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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 1,009 records · Page 56
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Simulating the Effect of Fracture Connectivity on Repository Performance with GDSA Framework - 18589

This work examines the possible migration of radionuclides from a deep geologic nuclear waste repository sited in fractured crystalline host rock. The key safety concern is the potential effect on waste isolation of the inter-connectivity of the fracture network, which is primarily established by the temporal evolution of the temperature and stress fields at the time of original rock intrusion and cooling. Two end members are considered in these simulations, one with a high degree of connectivity to the biosphere, such that advective transport through the fracture and fault network controls radionuclide migration, and the other with a low degree of connectivity, such that slow diffusive transport through the crystalline rock matrix is the controlling process for radionuclide migration to the biosphere. Both end members have several areally extensive, high-transmissivity deformation zones, whose distance to the repository is an important factor for waste isolation capability. Uncertainties in fracture properties (transmissivity, orientation, radius) and fracture distribution also give rise to uncertainty in waste isolation capability (i.e., the overall connectivity of the repository with the surface biosphere). These types of natural system uncertainties are generally present in any geologic site-characterization program and thus represent an important factor in assessing repository performance in hard rock environments. The waste considered in these simulations are spent fuel rod assemblies from the U.S. commercial nuclear reactor fleet. Thermal output of the waste must be considered in the simulations and can influence the rate and timing of waste package failure, waste form degradation, and fluid flux due to thermal expansion around the repository horizon. To achieve a high-fidelity representation of radionuclide transport in fractures and rock matrix, combined with thermal energy transport and fluid flow in fractures and matrix, the mathematical model is solved numerically in a parallel high-performance computing (HPC) environment on a finite volume unstructured grid consisting of approximately 5 million cells, using Geologic Disposal Safety Assessment (GDSA) Framework (https://pa.sandia.gov), an open-source performance assessment tool for deep underground disposal of nuclear waste. GDSA Framework uses PFLOTRAN to solve the balance equations on a three-dimensional grid with heterogeneous properties, using multiple processors in a parallel configuration based on domain decomposition. The fracture networks in these simulations are originally generated as discrete fracture networks (DFNs), which are sets of two-dimensional planes distributed in a three-dimensional domain. The method used in GDSA Framework maps the stochastically generated DFN to an equivalent continuous porous medium (ECPM) domain that allows for the simulation of coupled heat flow, fluid flow, and radionuclide transport, including heat conduction through the matrix of the fractured rock, which is a process not easily modeled in a DFN representation. Computational efficiency is also greatly enhanced using the ECPM method, allowing for a realistic representation and analysis of uncertainties in a multi-realization performance assessment of a deep geologic repository. The effect of fracture connectivity on the waste isolation safety function, as brought to light by these GDSA Framework simulations, points to the importance of including a realistic representation of uncertainties in fracture properties and distribution (effectively, uncertainty in spatial heterogeneity) in repository safety assessment simulations. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2018

Recursive integral method with Cayley transformation

Summary The recently developed RIM (recursive integral method) finds eigenvalues in a region of the complex plane. It computes an indicator to test if the region contains eigenvalues using an approximate spectral projection. If the indicator shows that the region contains eigenvalues, it is subdivided into smaller regions, which are then recursively tested and subdivided until any eigenvalues are isolated to a specified precision. We propose an enhancement to RIM that uses Cayley transformations and Arnoldi's method to greatly decrease the number of factorizations required to solve the linear systems that arise from a discretized contour integral to compute the indicator, which substantially reduces the computational cost. We demonstrate the efficacy of our method with numerical examples and compare with the implicitly restarted Arnoldi method, as implemented in eigs in MATLAB.

Huang, R.↗
DOE OSTI2023

Preservation of kinetics parameters generated by Monte Carlo calculations in two-step deterministic calculations

The generation of accurate kinetic parameters such as mean generation time Λ and effective delayed neutron fraction β eff via Monte Carlo codes is established. Employing these in downstream deterministic codes warrants another step to ensure no additional error is introduced by the low-order transport operator when computing forward and adjoint fluxes for bilinear weighting of these parameters. Another complexity stems from applying superhomogenization (SPH) equivalence in non-fundamental mode approximations, where reference and low-order calculations rely on a 3D full core model. In these cases, SPH factors can optionally be computed for only part of the geometry while preserving reaction rates and K-effective, but the impact of such approximations on kinetics parameters has not been thoroughly studied. This paper aims at studying the preservation of bilinearly-weighted quantities in the Serpent–Griffin calculation procedure. Diffusion and transport evaluations of IPEN/MB-01, Godiva, and Flattop were carried out with the Griffin reactor physics code, testing available modeling options using Serpent-generated multigroup cross sections and equivalence data. Verifying Griffin against Serpent indicates sensitivities to multigroup energy grid selection and regional application of SPH equivalence, introducing significant errors; these were demonstrated to be reduced through the use of a transport method together with a finer energy grid.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2017

Approximate solutions of acoustic 3D integral equation and their application to seismic modeling and full-waveform inversion

Over the recent decades, a number of fast approximate solutions of Lippmann–Schwinger equation, which are more accurate than classic Born and Rytov approximations, were proposed in the field of electromagnetic modeling. Those developments could be naturally extended to acoustic and elastic fields; however, until recently, they were almost unknown in seismology. This paper presents several solutions of this kind applied to acoustic modeling for both lossy and lossless media. We evaluated the numerical merits of those methods and provide an estimation of their numerical complexity. In our numerical realization we use the matrix-free implementation of the corresponding integral operator. We study the accuracy of those approximate solutions and demonstrate, that the quasi-analytical approximation is more accurate, than the Born approximation. Further, we apply the quasi-analytical approximation to the solution of the inverse problem. It is demonstrated that, this approach improves the estimation of the data gradient, comparing to the Born approximation. The developed inversion algorithm is based on the conjugate-gradient type optimization. Numerical model study demonstrates that the quasi-analytical solution significantly reduces computation time of the seismic full-waveform inversion. We also show how the quasi-analytical approximation can be extended to the case of elastic wavefield.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

FELIX-2.0: New version of the finite element solver for the time dependent generator coordinate method with the Gaussian overlap approximation

The time-dependent generator coordinate method (TDGCM) is a powerful method to study the largeamplitude collective motion of quantum many-body systems such as atomic nuclei. Under the GaussianOverlap Approximation (GOA), the TDGCM leads to a local, time-dependent Schrödinger equation in amulti-dimensional collective space. In this paper, we present the version 2.0 of the code FELIX that solvesthe collective Schrödinger equation in a finite element basis. This new version features: (i) the ability tosolve a generalized TDGCM+GOA equation with a metric term in the collective Hamiltonian, (ii) supportfor new kinds of finite elements and different types of quadrature to compute the discretized Hamiltonianand overlap matrices, (iii) the possibility to leverage the spectral element scheme, (iv) an explicit Krylovapproximation of the time propagator for time integration instead of the implicit Crank–Nicolson methodimplemented in the first version, (v) an entirely redesigned workflow. We benchmark this release on ananalytic problem as well as on realistic two-dimensional calculations of the low-energy fission of240Puand256Fm. Low to moderate numerical precision calculations are most efficiently performed with simplexelements with a degree 2 polynomial basis. Higher precision calculations should instead use the spectralelement method with a degree 4 polynomial basis. We emphasize that in a realistic calculation of fissionmass distributions of240Pu, FELIX-2.0 is about 20 times faster than its previous release (within a numericalprecision of a few percents).

Regnier, D.↗
DOE OSTI2023

A Predictor-Corrector Strategy for Adaptivity in Dynamical Low-Rank Approximations

Here, in this paper, we present a predictor-corrector strategy for constructing rank-adaptive, dynamical low-rank approximations (DLRAs) of matrix-valued ODE systems. The strategy is a compromise between (i) low-rank step-truncation approaches that alternately evolve and compress solutions and (ii) strict DLRA approaches that augment the low-rank manifold using subspaces generated locally in time by the DLRA integrator. The strategy is based on an analysis of the error between a forward temporal update into the ambient full-rank space, which is typically computed in a step-truncation approach before recompressing, and the standard DLRA update, which is forced to live in a low-rank manifold. We use this error, without requiring its full-rank representation, to correct the DLRA solution. A key ingredient for maintaining a low-rank representation of the error is a randomized SVD, which introduces some degree of stochastic variability into the implementation. The strategy is formulated and implemented in the context of discontinuous Galerkin spatial discretizations of PDEs and applied to several versions of DLRA methods found in the literature as well as a new variant. Numerical experiments comparing the predictor-corrector strategy to other methods demonstrate robustness to overcome shortcomings of step truncation or strict DLRA approaches: The former may require more memory than is strictly needed, while the latter may miss transients solution features that cannot be recovered. The effect of randomization, tolerances, and other implementation parameters is also explored.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

High-Fidelity and High-Performance Computational Simulations for Rapid Design Optimization of Sulfur Thermal Energy Storage

Industrial process heating (IPH) accounts for approximately 70% of US manufacturing energy use and is primarily produced by fossil fuel combustion. Approximately 1500 TWht (approximately 60%) of IPH demand is in the temperature range of 100-300. Industrial applications in this temperature range include drying, hydrothermal processing, thermal enhanced oil recovery, food and beverage, bioethanol production, etc. Cost-effective thermal energy storage (TES) that increases the utilization of waste and renewable heat (solar, geothermal, etc.) could provide significant energy savings and reliable heat sources, decrease emissions, and increase US manufacturing competitiveness through reductions in fuel consumption. TES development has historically been dominated by technologies suitable for deployment with concentrating solar power (CSP). State-of-the-art thermal storage deployed commercially with power tower CSP plants uses a 60%/40% NaNO3/KNO3 molten salt and operates between temperatures of approximately 280 degrees Celsius and 570 degrees Celsius using a two-tank configuration. However, these nitrate salts are unsuitable for operation outside of this temperature range due to a high freezing point of approximately 220 degrees Celsius, and limits on high-temperature salt stability and corrosion resistance of containment alloys. Other materials being investigated for TES include those based on: (1) sensible energy storage (various molten salt compositions, inert solid particles, rocks or pebble beds, sulfur, water, concrete, graphite, etc.), (2) latent energy storage in materials that undergo solid-liquid phase change at relevant temperatures (organic materials for low-temperature applications, inorganic salts and/or metals for high-temperature applications), or (3) thermochemical energy storage (hydrides, hydroxides, carbonates, metal oxides, etc.). The application temperature and challenges pertaining to storage material and/or containment cost, energy density, long-term thermal and cyclic stability, and charge/discharge heat transfer effectiveness drive material selection for a given IPH or electricity generation application. Sulfur is a cheap commodity at $80/ton compared to $1100 - 1300/ton for conventional salts. When using a metric of storage cost per kWh, sulfur costs around 2-3 $/kWh. Previous sulfur TES development focused on high temperature (>600 degrees) concentrated solar power applications with sulfur encapsulated in pipes and flow of gaseous HTF (air) in the shell side. However, for lower-temperature IPH applications in the range of approximately 100-300 degrees Celsius Element 16 adopted a compact and scalable TES design with molten sulfur in the shell and HTF pipes submerged in the molten sulfur bath. The low-cost molten sulfur TES for dispatchable IPH has deployment potential for broad applications. The spatial and temporal evolution of the HTF and sulfur temperature is critical to the TES system performance, and thus detailed modeling can improve understanding of the performance and facilitate design improvements. Using high performance computing and computational fluid dynamics (CFD) a low-cost molten sulfur thermal energy storage (TES) system for industrial process heating (IPH) applications was developed. The unique challenges in CFD modeling of sulfur TES are the sharp property changes of sulfur relevant to the working temperatures. Above 159, liquid sulfur undergoes polymerization, and the viscosity of sulfur rapidly increases by several orders of magnitude between 159 degrees Celsius and 188 degrees Celsius, followed by a decrease in viscosity beyond 188 degrees Celsius due to thermal bound dissociation. In addition, various concentrations of H2S impurities can also modify sulfur viscosity. This numerical challenge is especially relevant to transient simulation of the sulfur TES charging and discharging processes as the extreme property variations limit the applicability of traditional heat transfer correlations. Transient CFD simulations including the temperature-dependent sulfur properties and geometric complexity of the TES design were used to predict the effect of natural convection during charging and discharging on the heat transfer process, sulfur temperature uniformity, charge/discharge rates, and performance of the storage devices. The CFD model was validated with experimental results for a full charge and discharge cycle. The work will show 3D and 2D simulation comparisons aimed to facilitate rapid design iterations and a machine learning based design optimization approach.

CFD↗
DOE OSTI2022

Deep learning to estimate permeability using geophysical data

Time-lapse electrical resistivity tomography (ERT) is a popular geophysical method to estimate three-dimensional (3D) permeability fields from electrical potential difference measurements. Traditional inversion and data assimilation methods are used to ingest this ERT data into hydrogeophysical models to estimate permeability. Due to ill-posedness and the curse of dimensionality, existing inversion strategies provide poor estimates and low resolution of the 3D permeability field. Recent advances in deep learning provide us with powerful algorithms to overcome this challenge. This paper presents a deep learning (DL) framework to estimate the 3D subsurface permeability from time-lapse ERT data. To test the feasibility of the proposed framework, we train DL-enabled inverse models on simulation data. Each measurement in both synthetic and field data is standardized by removing the mean and scaling the time-series to unit variance. This pre-processing step is necessary to bring simulation data closer to field observations. Subsurface process models based on hydrogeophysics are used to generate this synthetic data. Training performed on limited simulation data resulted in the DL model over-fitting. An advanced data augmentation based on mixup is implemented to generate additional training samples to overcome this issue. This mixup technique creates weakly labeled (low-fidelity) samples from strongly labeled (high-fidelity) data. The weakly labeled training data is then used to develop DL-enabled inverse models and reduce over-fitting. As both time-lapse ERT (1133048 features/realization) and 3D permeability (585453 features/realization) data samples are from a high-dimensional space, principal component analysis (PCA) is employed to reduce dimensionality. Encoded ERT and encoded permeability are generated using the trained PCA estimators. A deep neural network is then trained to map the encoded ERT to encoded permeability. This mixup training and unsupervised learning allowed us to build a fast and reasonably accurate DL-based inverse model under limited simulation data. Results show that proposed weak supervised learning can capture salient spatial features in the 3D permeability field. Quantitatively, the average mean squared error (in terms of the natural log) on the strongly labeled training, validation, and test datasets is less than 0.5. The R 2 -score (global metric) is greater than 0.75, and the percent error in each cell (local metric) is less than 10%. Finally, an added benefit in terms of computational cost is that the proposed DL-based inverse model is at least O(10 4 ) times faster than running a forward model once it is trained. Data generation, DL model training, and hyperparameter tuning to identify optimal neural network architectures utilized high-performance computing resources while the DL inference is performed on a standard laptop. Approximately, O(10 5 ) processor hours are used for generating data and DL tuning and training. We acknowledge that the data generation and DL model development are expensive. But once a DL model is trained, it can be re-used for inversion rapidly for the given system, with set physics and domain. Note that traditional inversion may require multiple forward model simulations (e.g., in the order of 10 to 1000), which are very expensive. This computational savings ≈ O(10 5 ) – O(10 7 )) makes the proposed DL-based inverse model attractive for subsurface imaging and real-time ERT monitoring applications due to fast and yet reasonably accurate estimations of permeability field.

58 GEOSCIENCES↗
DOE OSTI2020

Multigrid deflation for Lattice QCD

Computing the trace of the inverse of large matrices is typically addressed through statistical methods. Deflating out the lowest eigenvectors or singular vectors of the matrix reduces the variance of the trace estimator. This work summarizes our efforts to reduce the computational cost of computing the deflation space while achieving the desired variance reduction for Lattice QCD applications. Previous efforts computed the lower part of the singular spectrum of the Dirac operator by using an eigensolver preconditioned with a multigrid linear system solver. Despite the improvement in performance in those applications, as the problem size grows the runtime and storage demands of this approach will eventually dominate the stochastic estimation part of the computation. In this work, we propose to compute the deflation space in one of the following two ways. First, by using an inexact eigensolver on the Hermitian, but maximally indefinite, operator. Second, by exploiting the fact that the multigrid prolongator for this operator is rich in components toward the lower part of the singular spectrum. We show experimentally that the inexact eigensolver can approximate the lower part of the spectrum even for ill-conditioned operators. Also, the deflation based on the multigrid prolongator is more efficient to compute and apply, and, despite its limited ability to approximate the fine level spectrum, it obtains similar variance reduction on the trace estimator as deflating with approximate eigenvectors from the fine level operator.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Gleipnir: toward practical error analysis for Quantum programs

Practical error analysis is essential for the design, optimization, and evaluation of Noisy Intermediate-Scale Quantum(NISQ) computing. However, bounding errors in quantum programs is a grand challenge, because the effects of quantum errors depend on exponentially large quantum states. In this work, we present Gleipnir, a novel methodology toward practically computing verified error bounds in quantum programs. Gleipnir introduces the (ρ,δ)-diamond norm, an error metric constrained by a quantum predicate consisting of the approximate state ρ and its distance δ to the ideal state ρ. This predicate (ρ,δ) can be computed adaptively using tensor networks based on the Matrix Product States. Gleipnir features a lightweight logic for reasoning about error bounds in noisy quantum programs, based on the (ρ,δ)-diamond norm metric. Furthermore, our experimental results show that Gleipnir is able to efficiently generate tight error bounds for real-world quantum programs with 10 to 100 qubits, and can be used to evaluate the error mitigation performance of quantum compiler transformations.

Tao, Runzhou↗
DOE OSTI2017

Gluon orbital angular momentum at small x

We present a general analysis of the orbital angular momentum (OAM) distribution of gluons L g (x) inside the nucleon with particular emphasis on the small- x region. We derive a novel operator representation of L g (x) in terms of Wilson lines and argue that it is approximately proportional to the gluon helicity distribution L g (x) ≈ - 2 Δ G (x) at small x . Here, we also compute longitudinal single-spin asymmetry in exclusive diffractive dijet production in lepton-nucleon scattering in the next-to-eikonal approximation and show that the asymmetry is a direct probe of the gluon helicity/OAM distribution as well as the QCD odderon exchange.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Modeling of particle transport, neutrals and radiation in magnetically-confined plasmas with Aurora

In this work, we present Aurora, an open-source package for particle transport, neutrals and radiation modeling in magnetic confinement fusion plasmas. Aurora's modern multi-language interface enables simulations of 1.5D impurity transport within high-performance computing frameworks, particularly for the inference of particle transport coefficients. A user-friendly Python library allows simple interaction with atomic rates from the Atomic Data and Atomic Structure database as well as other sources. This enables a range of radiation predictions, both for power balance and spectroscopic analysis. We discuss here the superstaging approximation for complex ions, as a way to group charge states and reduce computational cost, demonstrating its wide applicability within the Aurora forward model and beyond. Aurora also facilitates neutral particle analysis, both from experimental spectroscopic data and other simulation codes. Leveraging Aurora's capabilities to interface SOLPS-ITER results, we demonstrate that charge exchange is unlikely to affect the total radiated power from the ITER core during high performance operation. Finally, we describe the ImpRad module in the one modeling framework for integrated task framework, developed to enable experimental analysis and transport inferences on multiple devices using Aurora.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Removing instabilities in the hierarchical equations of motion: Exact and approximate projection approaches

The hierarchical equations of motion (HEOM) provide a numerically exact approach for computing the reduced dynamics of a quantum system linearly coupled to a bath. We have found that HEOM contains temperature-dependent instabilities that grow exponentially in time. In the case of continuous-bath models, these instabilities may be delayed to later times by increasing the hierarchy dimension; however, for systems coupled to discrete, nondispersive modes, increasing the hierarchy dimension does little to alleviate the problem. We show that these instabilities can also be removed completely at a potentially much lower cost via projection onto the space of stable eigenmodes; furthermore, we find that for discrete-bath models at zero temperature, the remaining projected dynamics computed with few hierarchy levels are essentially identical to the exact dynamics that otherwise might require an intractably large number of hierarchy levels for convergence. Recognizing that computation of the eigenmodes might be prohibitive, e.g., for large or strongly coupled models, we present a Prony filtration algorithm that may be useful as an alternative for accomplishing this projection when diagonalization is too costly. We present results demonstrating the efficacy of HEOM projected via diagonalization and Prony filtration. Finally, we discuss issues associated with the non-normality of HEOM.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Computation of the Biot–Savart line integral with higher-order convergence using straight segments

One common approach to computing the magnetic field produced by a filamentary current-carrying coil is to approximate the coil as a series of straight segments. The Biot–Savart field from each straight segment is analytically known. However, if the endpoints of the straight segments are chosen to lie on the coil, then the accuracy of the Biot–Savart computation is generally only the second order in the number of endpoints. In this work, we propose a simple modification: shift each end point of the coil in the outward normal direction by an amount proportional to the local curvature. With this modification, the Biot–Savart accuracy increases to the fourth order and the numerical error is dramatically reduced for a given number of discretization points.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

A Method for Dimensionally Adaptive Sparse Trigonometric Interpolation of Periodic Functions

We present a method for dimensionally adaptive sparse trigonometric interpolation of multidimensional periodic functions belonging to a smoothness class of finite order. This method targets applications where periodicity must be preserved and the precise anisotropy is not known a priori. To the authors' knowledge, this is the first instance of a dimensionally adaptive sparse interpolation algorithm that uses a trigonometric interpolation basis. The motivating application behind this work is the adaptive approximation of a multi-input model for a molecular potential energy surface (PES) where each input represents an angle of rotation. Our method is based on an anisotropic quasi-optimal estimate for the decay rate of the Fourier coefficients of the model; a least-squares fit to the coefficients of the interpolant is used to estimate the anisotropy. Thus, our adaptive approximation strategy begins with a coarse isotropic interpolant, which is gradually refined using the estimated anisotropic rates. The procedure takes several iterations where ever-more accurate interpolants are used to generate ever-improving anisotropy rates. We present several numerical examples of our algorithm where the adaptive procedure successfully recovers the theoretical “best” convergence rate, including an application to a periodic PES approximation. An open-source implementation of our algorithm resides in the Tasmanian UQ library developed at Oak Ridge National Laboratory.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Checkpoint-Restart and Platform Design Criteria

Long computations often use checkpoint/restart to survive the inevitable failures. Optimal checkpoint/restart strategy can be derived in terms of special functions, and approximated within the regime of interest. As a further step under nominal assumptions, platforms can be optimized for maximum progress rate, computed in terms of non-dimensional parameter JMTTI/Delta, where JMTTI is the Job Mean Time To Interrupt and Delta is the time it takes to write (or read) a checkpoint. Scaling to a larger platform of the same technology requires scaling checkpoint bandwidth quadratically to maintain the same progress rate. This was observed during the design of LANL’s Roadrunner in 2007, led to burst buffers proposed in 2009 and introduced on Trinity in 2015. The need to compute reliably continues to impact the design of future exascale platforms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Distributed approximate minimal Steiner trees with millions of seed vertices on billion-edge graphs

In this report, we present a parallel 2-approximation Steiner minimal tree algorithm and its MPI-based distributed implementation. In place of expensive distance computations between all pairs of seed vertices, the solution we employ exploits a cheaper Voronoi cell computation. Our design leverages asynchronous processing and message prioritization to accelerate convergence of distance computations, and harnesses vertex and edge centric processing to offer fast time-to-solution. We demonstrate scalability and performance using real-world graphs with up to 128 billion edges and 512 compute nodes, and show the ability to find Steiner trees with up to one million seed vertices. Using 12 data instances, we present comparison with the state-of-the-art exact solver, SCIP-Jack, and two sequential 2-approximate algorithms. We empirically show that, on average, the total distance of the Steiner tree identified by our solution is 1.1290 times greater than the Steiner minimal tree – well within the theoretical approximation bound of 2.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Milestone Completion Report WBS 1.3.5.05 ECP/VTK-m FY17Q4 [MS-17/03-06] Key Reduce / Spatial Division / Basic Advect / Normals STDA05-4.

The FY17Q4 milestone of the ECP/VTK-m project includes the completion of a key-reduce scheduling mechanism, a spatial division algorithm, an algorithm for basic particle advection, and the computation of smoothed surface normals. With the completion of this milestone, we are able to, respectively, more easily group like elements (a common visualization algorithm operation), provide the fundamentals for geometric search structures, provide the fundamentals for many flow visualization algorithms, and provide more realistic rendering of surfaces approximated with facets.

97 MATHEMATICS AND COMPUTING↗