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DOE OSTI2023

Improvements of Nuclear Data Evaluations for Lead Isotopes in Support of Next Generation Lead-Cooled Fast Systems

The neutron evaluation of the isotopes that comprise natural lead were undertaken as a part of DOE-NEUP Project #19-16739. The goal of the project was to update the neutron cross sections to account for new differential measurements and incorporate the most up-to-date physics. Shortcomings in the lead cross sections was made known by several independent reports. The work performed here repeated the simulation of all the “benchmark” validation systems and concluded that the major issue is the scattering cross sections in the major lead isotopes above 100 keV. Re-evaluation of 206,207,208 Pb included both the resolved resonance region and fast region evaluations of the cross sections. Combined these regions cover energies from thermal to 20 MeV. The most drastic improvement is the resolved resonance region evaluation of 208 Pb which is now extended from 1.0 to 1.5 MeV. Parameterization of these resonances in the R-matrix provides a superior reconstruction of not only the experimental cross section but also the scattering distributions via the Blatt-Biedenharn formalism. Fast region evaluations of the three major isotopes were done to include new inelastic experimental data from the neutron Time-of-Flight facility at CERN. The culmination of all the changes to the cross section is a drastic improvement in the scattering kernel as shown in Rensselaer Polytechnic Institute (RPI) Quasi-Differential scattering measurements and improved prediction of keff for fast integral experiments. Alongside the new cross sections, new nuclear data covariance (uncertainties) have been computed and are included in the evaluation. Little is changed in the magnitude of the uncertainties but the correlations within the covariance display non-trivial changes. The new evaluations of 206,207,208 Pb have been submitted to the National Nuclear Data Center to be included in the ENDF/B-VIII.1 library. While the cross sections have been updated extensively, knowledge and modeling of the cross sections between 1.0 and 3.0 MeV for the isotopes remain a challenge. Most notably is the double differential elastic cross section for 208 Pb and 206 Pb. New quasi-differential measurements for pure samples of these two nuclei would go a long way in reducing compensating errors in the evaluations. Qualitatively, the project has produced a prosperous collaboration between the nuclear data group at RPI with staff scientists at Brookhaven National Laboratory, Naval Nuclear Laboratory, Oak Ridge National Laboratory, Los Alamos National Laboratory, Lawrence Livermore National Laboratory, and Sandia National Laboratories. Quantitatively this is reflected in seven conference presentations, at least one journal submission, and one doctoral thesis.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Enhanced dynamic equivalent identification method of large-scale power systems using multiple events

The increasing complexity of the interconnected power system makes high-fidelity dynamic simulation models computationally more intensive. To improve computation efficiency, model reduction techniques have been investigated to only preserve the dynamics in a limited area of interest (study area), while deriving equivalent representation for the external area. For this purpose, a measurement-based reduction approach using system identification techniques has been previously proposed. Accordingly, external areas are represented by dynamic equivalent loads using transfer function estimation. In this paper, in order to enhance the accuracy of the reduced model in preserving dynamics of the study area, multiple “grid” events of different types and at different locations are considered for identifying the parameters of the equivalent loads. Additionally, case studies are carried out in the NPCC 140-bus system. Comparisons are made between multiple events training and single event training, highlighting the advantages of the proposed method in providing a better representation of the grid dynamics under different operating conditions.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2020

A Multi-Function AAA Algorithm Applied to Frequency Dependent Line Modeling

Modeling of power distribution system components that are valid for a wide range of frequencies are crucial for highly accurate modeling of electromagnetic transient (EMT) events. This has recently become of interest due to the improvements needed for the resilient operation of distribution systems. Vector fitting (VF) is a very popular and commonly used algorithm for wide band representations of power system components in EMT simulations. In this research, we present a new multi-input rational approximation algorithm (MIAAA) and illustrate its advantages with respect to VF using examples of approximations of admittance matrices discussed in the literature. We show that MIAAA not only outperforms VF in terms of achieving better accuracy using lesser number of poles, but also has no numerical issues achieving convergence. In contrast to VF, MIAAA is not sensitive to the location of input sample points and it does not require good estimates for the location of the desired approximation poles. The novelty of this research work is the use of recent mathematical results to solve existing challenges in distribution system modeling and to develop rational approximations for power system models that intend to be optimal in terms of accuracy and performance.

41 EE - Solar Energy Technologies Office (EE-4S)↗

DOE OSTI2025

Grey-Box System Identification of Grid-Forming Inverters

This paper demonstrates the use of grey-box system identification methods for simplifying and understanding the nonlinear power dynamics of grid-forming inverters (GFMs). The power and frequency outputs of complex high-order GFM models are fed into system identification software in order to fit them to a predetermined LTI system and learn system parameters such as (synthetic) inertia and droop constants. The same process is then run for a high-order synchronous generator model, and the outputs are fit to the same set of LTI equations. Simulation of a network of GFM inverters with diverse control architecture is also performed for the same process. The intent is threefold: first, to demonstrate the appropriateness of unified LTI models for describing the power and frequency dynamics of individual resources and connected networks, in order to facilitate analysis of larger heterogeneous networked systems; second, to discover the relationship between internal control parameters of GFMs and their externally observed values; and third, to validate that grey-box data-driven system identification techniques can be a valuable tool to discover the values of important parameters in the absence of explicit vendor models.

analytical models↗

DOE OSTI2020

TURBOMOLE: Modular program suite for ab initio quantum-chemical and condensed-matter simulations

TURBOMOLE is a collaborative, multi-national software development project aiming to provide highly efficient and stable computational tools for quantum chemical simulations of molecules, clusters, periodic systems, and solutions. The TURBOMOLE software suite is optimized for widely available, inexpensive, and resource-efficient hardware such as multi-core workstations and small computer clusters. TURBOMOLE specializes in electronic structure methods with outstanding accuracy–cost ratio, such as density functional theory including local hybrids and the random phase approximation (RPA), GW-Bethe–Salpeter methods, second-order Møller–Plesset theory, and explicitly correlated coupled-cluster methods. TURBOMOLE is based on Gaussian basis sets and has been pivotal for the development of many fast and low-scaling algorithms in the past three decades, such as integral-direct methods, fast multipole methods, the resolution-of-the-identity approximation, imaginary frequency integration, Laplace transform, and pair natural orbital methods. This review focuses on recent additions to TURBOMOLE’s functionality, including excited-state methods, RPA and Green’s function methods, relativistic approaches, high-order molecular properties, solvation effects, and periodic systems. A variety of illustrative applications along with accuracy and timing data are discussed. Moreover, available interfaces to users as well as other software are summarized. TURBOMOLE’s current licensing, distribution, and support model are discussed, and an overview of TURBOMOLE’s development workflow is provided. Challenges such as communication and outreach, software infrastructure, and funding are highlighted.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Measurements and Prediction of Ash Deposition in a Cyclone-Fired Boiler Operating under Variable Load Conditions

Measurements of ash deposition rates were made between the secondary superheater and reheater sections of a 450 MW cyclone-fired lignite boiler as the operational load varied from 33 to 100%. Significant reductions in deposition rates with a decrease in operational load were observed. To uncover the causative mechanisms behind these observations, operational data from the power plant were used to carry out computational fluid dynamic (CFD) simulations of the boiler. After ascertaining that the gas temperatures and velocities at various sections within the boiler were being represented adequately, decoupled simulations of the ash deposition process on the deposit probe were carried out using a finely resolved boundary layer mesh. Fly ash particle size distribution (PSD) and its concentration for the decoupled calculations were determined from stand-alone cyclone barrel simulations. The ash partitioning (mass %) between the fly ash and slag was found to be ~50:50, which was in line with previous field observations, and it did not vary significantly across different cyclone loads. The predicted PSD of the deposit ash was concentrated in the size range 10–30 microns, which was in agreement with cross-sectional images of the deposit obtained from the measurements. At lower loads, sharp variations in the deposition rates were predicted in the gas temperature range 950–1150 K. The particle kinetic energy—particle viscosity-based capture methodology utilized in this study in conjunction with appropriate ash compositions, ash viscosity models and gas temperature estimates can help estimate slagging propensities at different loads reasonably well in these systems.

Krishnamoorthy, Gautham (ORCID:0000000255205092)↗

DOE OSTI2020

Analysis of a Fluidized-Bed Particle/Supercritical-CO2 Heat Exchanger in a Concentrating Solar Power System

Concentrating solar power (CSP) development has focused on increasing the energy conversion efficiency and lowering the capital cost. To improve performance, CSP research is moving to high-temperature and high-efficiency designs. One technology approach is to use inexpensive, high-temperature heat transfer fluids and storage, integrated with a high-efficiency power cycle such as the supercritical carbon dioxide (sCO 2 ) Brayton power cycle. The sCO 2 Brayton power cycle has strong potential to achieve performance targets of 50% thermal-to-electric efficiency and dry cooling at an ambient temperature of up to 40 °C and to reduce the cost of power generation. Solid particles have been proposed as a possible high-temperature heat transfer or storage medium that is inexpensive and stable at high temperatures above 1000 °C. The particle/sCO 2 heat exchanger (HX) provides a connection between the particles and sCO 2 fluid in emerging sCO 2 power cycles. This article presents heat transfer modeling to analyze the particle/sCO 2 HX design and assess design tradeoffs including the HX cost. The heat transfer process was modeled based on a particle/sCO 2 counterflow configuration, and empirical heat transfer correlations for the fluidized bed and sCO 2 were used to calculate heat transfer area and estimate the HX cost. A computational fluid dynamics simulation was applied to characterize particle distribution and fluidization. This article shows a path to achieve the cost and performance objectives for a particle/sCO 2 HX design by using fluidized-bed technology.

14 SOLAR ENERGY↗

DOE OSTI2021

Guided Resilience Self Assessment Application

Reliable electricity access is vital for everything from hospitals to national security. When grid disturbances occur, it is crucial to minimize the amount of time it takes to recover. Grid resiliency considers both the preparation for and recovery from high-impact low-frequency disturbances (HILF) such as weather events and cyber attacks. The Department of Energy (DOE) Wind Energy Technologies Office (WETO) funds the multi-laboratory Microgrids, Infrastructure Resilience, and Advanced Control Launchpad (MIRACL) project to investigate technologies to support and grow distributed wind. Researchers at Idaho National Laboratory (INL) contribute to resilience and cybersecurity efforts for the project, and have produced a resilience framework to evaluate system resilience based on individual system specifications. In order to make this framework easy for anyone to apply, I have coded a web application that allows users to input their power system qualities, goals, and perceived risks and then receive suggestions on how to improve their grid resiliency. The web application follows the seven steps in the planning stage of the framework process, allowing the user to input information about their grid and select from common goals, metrics, and hazards, as well as add their own. The application currently provides information about how to complete each step, requiring minimal prior knowledge of the framework. Future work for this application will include allowing the user to submit line drawings of their system and incorporate modeling tools so that the hazard simulations of applying the framework is completed for the user.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

An Accurate, Error-Tolerant, and Energy-Efficient Neural Network Inference Engine Based on SONOS Analog Memory

In this work, we demonstrate SONOS (silicon-oxide-nitrideoxide- silicon) analog memory arrays that are optimized for neural network inference. The devices are fabricated in a 40nm process and operated in the subthreshold regime for in-memory matrix multiplication. Subthreshold operation enables low conductances to be implemented with low error, which matches the typical weight distribution of neural networks, which is heavily skewed toward near-zero values. This leads to high accuracy in the presence of programming errors and process variations. We simulate the end-to-end neural network inference accuracy, accounting for the measured programming error, read noise, and retention loss in a fabricated SONOS array. Evaluated on the ImageNet dataset using ResNet50, the accuracy using a SONOS system is within 2.16% of floating-point accuracy without any retraining. The unique error properties and high On/Off ratio of the SONOS device allow scaling to large arrays without bit slicing, and enable an inference architecture that achieves 20 TOPS/W on ResNet50, a >10× gain in energy efficiency over state-of-the-art digital and analog inference accelerators.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Scalable line and plane relaxation in a parallel structured multigrid solver

The efficient solution of sparse, linear systems that arise through the discretization of partial differential equations remains a key challenge for a range of high performance scientific simulations. One approach for reducing data movement and improving performance is by exposing and exploiting structure in a problem through the use of robust structured multilevel solvers. By choosing coarsening that preserves the structure of the problem, these methods maintain efficient structured computation and communication throughout the multigrid hierarchy. However, when coarsening is not permitted to be dependent on the operator, anisotropy must be addressed by the smoother — producing error compatible for coarse-grid correction with structured coarsening. Here, the components required in a scalable parallel structured solver are described with a focus on memory and communication efficiency of robust smoothers. While the implementation of communication and memory reduction techniques in smoothers integrated in a complete 3D solver present a significant engineering challenge, a novel approach is proposed that addresses these challenges systematically through a change to the solver’s execution model. Enabled by user-level threading paired with a set of data and communication abstractions, this approach permits seamless aggregation of communication in plane smoothers — directly reusing code for a 2D distributed multilevel cycle. Results show an effective reduction in communication costs for coarse-grid problems, and result in a speedup of 8.7x in smoothing routines shown in Fig. 12 using this approach. This produces a significant improvement to strong scalability while maintaining favorable weak scaling behavior. Finally, a parallel scaling study using a series of refined meshes is included that demonstrates the effectiveness of this approach in an application of interest.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Computational modeling and neutron imaging to understand interface shape and solute segregation during the vertical gradient freeze growth of BaBrCl:Eu

In this work we apply continuum models to analyze phase change, heat transfer, fluid flow, solute transport, and segregation in order to understand prior neutron imaging observations of the vertical gradient freeze growth of Eu-doped BaBrCl. The models provide a rigorous framework in which to understand the mechanisms that are responsible for the complicated evolution of interface shape and dopant distribution in the growth experiment. We explain how a transition in the solid/liquid interface shape from concave to convex is driven by changes in radial heat transfer caused by furnace design. We also provide a mechanistic explanation of how dynamic growth conditions and changes of the flow structure in the melt result in complicated segregation patterns in this system. A growth pause caused by controller lock-up is shown to result in a band of solute depletion in accordance with classical theory. However, changing flow patterns during growth result in a non-monotonic axial distribution of solute that cannot be explained by simple application of classical segregation models. We assert that the approach presented here, namely the use of rigorous models in conjunction advanced diagnostics, such as neutron imaging, provides an exciting path forward for process optimization and control, accelerating the incremental advances that have, in the past, typically relied on empiricism, experience, and intuition.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Gaussian approximation potential for amorphous Si : H

Hydrogenation of amorphous silicon (a–Si : H) is critical for reducing defect densities, passivating midgap states and surfaces, and improving photoconductivity in silicon-based electro-optical devices. Modeling the atomic-scale structure of this material is critical to understanding these processes, which in turn is needed to describe c–Si/a–Si : H heterojunctions that are at the heart of modern solar cells with world-record efficiency. Density functional theory (DFT) studies achieve the required high accuracy but are limited to moderate system sizes of 100 atoms or so by their high computational cost. Simulations of amorphous materials have been hindered by this high cost because large structural models are required to capture the medium-range order that is characteristic of such materials. Empirical potential models are much faster, but their accuracy is not sufficient to correctly describe the frustrated local structure. Data-driven, machine-learned interatomic potentials have broken this impasse and have been highly successful in describing a variety of amorphous materials in their elemental phase. Here, we extend the Gaussian approximation potential (GAP) for silicon by incorporating the interaction with hydrogen, thereby significantly improving the degree of realism with which amorphous silicon can be modeled. We show that our Si : H GAP enables the simulation of hydrogenated silicon with an accuracy very close to DFT but with computational expense and run times reduced by several orders of magnitude for large structures. Here, we demonstrate the capabilities of the Si : H GAP by creating models of hydrogenated liquid and amorphous silicon and showing that their energies, forces, and stresses are in excellent agreement with DFT results, and their structure as captured by bond and angle distributions are in agreement with both DFT and experiments.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Conjugate Heat Transfer Analysis in Pressurized Helium Gas Cooling Channels

Los Alamos National Laboratory (LANL) is working with NorthStar Medical Radioisotopes (NMR) on their efforts to produce Mo-99 from the irradiation of Mo-100 targets. The NMR target consists of an Inconel window that allows the electron beam to penetrate and irradiate a stack of Mo-100 disks. The irradiation process generates large amounts of heat and is cooled using pressurized helium gas flowing at 400 g/s. LANL provides both numerical analysis support and experimental support. Computational fluid dynamics (CFD) and conjugate heat transfer (CHT) analysis are performed on the NMR target to analyze the helium flow and volumetric heating through the NMR system. In this iteration of numerical analysis, we update the Mo-100 disk thickness to 0.74 mm and the gap between the Inconel window and the first disk to 0.69 mm. Estimates of the heat flux from the electron beams from Monte Carlo N-Particle code (MCNP) analysis were combined with CFD to perform the CHT analysis. The pressure drop through the targets, force applied on the first disk, beam window and target disk temperatures are some of the quantities estimated using the simulations. The pressure drop through the target was estimated as 0.198 MPa, while the force due to venturi effects across the first disk was estimated to be 100 N. The results show maximum window temperatures over 600 °C and peak disk temperatures over 1600 °C. Past work has shown that beyond 650-700 °C, the Inconel window becomes susceptible to yield and rupture. The increased temperature in these results reduces the margin of error possible on beam spot size. The disk temperatures showed a sinusoidal distribution with the 6 th – 8 th disk from each window exhibiting highest disk temperatures. The peak temperature of the stainless steel housing was close to 316 °C and that of the laminations and spacers was approximately 582 °C.

43 PARTICLE ACCELERATORS↗

DOE OSTI2023

Bead–Spring Simulation of Ionomer Melts—Studying the Effects of Chain-Length and Associating Group Fraction on Equilibrium Structure and Extensional Flow Behavior

Ionomers are associative polymers with diverse applications ranging from selective membranes and high-performance adhesives to abrasion- and chemical-resistant coatings, insulation layers, vacuum packaging, and foamed sheets. Within equilibrium melt, the ionic or associating groups are known to form thermally reversible, associative clusters whose presence can significantly affect the system’s mechanical, viscoelastic, and transport properties. It is, thus, of great interest to understand how to control such clusters’ size distribution, shape, and stability through the designed choice of polymer architecture and the ionic groups’ fraction, arrangement, and interaction strength. In this work, we represent linear associating polymers using a Kremer–Grest type bead–spring model and perform large-scale MD simulations to explore the effect of polymer chain-length (l) and fraction (f s ) of randomly placed associating groups on the size distribution and stability of formed clusters. We consider different chain-lengths (below and above entanglement), varying fractions of associating groups (represented by ‘sticky’ beads) between 5 and 20%, and a fixed sticky–sticky nonbond interaction strength of four times that between regular non-associating beads. For all melts containing associating groups the equilibrium structure factor S(q) displays a signature ionomer peak at low wave vector q whose intensity increases with increasing f s and l. The average cluster size Nc increases with f s . However, the effect of chain-length on Nc appears to be pronounced only at higher values of f s . Under extensional flows, the computed stress (and viscosity) is higher at higher f s and l regardless of strain rate. Beyond a critical strain rate, we observe fragmentation of the associative clusters, which has interesting effects on the stress/viscous response.

36 MATERIALS SCIENCE↗

DOE OSTI2024

COMPUTER-AIDED LATTICE DESIGN AND ADVANCED MODELING FOR THE DEVELOPMENT OF LIGHTWEIGHT STRUCTURAL MATERIALS

The notion of a “fission battery” conveys a vision focused on realizing very simple “plug-and-play” nuclear systems that can be integrated into a variety of applications requiring affordable, reliable energy in the form of electricity and/or heat and function without operations and maintenance staff. Fission batteries require lightweight structural materials to increase their mobility, and the lightweight materials must demonstrate structural resilience under various conditions. The objective of this work is to develop lattice structured lightweight structural material featuring a good combination of mechanical properties using advanced modeling and simulation together with an advanced additive manufacturing technique such as laser powder bed fusion. The preliminary results show that different lattice structures and types can be successfully meshed using nTopology software, and the lattice structure data can be successfully transformed to Multiphysics Object-Oriented Simulation (MOOSE) Environment input. Finite Element Analysis (FEA) displays that, at macro/engineering scale simulation, the weight saving design has an obvious effect on tensile behavior such as effective elastic modulus and yield stress. The novel approaches of this work are (1) development of lattice structures for improved mechanical properties using advanced simulation and modeling techniques; and (2) model predictions of the mechanical properties (e.g., strength and stress distribution) of macroscopic materials in order to preliminarily select a lattice structure for additive manufacturing.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Machine learning bridges local static structure with multiple properties in metallic glasses

A long-standing challenge in the metallic glass (MG) community has been how to quantitatively gauge the influence of the intricate local packing environment on the response (such as the propensity for atomic rearrangement) of the atomic configuration to external stimuli. Here we establish this structure–property relation by representing the complex amorphous structure using a single, flexibility-orientated structural quantity. This structural flexibility (SF) couples to a bona fide structural representation, the pair distribution function (PDF) of individual atoms, through a weighting function that reflects what matters in the static atomic configuration to dynamic responses. Machine learning is used, employing microscopic flexibility volume as the supervisory signal, to establish via direct regression an optimized weighting vector, which is proven robust for all quenching rates, deformation conditions, and different compositions in a given (e.g., Cu x Zr 100-x ) alloy system. Additionally, the SF is evaluated solely from the particle positions (PDF), for any structure variation, from the atomic scale up to sample average. Strong correlations are demonstrated between SF and a broad range of properties, including vibrational, diffusional, as well as elastic and plastic relaxation responses.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Methods for Carbon Mass Closure in Polyolefin Hydrocracking

Heterogeneous catalytic hydrocracking of polyolefins is a promising approach for the processing of postconsumer plastics, but product quantification methods remain inconsistent across the literature. In systems that generate a large fraction of vapor-phase products, typical product capture methods can result in large carbon balance deficits, exceeding 50%, compromising reported yields and selectivities. Here, we identify the major sources of product loss and develop enhanced capture methods to improve the quantification accuracy. Seven supplemental techniques were evaluated, targeting either increased vapor recovery (by increasing the volatility or system volume) or enhanced retention in the liquid phase (by decreasing volatility). Among these, a flow collection approach using a continuous helium sweep and downstream gas sampling bag capture yielded the highest recovery, achieving a 96 ± 9.2% carbon balance closure. We show that the efficacy of these methods is strongly dependent on product distribution. In general, solvent addition was most effective when condensable species dominate the product distribution, while flow collection was preferred when both condensable species and light gases are present in high concentrations. These results highlight the need for method-specific workup strategies and demonstrate that no single protocol is universally optimal. We provide general guidelines for selecting and implementing robust product capture techniques, enabling accurate yield and selectivity determinations in polyolefin hydrocracking systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

TuckerMPI: A Parallel C++/MPI Software Package for Large-scale Data Compression via the Tucker Tensor Decomposition

With this study, our goal is compression of massive-scale grid-structured data, such as the multi-terabyte output of a high-fidelity computational simulation. For such data sets, we have developed a new software package called TuckerMPI, a parallel C++/MPI software package for compressing distributed data. The approach is based on treating the data as a tensor, i.e., a multidimensional array, and computing its truncated Tucker decomposition, a higher-order analogue to the truncated singular value decomposition of a matrix. The result is a low-rank approximation of the original tensor-structured data. Compression efficiency is achieved by detecting latent global structure within the data, which we contrast to most compression methods that are focused on local structure. In this work, we describe TuckerMPI, our implementation of the truncated Tucker decomposition, including details of the data distribution and in-memory layouts, the parallel and serial implementations of the key kernels, and analysis of the storage, communication, and computational costs. We test the software on 4.5 and 6.7 terabyte data sets distributed across 100 s of nodes (1,000 s of MPI processes), achieving compression ratios between 100 and 200,000×, which equates to 99--99.999% compression (depending on the desired accuracy) in substantially less time than it would take to even read the same dataset from a parallel file system. Moreover, we show that our method also allows for reconstruction of partial or down-sampled data on a single node, without a parallel computer so long as the reconstructed portion is small enough to fit on a single machine, e.g., in the instance of reconstructing/visualizing a single down-sampled time step or computing summary statistics. The code is available at https://gitlab.com/tensors/TuckerMPI.

97 MATHEMATICS AND COMPUTING↗