01CA169331 and GE Healthcare. K. Li, D. Gomez-Cardona, M. G. Lubner: Nothing to disclose. P. J. Pickhardt: Co-founder, VirtuoCTC, LLC Stockholder, Cellectar Biosciences, Inc. G.-H. Chen: Research funded, GE Healthcare; Research funded, Siemens AX.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2018

Performance of preconditioned iterative solvers in MFiX–Trilinos for fluidized beds

MFiX, a general-purpose Fortran-based suite, simulates the complex flow in fluidized bed applications via BiCGStab and GMRES methods along with plane relaxation preconditioners. Trilinos, an object-oriented framework, contains various first- and second-generation Krylov subspace solvers and preconditioners. We developed a framework to integrate MFiX with Trilinos as MFiX does not possess advanced linear methods. The framework allows MFiX to access advanced linear solvers and preconditioners in Trilinos. The integrated solver is called MFiX–Trilinos, here after. In the present work, we study the performance of variants of GMRES and CGS methods in MFiX–Trilinos and BiCGStab and GMRES solvers in MFiX for a 3D gas–solid fluidized bed problem. Two right preconditioners employed along with various solvers in MFiX–Trilinos are Jacobi and smoothed aggregation. The flow from MFiX–Trilinos is validated against the same from MFiX for BiCGStab and GMRES methods. And, the effect of the preconditioning on the iterative solvers in MFiX–Trilinos is also analyzed. In addition, the effect of left and right smoothed aggregation preconditioning on the solvers is studied. Finally, the performance of the first- and second-generation solver stacks in MFiX–Trilinos is studied as well for two different problem sizes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Fast Multigrid Reduction-in-Time for Advection via Modified Semi-Lagrangian Coarse-Grid Operators

Many iterative parallel-in-time algorithms have been shown to be highly efficient for diffusion-dominated partial differential equations (PDEs) but are inefficient or even divergent when applied to advection-dominated PDEs. We consider the application of the multigrid reduction-in-time (MGRIT) algorithm to linear advection PDEs. Here, the key to efficient time integration with this method is using a coarse-grid operator that provides a sufficiently accurate approximation to the so-called ideal coarse-grid operator. For certain classes of semi-Lagrangian discretizations, we present a novel semi-Lagrangian-based coarse-grid operator that leads to fast and scalable multilevel time integration of linear advection PDEs. The coarse-grid operator is composed of a semi-Lagrangian discretization followed by a correction term, with the correction designed so that the leading-order truncation error of the composite operator is approximately equal to that of the ideal coarse-grid operator. Parallel results show substantial speed-ups over sequential time integration for variable-wave-speed advection problems in one and two spatial dimensions, and using high-order discretizations up to order five. The proposed approach establishes the first practical method that provides small and scalable MGRIT iteration counts for advection problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Inferring and evaluating satellite-based constraints on NO x emissions estimates in air quality simulations

Satellite observations of tropospheric NO 2 columns can provide top-down observational constraints on emissions estimates of nitrogen oxides (NO x ). Mass-balance-based methods are often applied for this purpose but do not isolate near-surface emissions from those aloft, such as lightning emissions. Here, we introduce an inverse modeling framework that couples satellite chemical data assimilation to a chemical transport model. In the framework, satellite-constrained emissions totals are inferred using model simulations with and without data assimilation in the iterative finite-difference mass-balance method. The approach improves the finite-difference mass-balance inversion by isolating the near-surface emissions increment. We apply the framework to separately estimate lightning and anthropogenic NO x emissions over the Northern Hemisphere for 2019. Using overlapping observations from the Ozone Monitoring Instrument (OMI) and the Tropospheric Monitoring Instrument (TROPOMI), we compare separate NO x emissions inferences from these satellite instruments, as well as the impacts of emissions changes on modeled NO 2 and O 3 . OMI inferences of anthropogenic emissions consistently lead to larger emissions than TROPOMI inferences, attributed to a low bias in TROPOMI NO 2 retrievals. Updated lightning NO x emissions from either satellite improve the chemical transport model's low tropospheric O 3 bias. The combined lighting and anthropogenic emissions updates improve the model's ability to reproduce measured ozone by adjusting natural, long-range, and local pollution contributions. Thus, the framework informs and supports the design of domestic and international control strategies.

54 ENVIRONMENTAL SCIENCES↗
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↗
DOE OSTI2023

Performance Analysis and Optimal Node-aware Communication for Enlarged Conjugate Gradient Methods

Krylov methods are a key way of solving large sparse linear systems of equations but suffer from poor strong scalability on distributed memory machines. Furthermore, this is due to high synchronization costs from large numbers of collective communication calls alongside a low computational workload. Enlarged Krylov methods address this issue by decreasing the total iterations to convergence, an artifact of splitting the initial residual and resulting in operations on block vectors. In this article, we present a performance study of an enlarged Krylov method, Enlarged Conjugate Gradients (ECG), noting the impact of block vectors on parallel performance at scale. Most notably, we observe the increased overhead of point-to-point communication as a result of denser messages in the sparse matrix-block vector multiplication kernel. Additionally, we present models to analyze expected performance of ECG, as well as motivate design decisions. Most importantly, we introduce a new point-to-point communication approach based on node-aware communication techniques that increases efficiency of the method at scale.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Two-Level Chebyshev Filter Based Complementary Subspace Method: Pushing the Envelope of Large-Scale Electronic Structure Calculations

We describe here a novel iterative strategy for Kohn–Sham density functional theory calculations aimed at large systems (>1,000 electrons), applicable to metals and insulators alike. In lieu of explicit diagonalization of the Kohn–Sham Hamiltonian on every self-consistent field (SCF) iteration, we employ a two-level Chebyshev polynomial filter based complementary subspace strategy to (1) compute a set of vectors that span the occupied subspace of the Hamiltonian; (2) reduce subspace diagonalization to just partially occupied states; and (3) obtain those states in an efficient, scalable manner via an inner Chebyshev filter iteration. By reducing the necessary computation to just partially occupied states and obtaining these through an inner Chebyshev iteration, our approach reduces the cost of large metallic calculations significantly, while eliminating subspace diagonalization for insulating systems altogether. We describe the implementation of the method within the framework of the discontinuous Galerkin (DG) electronic structure method and show that this results in a computational scheme that can effectively tackle bulk and nano systems containing tens of thousands of electrons, with chemical accuracy, within a few minutes or less of wall clock time per SCF iteration on large-scale computing platforms. We anticipate that our method will be instrumental in pushing the envelope of large-scale ab initio molecular dynamics. As a demonstration of this, we simulate a bulk silicon system containing 8,000 atoms at finite temperature, and obtain an average SCF step wall time of 51 s on 34,560 processors; thus allowing us to carry out 1.0 ps of ab initio molecular dynamics in approximately 28 h (of wall time).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

SU-C-BRD-07: Three-Dimensional Dose Reconstruction in the Presence of Inhomogeneities Using Fast EPID-Based Back-Projection Method

Purpose: Three-dimensional dose verification can detect errors introduced by the treatment planning system (TPS) or differences between planned and delivered dose distribution during the treatment. The aim of the study is to extend a previous in-house developed three-dimensional dose reconstructed model in homogeneous phantom to situtions in which tissue inhomogeneities are present. Methods: The method was based on the portal grey images from an electronic portal imaging device (EPID) and the relationship between beamlets and grey-scoring voxels at the position of the EPID. The relationship was expressed in the form of grey response matrix that was quantified using thickness-dependence scatter kernels determined by series of experiments. From the portal grey-value distribution information measured by the EPID the two-dimensional incident fluence distribution was reconstructed based on the grey response matrix using a fast iterative algorithm. The accuracy of this approach was verified using a four-field intensity-modulated radiotherapy (IMRT) plan for the treatment of lung cancer in anthopomorphic phantom. Each field had between twenty and twenty-eight segments and was evaluated by comparing the reconstructed dose distribution with the measured dose. Results: The gamma-evaluation method was used with various evaluation criteria of dose difference and distance-to-agreement: 3%/3mm and 2%/2 mm. The dose comparison for all irradiated fields showed a pass rate of 100% with the criterion of 3%/3mm, and a pass rate of higher than 92% with the criterion of 2%/2mm. Conclusion: Our experimental results demonstrate that our method is capable of accurately reconstructing three-dimensional dose distribution in the presence of inhomogeneities. Using the method, the combined planning and treatment delivery process is verified, offing an easy-to-use tool for the verification of complex treatments.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

MO-F-CAMPUS-I-04: Characterization of Fan Beam Coded Aperture Coherent Scatter Spectral Imaging Methods for Differentiation of Normal and Neoplastic Breast Structures

Purpose: This study intends to characterize the spectral and spatial resolution limits of various fan beam geometries for differentiation of normal and neoplastic breast structures via coded aperture coherent scatter spectral imaging techniques. In previous studies, pencil beam raster scanning methods using coherent scatter computed tomography and selected volume tomography have yielded excellent results for tumor discrimination. However, these methods don’t readily conform to clinical constraints; primarily prolonged scan times and excessive dose to the patient. Here, we refine a fan beam coded aperture coherent scatter imaging system to characterize the tradeoffs between dose, scan time and image quality for breast tumor discrimination. Methods: An X-ray tube (125kVp, 400mAs) illuminated the sample with collimated fan beams of varying widths (3mm to 25mm). Scatter data was collected via two linear-array energy-sensitive detectors oriented parallel and perpendicular to the beam plane. An iterative reconstruction algorithm yields images of the sample’s spatial distribution and respective spectral data for each location. To model in-vivo tumor analysis, surgically resected breast tumor samples were used in conjunction with lard, which has a form factor comparable to adipose (fat). Results: Quantitative analysis with current setup geometry indicated optimal performance for beams up to 10mm wide, with wider beams producing poorer spatial resolution. Scan time for a fixed volume was reduced by a factor of 6 when scanned with a 10mm fan beam compared to a 1.5mm pencil beam. Conclusion: The study demonstrates the utility of fan beam coherent scatter spectral imaging for differentiation of normal and neoplastic breast tissues has successfully reduced dose and scan times whilst sufficiently preserving spectral and spatial resolution. Future work to alter the coded aperture and detector geometries could potentially allow the use of even wider fans, thereby making coded aperture coherent scatter imaging a clinically viable method for breast cancer detection. United States Department of Homeland Security; Duke University Medical Center - Department of Radiology; Carl E Ravin Advanced Imaging Laboratories; Duke University Medical Physics Graduate Program.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2017

Human factors case study: An iterative approach to verifying and validating a new suite of reactor inspection and maintenance tooling - 177

An iterative approach was taken to perform the HF Verification and Validation (V and V) activities for a complex set of reactor inspection and maintenance tooling equipment known as the Bruce Reactor Inspection and Maintenance System (BRIMS). This paper is divided into the verification activities (of Human System Information Task Support and Design verifications) and the validation activities. The validation method used a graded approach by breaking validation activities into early usability testing and high fidelity validations. Early usability testing, allowed for issues and design concepts to be identified and explored. High fidelity validation activities tested that the final design requirements and operational goals of the system were met in the production equipment. The validation method has been described in detail by depicting the following: task selection criteria, tools, performance measures and data collection. Validation results demonstrate the benefits of the graded approach as issues were to be identified early in the design process, improvements were made during detailed design and additional testing could confirm that issues were resolved prior to commissioning. To capture and share the success of this iterative V and V approach lessons learned have been created for use in future V and V projects. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2015

SU-E-J-16: Automatic Image Contrast Enhancement Based On Automatic Parameter Optimization for Radiation Therapy Setup Verification

Purpose: In RT patient setup 2D images, tissues often cannot be seen well due to the lack of image contrast. Contrast enhancement features provided by image reviewing software, e.g. Mosaiq and ARIA, require manual selection of the image processing filters and parameters thus inefficient and cannot be automated. In this work, we developed a novel method to automatically enhance the 2D RT image contrast to allow automatic verification of patient daily setups as a prerequisite step of automatic patient safety assurance. Methods: The new method is based on contrast limited adaptive histogram equalization (CLAHE) and high-pass filtering algorithms. The most important innovation is to automatically select the optimal parameters by optimizing the image contrast. The image processing procedure includes the following steps: 1) background and noise removal, 2) hi-pass filtering by subtracting the Gaussian smoothed Result, and 3) histogram equalization using CLAHE algorithm. Three parameters were determined through an iterative optimization which was based on the interior-point constrained optimization algorithm: the Gaussian smoothing weighting factor, the CLAHE algorithm block size and clip limiting parameters. The goal of the optimization is to maximize the entropy of the processed Result. Results: A total 42 RT images were processed. The results were visually evaluated by RT physicians and physicists. About 48% of the images processed by the new method were ranked as excellent. In comparison, only 29% and 18% of the images processed by the basic CLAHE algorithm and by the basic window level adjustment process, were ranked as excellent. Conclusion: This new image contrast enhancement method is robust and automatic, and is able to significantly outperform the basic CLAHE algorithm and the manual window-level adjustment process that are currently used in clinical 2D image review software tools.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2012

Quantitative cone-beam CT imaging in radiation therapy using planning CT as a prior: First patient studies

Purpose: Quantitative cone-beam CT (CBCT) imaging is on increasing demand for high-performance image guided radiation therapy (IGRT). However, the current CBCT has poor image qualities mainly due to scatter contamination. Its current clinical application is therefore limited to patient setup based on only bony structures. To improve CBCT imaging for quantitative use, we recently proposed a correction method using planning CT (pCT) as the prior knowledge. Promising phantom results have been obtained on a tabletop CBCT system, using a correction scheme with rigid registration and without iterations. More challenges arise in clinical implementations of our method, especially because patients have large organ deformation in different scans. In this paper, we propose an improved framework to extend our method from bench to bedside by including several new components. Methods: The basic principle of our correction algorithm is to estimate the primary signals of CBCT projections via forward projection on the pCT image, and then to obtain the low-frequency errors in CBCT raw projections by subtracting the estimated primary signals and low-pass filtering. We improve the algorithm by using deformable registration to minimize the geometry difference between the pCT and the CBCT images. Since the registration performance relies on the accuracy of the CBCT image, we design an optional iterative scheme to update the CBCT image used in the registration. Large correction errors result from the mismatched objects in the pCT and the CBCT scans. Another optional step of gas pocket and couch matching is added into the framework to reduce these effects. Results: The proposed method is evaluated on four prostate patients, of which two cases are presented in detail to investigate the method performance for a large variety of patient geometry in clinical practice. The first patient has small anatomical changes from the planning to the treatment room. Our algorithm works well even without the optional iterations and the gas pocket and couch matching. The image correction on the second patient is more challenging due to the effects of gas pockets and attenuating couch. The improved framework with all new components is used to fully evaluate the correction performance. The enhanced image quality has been evaluated using mean CT number and spatial nonuniformity (SNU) error as well as contrast improvement factor. If the pCT image is considered as the ground truth, on the four patients, the overall mean CT number error is reduced from over 300 HU to below 16 HU in the selected regions of interest (ROIs), and the SNU error is suppressed from over 18% to below 2%. The average soft-tissue contrast is improved by an average factor of 2.6. Conclusions: We further improve our pCT-based CBCT correction algorithm for clinical use. Superior correction performance has been demonstrated on four patient studies. By providing quantitative CBCT images, our approach significantly increases the accuracy of advanced CBCT-based clinical applications for IGRT.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2014

Applying Nonlinear Diffusion Acceleration to Fixed-Source Problems with Anisotropic Scattering - Paper 15

Work over the last several years has demonstrated the impressive performance gains that can be attained by using Moment-Based Acceleration (MBA), or High-Order/Low-Order (HOLO), methods in a variety of transport applications. In the field of neutronics, Nonlinear Diffusion Acceleration (NDA) has been used to accelerate the solution to the fixed-source problem and the k-eigenvalue problem. These methods efficiently move a major portion of the computational work out of the full phase-space (high-order (HO)) domain into a reduced phase-space (low-order (LO)) setting. In previous implementations, NDA has only been applied to isotropic scattering problems. In this paper, we will extend this methodology to anisotropic scattering. This initial work on anisotropic scattering will focus on the 1-D multi-group neutron transport equation. This summary focuses on a fixed-source problem, but the extension to criticality problems is straight-forward via NDA-NCA. Within this paper, we have described a method for extending Nonlinear Diffusion Acceleration to solve problems with anisotropic scattering. We demonstrated that a consistent low-order system, resembling the low-order system from, could be constructed. We demonstrated that the NDA method performed exceptionally in the presence of anisotropic scattering. NDA reduced the number of iterations required to meet the convergence tolerance by a factor of 500 over source iteration for a one fixed-source problem and by 3.5-50 x for the Henyey-Greenstein problems. This method is equally well-suited for eigenvalue problems. The NDA method allows us to transition the eigenvalue iteration to the low-order domain.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2022

Multiarea Distribution System State Estimation via Distributed Tensor Completion

Here, this paper proposes a model-free distribution system state estimation method based on tensor completion using canonical polyadic decomposition. In particular, we consider a setting where the network is divided into multiple areas. The measured physical quantities at buses located in the same area are processed by an area controller. A three-way tensor is constructed to collect these measured quantities. The measurements are analyzed locally to recover the full state information of the network. A distributed closed-form iterative algorithm based on the alternating direction method of multipliers is developed to obtain the low-rank factors of the whole network state tensor where information exchange happens only between neighboring areas. The convergence properties of the distributed algorithm and the sufficient conditions on the number of samples for each smaller network that guarantee the identifiability of the factors of the state tensor are presented. To demonstrate the efficacy of the proposed algorithm and to check the identifiability conditions, numerical simulations are carried out using the IEEE 123-bus system and a large-scale real utility feeder.

24 POWER TRANSMISSION AND DISTRIBUTION↗