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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.

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At least 811 records · Page 45
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Distributed Data-Driven Optimization for Voltage Regulation in Distribution Systems

Here, this paper proposes a distributed data-driven optimization framework for voltage regulation in distribution systems. The recursive kernel regression and alternating direction method of multipliers (ADMM) are selected to cover the system learning and distributed optimization tasks. The proposed distributed data-driven framework is capable of having a rapid response to system or load changes while considering the operation optimality. Besides, the distributed algorithm parallels the computation tasks and reduces the computational expense of a single agent. To validate the performance of the proposed method, a hypothetical 7-Bus system and the IEEE 123-Bus system are selected to show the effectiveness of the proposed data-driven framework. According to the numerical study results, the proposed method offers great flexibility for selecting customized kernel models for different regions and can effectively improve the system voltage profile in a distributed manner.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2013

Motion as a perturbation: Measurement-guided dose estimates to moving patient voxels during modulated arc deliveries

Purpose: To present a framework for measurement-guided VMAT dose reconstruction to moving patient voxels from a known motion kernel and the static phantom data, and to validate this perturbation-based approach with the proof-of-principle experiments. Methods: As described previously, the VMAT 3D dose to a static patient can be estimated by applying a phantom measurement-guided perturbation to the treatment planning system (TPS)-calculated dose grid. The fraction dose to any voxel in the presence of motion, assuming the motion kernel is known, can be derived in a similar fashion by applying a measurement-guided motion perturbation. The dose to the diodes in a helical phantom is recorded at 50 ms intervals and is transformed into a series of time-resolved high-density volumetric dose grids. A moving voxel is propagated through this 4D dose space and the fraction dose to that voxel in the phantom is accumulated. The ratio of this motion-perturbed, reconstructed dose to the TPS dose in the phantom serves as a perturbation factor, applied to the TPS fraction dose to the similarly situated voxel in the patient. This approach was validated by the ion chamber and film measurements on four phantoms of different shape and structure: homogeneous and inhomogeneous cylinders, a homogeneous cube, and an anthropomorphic thoracic phantom. A 2D motion stage was used to simulate the motion. The stage position was synchronized with the beam start time with the respiratory gating simulator. The motion patterns were designed such that the motion speed was in the upper range of the expected tumor motion (1-1.4 cm/s) and the range exceeded the normally observed limits (up to 5.7 cm). The conformal arc plans for X or Y motion (in the IEC 61217 coordinate system) consisted of manually created narrow (3 cm) rectangular strips moving in-phase (tracking) or phase-shifted by 90 Degree-Sign (crossing) with respect to the phantom motion. The XY motion was tested with the computer-derived VMAT MLC sequences. For all phantoms and plans, time-resolved (10 Hz) ion chamber dose was collected. In addition, coronal (XY) films were exposed in the cube phantom to a VMAT beam with two different starting phases, and compared to the reconstructed motion-perturbed dose planes. Results: For the X or Y motions with the moving strip and geometrical phantoms, the maximum difference between perturbation-reconstructed and ion chamber doses did not exceed 1.9%, and the average for any motion pattern/starting phase did not exceed 1.3%. For the VMAT plans on the cubic and thoracic phantoms, one point exhibited a 3.5% error, while the remaining five were all within 1.1%. Across all the measurements (N = 22), the average disagreement was 0.5 {+-} 1.3% (1 SD). The films exhibited {gamma}(3%/3 mm) passing rates {>=}90%. Conclusions: The dose to an arbitrary moving voxel in a patient can be estimated with acceptable accuracy for a VMAT delivery, by performing a single QA measurement with a cylindrical phantom and applying two consecutive perturbations to the TPS-calculated patient dose. The first one accounts for the differences between the planned and delivered static doses, while the second one corrects for the motion.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2014

SU-E-T-439: An Improved Formula of Scatter-To-Primary Ratio for Photon Dose Calculation

Purpose: Scatter-to-primary ratio (SPR) is an important dosimetric quantity that describes the contribution from the scatter photons in an external photon beam. The purpose of this study is to develop an improved analytical formula to describe SPR as a function of circular field size (r) and depth (d) using Monte Carlo (MC) simulation. Methods: MC simulation was performed for Mohan photon spectra (Co-60, 4, 6, 10, 15, 23 MV) using EGSNRC code. Point-spread scatter dose kernels in water are generated. The scatter-to-primary ratio (SPR) is also calculated using MC simulation as a function of field size for circular field size with radius r and depth d. The doses from forward scatter and backscatter photons are calculated using a convolution of the point-spread scatter dose kernel and by accounting for scatter photons contributing to dose before (z' d) reaching the depth of interest, d, where z' is the location of scatter photons, respectively. The depth dependence of the ratio of the forward scatter and backscatter doses is determined as a function of depth and field size. Results: We are able to improve the existing 3-parameter (a, w, d0) empirical formula for SPR by introducing depth dependence for one of the parameter d0, which becomes 0 for deeper depths. The depth dependence of d0 can be directly calculated as a ratio of backscatter-to-forward scatter doses for otherwise the same field and depth. With the improved empirical formula, we can fit SPR for all megavoltage photon beams to within 2%. Existing 3-parameter formula cannot fit SPR data for Co-60 to better than 3.1%. Conclusion: An improved empirical formula is developed to fit SPR for all megavoltage photon energies to within 2%.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2014

TH-A-9A-06: Inverse Planning of Gamma Knife Radiosurgery Using Natural Physical Models

Purpose: Treatment-planning systems rely on computer intensive optimization algorithms in order to provide radiation dose localization. We are investigating a new optimization paradigm based on natural physical modeling and simulations, which tend to evolve in time and find the minimum energy state. In our research, we aim to match physical models with radiation therapy inverse planning problems, where the minimum energy state coincides with the optimal solution. As a prototype study, we have modeled the inverse planning of Gamma Knife radiosurgery using the dynamic interactions between charged particles and demonstrate the potential of the paradigm. Methods: For inverse planning of Gamma Knife radiosurgery: (1) positive charges are uniformly placed on the surface of tumors and critical structures. (2) The Gamma Knife dose kernels of 4mm, 8mm and 16mm radii are modeled as geometric objects with variable charges. (3) The number of shots per each kernel radii is obtained by solving a constrained integer-linear problem. (4) The shots are placed into the tumor volume and move under electrostatic forces. The simulation is performed until internal forces are zero or maximum iterations are reached. (5) Finally, non-negative least squares (NNLS) is used to calculate the beam-on times for each shot. Results: A 3D C-shaped tumor surrounding a spherical critical structure was used for testing the new optimization paradigm. These tests showed that charges spread out evenly covering the tumor while keeping distance from the critical structure, resulting in a high quality plan. Conclusion: We have developed a new paradigm for dose optimization based on the simulation of physical models. As prototype studies, we applied electrostatic models to Gamma Knife radiosurgery and demonstrated the potential of the new paradigm. Further research and fine-tuning of the model are underway. NSF CBET-0853157.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

SU-E-T-265: Development of Dose-To-Water Conversion Models for Pre-Treatment Verification with the New AS1200 Imager

Purpose: To develop and evaluate models for dose verification of flattened (FF) and flattening filter free (FFF) beams for the new Varian aS1200 backscatter-shielded electronic portal imaging device (EPID). Methods: The model converts EPID images to incident energy fluence using deconvolution of EPID scatter kernels and fluence to dose in water using convolution with dose-to-water kernels. Model parameters were optimized using non-transmission EPID images of varying jaw defined field sizes for energies of 6 and 10 MV FF and FFF beams. Energy fluence was obtained from the Acuros planning system and reference dose profiles and output factors were measured at depths of 5, 10, 15 and 20 cm in a water phantom. Images for 34 IMRT fields acquired at 6 and 10 MV FF energy were converted to dose at 10 cm depth in water and compared to treatment planning system dose plane calculations using gamma criteria. Results: Gamma evaluations for the IMRT fields had mean (1 standard deviation) pass rates of 99.4% (0.8%) and mean gamma scores of 0.32 (0.06) with 2%, 2 mm criteria and 10% of maximum dose threshold. Conclusion: The developed model has been shown to be highly accurate for pre-treatment verification with the new aS1200 imager which does not display support-arm backscatter artefact and has improved dosimetric properties. Further investigation of FFF modes is in progress. The model is currently being evaluated at sites for potential clinical release.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

Spectrotemporal CT data acquisition and reconstruction at low dose

Purpose: X-ray computed tomography (CT) is widely used, both clinically and preclinically, for fast, high-resolution anatomic imaging; however, compelling opportunities exist to expand its use in functional imaging applications. For instance, spectral information combined with nanoparticle contrast agents enables quantification of tissue perfusion levels, while temporal information details cardiac and respiratory dynamics. The authors propose and demonstrate a projection acquisition and reconstruction strategy for 5D CT (3D + dual energy + time) which recovers spectral and temporal information without substantially increasing radiation dose or sampling time relative to anatomic imaging protocols. Methods: The authors approach the 5D reconstruction problem within the framework of low-rank and sparse matrix decomposition. Unlike previous work on rank-sparsity constrained CT reconstruction, the authors establish an explicit rank-sparse signal model to describe the spectral and temporal dimensions. The spectral dimension is represented as a well-sampled time and energy averaged image plus regularly undersampled principal components describing the spectral contrast. The temporal dimension is represented as the same time and energy averaged reconstruction plus contiguous, spatially sparse, and irregularly sampled temporal contrast images. Using a nonlinear, image domain filtration approach, the authors refer to as rank-sparse kernel regression, the authors transfer image structure from the well-sampled time and energy averaged reconstruction to the spectral and temporal contrast images. This regularization strategy strictly constrains the reconstruction problem while approximately separating the temporal and spectral dimensions. Separability results in a highly compressed representation for the 5D data in which projections are shared between the temporal and spectral reconstruction subproblems, enabling substantial undersampling. The authors solved the 5D reconstruction problem using the split Bregman method and GPU-based implementations of backprojection, reprojection, and kernel regression. Using a preclinical mouse model, the authors apply the proposed algorithm to study myocardial injury following radiation treatment of breast cancer. Results: Quantitative 5D simulations are performed using the MOBY mouse phantom. Twenty data sets (ten cardiac phases, two energies) are reconstructed with 88 μm, isotropic voxels from 450 total projections acquired over a single 360° rotation. In vivo 5D myocardial injury data sets acquired in two mice injected with gold and iodine nanoparticles are also reconstructed with 20 data sets per mouse using the same acquisition parameters (dose: ∼60 mGy). For both the simulations and the in vivo data, the reconstruction quality is sufficient to perform material decomposition into gold and iodine maps to localize the extent of myocardial injury (gold accumulation) and to measure cardiac functional metrics (vascular iodine). Their 5D CT imaging protocol represents a 95% reduction in radiation dose per cardiac phase and energy and a 40-fold decrease in projection sampling time relative to their standard imaging protocol. Conclusions: Their 5D CT data acquisition and reconstruction protocol efficiently exploits the rank-sparse nature of spectral and temporal CT data to provide high-fidelity reconstruction results without increased radiation dose or sampling time.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

SU-C-207B-05: Tissue Segmentation of Computed Tomography Images Using a Random Forest Algorithm: A Feasibility Study

Purpose: Develop an automated Random Forest algorithm for tissue segmentation of CT examinations. Methods: Seven materials were classified for segmentation: background, lung/internal gas, fat, muscle, solid organ parenchyma, blood/contrast, and bone using Matlab and the Trainable Weka Segmentation (TWS) plugin of FIJI. The following classifier feature filters of TWS were investigated: minimum, maximum, mean, and variance each evaluated over a pixel radius of 2n, (n = 0–4). Also noise reduction and edge preserving filters, Gaussian, bilateral, Kuwahara, and anisotropic diffusion, were evaluated. The algorithm used 200 trees with 2 features per node. A training data set was established using an anonymized patient’s (male, 20 yr, 72 kg) chest-abdomen-pelvis CT examination. To establish segmentation ground truth, the training data were manually segmented using Eclipse planning software, and an intra-observer reproducibility test was conducted. Six additional patient data sets were segmented based on classifier data generated from the training data. Accuracy of segmentation was determined by calculating the Dice similarity coefficient (DSC) between manual and auto segmented images. Results: The optimized autosegmentation algorithm resulted in 16 features calculated using maximum, mean, variance, and Gaussian blur filters with kernel radii of 1, 2, and 4 pixels, in addition to the original CT number, and Kuwahara filter (linear kernel of 19 pixels). Ground truth had a DSC of 0.94 (range: 0.90–0.99) for adult and 0.92 (range: 0.85–0.99) for pediatric data sets across all seven segmentation classes. The automated algorithm produced segmentation with an average DSC of 0.85 ± 0.04 (range: 0.81–1.00) for the adult patients, and 0.86 ± 0.03 (range: 0.80–0.99) for the pediatric patients. Conclusion: The TWS Random Forest auto-segmentation algorithm was optimized for CT environment, and able to segment seven material classes over a range of body habitus and CT protocol parameters with an average DSC of 0.86 ± 0.04 (range: 0.80–0.99).

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

TH-CD-207B-10: Effect of CT Reconstruction Filter On Measured Hounsfield Values in Lung Nodules

Purpose: Measured Hounsfield numbers in CT are used by radiologists to determine the presence of calcium or fat in lung nodules, either of which suggests a benign diagnosis. However, substantial variations in Hounsfield number may arise due to the use of different reconstruction parameters such as the filter/kernel, leading to measurement inaccuracies. This quality improvement project was developed to demonstrate measurement pitfalls and to identify acceptable conditions for incorporating Hounsfield values as a factor in lung nodule diagnosis. Methods: 12 mm-diameter spheres of polyurethane and urethane foam were placed into an anthropomorphic chest phantom, and 10 mm-diameter tubes with varying iodine concentrations were placed into a 16 cm PMMA cylindrical phantom. Additionally, 11 mm-diameter PMMA and HDPE spheres were placed in a 10 cm PMMA cylindrical phantom. Phantoms were scanned at 120 kVp using a Siemens Biograph mCT and on a Philips iCT and reconstructed using various reconstruction filters. Results: For the Siemens system, both sharp kernels and smooth kernels altered the Hounsfield numbers. Hounsfield numbers varied within a range of 8.9 HU for urethane foam and varied within 58.7 HU for polyurethane. The iodine measurements varied up to 37.9 HU for the lowest concentration. For the Philips system, Hounsfield numbers were relatively consistent but were higher for the “Detail” and “Lung Enhanced” filters, varying by 36.9 HU for PMMA and 15.9 HU for HDPE. Conclusion: Reconstruction filters can change the measured Hounsfield numbers of nodular objects, especially with detail-enhancing (sharpening) filters commonly used in lung imaging. Measured values should only be used for diagnostic decision support with filters that have demonstrated accuracy and consistency. While filter accuracy statements are available from manufacturers, radiologists are likely not aware of the extent of potential variations that can occur in a clinical setting.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2019

A three-phase workflow for general and expressive representations of nondeterminism in HPC applications

Nondeterminism is an increasingly entrenched property of high-performance computing (HPC) applications and has recently been shown to seriously hamper debugging and reproducibility efforts. Additionally, tools for addressing the nondeterministic debugging problem have emerged, but they do not provide methods for systematically cataloging the nondeterminism in a given application. We propose a three-phase workflow for representing executions of nondeterministic message passing interface programs as event graphs, quantifying their structural similarity with graph kernels, and applying machine learning techniques to investigate shared properties across applications. We present an empirical study comparing two graph kernels’ suitability for this task and propose future uses of the methodology.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Extensions of BLUP Models for Genomic Prediction in Heterogeneous Populations: Application in a Diverse Switchgrass Sample

Genomic prediction is a useful tool to accelerate genetic gain in selection using DNA marker information. However, this technology typically relies on standard prediction procedures, such as genomic BLUP, that are not designed to accommodate population heterogeneity resulting from differences in marker effects across populations. In this study, we assayed different prediction procedures to capture marker-by-population interactions in genomic prediction models. Prediction procedures included genomic BLUP and two kernel-based extensions of genomic BLUP which explicitly accounted for population heterogeneity. To model population heterogeneity, dissemblance between populations was either depicted by a unique coefficient (as previously reported), or a more flexible function of genetic distance between populations (proposed herein). Models under investigation were applied in a diverse switchgrass sample under two validation schemes: whole-sample calibration, where all individuals except selection candidates are included in the calibration set, and cross-population calibration, where the target population is entirely excluded from the calibration set. First, we showed that using fixed effects, from principal components or putative population groups, appeared detrimental to prediction accuracy, especially in cross-population calibration. Then we showed that modelling population heterogeneity by our proposed procedure resulted in highly significant improvements in model fit. In such cases, gains in accuracy were often positive. These results suggest that population heterogeneity may be parsimoniously captured by kernel methods. However, in cases where improvement in model fit by our proposed procedure is null-to-moderate, ignoring heterogeneity should probably be preferred due to the robustness and simplicity of the standard genomic BLUP model.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Enhancement of sub-thermal neutron flux through cold polyethylene

Total thermal neutron cross section measurements serve as the primary means of validation for thermal neutron scattering kernels, an important quantity for neutron transport calculations. In an effort to improve the quality of thermal neutron scattering kernels, researchers at Rensselaer Polytechnic Institute (RPI) designed and constructed a polyethylene based cold moderation system to enhance neutron flux below 10 meV when coupled with the Enhanced Thermal Target (ETT) at the RPI Gaerttner LINAC. The final design yielded an increase in sub-thermal neutron flux (below 10 meV) by a factor of 4.5 for a moderator temperature of 37.5 K relative to the ETT alone. A further increase to a factor of 6 is expected after a minor geometry modification and decrease in polyethylene temperature to 25 K. This novel capability will be used to conduct total thermal neutron cross section measurements from 0.0005–10 eV for different materials including moderator materials.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

Cleaning Images with Gaussian Process Regression

Many approaches to astronomical data reduction and analysis cannot tolerate missing data: corrupted pixels must first have their values imputed. This paper presents astrofix, a robust and flexible image imputation algorithm based on Gaussian process regression. Through an optimization process, astrofix chooses and applies a different interpolation kernel to each image, using a training set extracted automatically from that image. It naturally handles clusters of bad pixels and image edges and adapts to various instruments and image types. For bright pixels, the mean absolute error of astrofix is several times smaller than that of median replacement and interpolation by a Gaussian kernel. We demonstrate good performance on both imaging and spectroscopic data, including the SBIG 6303 0.4 m telescope and the FLOYDS spectrograph of Las Cumbres Observatory and the CHARIS integral-field spectrograph on the Subaru Telescope.

42 ENGINEERING↗
DOE OSTI2017

AGR-5/6/7 Fuel Specification

The Idaho National Laboratory (INL) Advanced Reactor Technologies (ART) Technology Development Office (TDO) program is developing and qualifying fuel for a first of a kind high temperature gas-cooled reactor (HTGR) and associated systems to generate electrical power and produce hydrogen or process heat. One of the critical technology development areas of the program is nuclear fuel development and qualification. Fuel qualification is needed to support licensing, operation, and near term deployment of an HTGR reactor.5 Toward this end, the Advanced Gas Reactor (AGR) program includes manufacturing fuels for a series of irradiation experiments in the Advanced Test Reactor (ATR) at INL.5 The fifth, sixth, and seventh irradiation experiments, called “AGR 5/6/7,” will use fuel manufactured entirely in engineering scale equipment to demonstrate the performance of fuels fabricated in a production environment. This fuel will be composited from multiple low enriched uranium carbide/oxide (LEUCO) kernel forming runs, multiple tristructural isotropic (TRISO) coating runs, and multiple overcoating runs. The fuel will be composited into lots as kernels, TRISO particles, and compacts. Previous AGR fuel specifications1,2,8,9 provide the basis for most of the following fuel specifications, which are specific to the AGR 5/6/7 experiment, and may not be immediately applicable to fuel produced for an HTGR reactor. Fuel specifications will be influenced by the final reactor design.

+↗
DOE OSTI2016

Statistical Sampling Plan for AGR-5/6/7 Fuel Materials

Kernels, coated particles, and compacts will be manufactured to predefined specifications for irradiation in the AGR 5/6/7 experiments. Many tests will be performed for quality assurance and most of these tests correspond to criteria that have to be met with 95% confidence, based on random samples. This report describes the statistical acceptance testing methods and gives minimum sample sizes for kernels to achieve 95% confidence. Coated particles and compacts will be addressed in revisions to this report. The methods used for sample size determination are described in detail in INL/EXT 05 00349, Statistical Methods Handbook for Advanced Gas Reactor Fuel Materials (Einerson 2005). The statistical approach is to collect a representative sample, apply an acceptance test to the sample, and accept or reject the product based on this test for each criterion. The criteria or “product specifications” are contained in SPC-1352, “AGR 5/6/7 Fuel Specification,” Revision 1 and are duplicated in this plan.

+↗
DOE OSTI2013

Numerical computation of doppler-broadening in the resonance domain

We have implemented an accurate and fast calculation of the Doppler-broadened kernel PT(E {yields} E') for neutron elastic scattering based on a gas model. An exponential cutoff which accounts for the asymptotic behavior of the error function helps limit the range of integration while eliminating difference effects. This allows for calculating a kernel library for {sup 238}U over a very fine energy grid covering the resonance range in only a few hours in a laptop. We give an example showing the impact of {sup 238}U elastic up-scattering on the values of self shielded cross sections. (authors)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Study on generating of thermal neutron scattering cross sections for LiH

LiH is designated as a promising moderator and shielding material because of its low density, high melting point and large fraction of H atoms. However, lack of the thermal neutron cross sections of LiH makes numerical calculation deviate from experimental data to some extent. As a result, it is necessary to study LiH thermal kernel effect. The phonon property of LiH has been investigated by first-principles calculations using the plane-wave pseudo potential method with CASTEP code. The scattering law and the thermal neutron scattering cross sections for Li and H have been generated using this distribution. The results have been compared with zirconium hydride data. The GASKET and NJOY/LEAPR codes have been used in the calculation of scattering law, whose results have been compared with the reference; the discrepancy mainly comes from phonon spectrums and its expansion. LEAPR had the capability to compute scattering through larger energy and momentum transfers than GASKET did. By studying LiH phonon spectrum and constructing the model of LiH thermal kernel and scattering matrix, the ACE format LiH thermal neutron cross sections for MCNP software could be made and used for reactor Neutronics calculation. (authors)

36 MATERIALS SCIENCE↗
DOE OSTI2014

Cirrus feedback on interannual climate fluctuations

Cirrus clouds are not only important in determining the current climate, but also play an important role in climate change and variability. Analysis of satellite observations shows that the amount and altitude of cirrus clouds (optical depth <3.6, cloud top pressure <440 hPa) increase in response to inter-annual surface warming. Thus, cirrus clouds are likely to act as a positive feedback on short-term climate fluctuations, by reducing the planet’s ability to radiate longwave radiation to space in response to planetary surface warming. Using cirrus cloud radiative kernels, the magnitude of cirrus feedback is estimated to be 0.20±0.21W/m 2 /°C, which is comparable to the surface albedo feedback. Most of the cirrus feedback comes from increasing cloud amount in the tropical tropopause layer (TTL) and subtropical upper troposphere.

58 GEOSCIENCES↗
DOE OSTI2017

Fast synchronization-free algorithms for parallel sparse triangular solves with multiple right-hand sides

The sparse triangular solve kernels, SpTRSV and SpTRSM, are important building blocks for a number of numerical linear algebra routines. Parallelizing SpTRSV and SpTRSM on today's many-core platforms, such as GPUs, is not an easy task since computing a component of the solution may depend on previously computed components, enforcing a degree of sequential processing. As a consequence, most existing work introduces a preprocessing stage to partition the components into a group of level-sets or colour-sets so that components within a set are independent and can be processed simultaneously during the subsequent solution stage. However, this class of methods requires a long preprocessing time as well as significant runtime synchronization over-heads between the sets. To address this, we

HPC↗