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At least 73 records · Page 4

Automatic Differentiation for Adjoint Stencil Loops

Stencil loops are a common motif in computations including convolutional neural networks, structured-mesh solvers for partial differential equations, and image processing. Stencil loops are easy to parallelise, and their fast execution is aided by compilers, libraries, and domain-specific languages. Reverse-mode automatic differentiation, also known as algorithmic differentiation, autodiff, adjoint differentiation, or back-propagation, is sometimes used to obtain gradients of programs that contain stencil loops. Unfortunately, conventional automatic differentiation results in a memory access pattern that is not stencil-like and not easily parallelisable. In this paper we present a novel combination of automatic differentiation and loop transformations that preserves the structure and memory access pattern of stencil loops, while computing fully consistent derivatives. The generated loops can be parallelised and optimised for performance in the same way and using the same tools as the original computation. We have implemented this new technique in the Python tool PerforAD, which we release with this paper along with test cases derived from seismic imaging and computational fluid dynamics applications.

Automatic Differentiation↗

Electrochemically Smart Bimetallic Materials Featuring Group 11 Metals: In-situ Conductive Network Generation and Its Impact on Cell Capacity

Our results for this program “Electrochemically smart bimetallic materials featuring Group 11 metals: in-situ conductive matrix generation and its impact on battery capacity, power and reversibility” have been highly successful: 1) we demonstrated material structures which generated in-situ conductive networks through electrochemical activation with increases in conductivity up to 10,000 fold, 2) we pioneered in situ analytical methodology to map the cathodes at several stages of discharge through the use of Energy Dispersive X-ray Diffraction (EDXRD) to elucidate the kinetic dependence of the conductive network formation, and 3) we successfully designed synthetic methodology for direct control of material properties including crystallite size and surface area which showed significant impact on electrochemical behavior.

30 DIRECT ENERGY CONVERSION↗

Status Report on the Component Models Developed in the Modelica Framework: Reverse Osmosis Desalination Plant & Thermal Energy Storage

This report has been prepared as part of an effort to design and build a Modeling and Simulation (M&S) framework to assess the economic viability of a Nuclear-Renewable Hybrid Energy System (N-R HES). In order to facilitate dynamic M&S of such an integrated system, research groups in multiple national laboratories and universities have been developing various subsystems as dynamic physics-based components using the Modelica programming language. In Fiscal Years (FYs) 2015, Idaho National Laboratory (INL) performed a dynamic analysis of two region-specific N-R HES configurations, including the gas-to-liquid (natural gas to Fischer-Tropsch synthetic fuel) and brackish water Reverse Osmosis (RO) desalination plants as industrial processes. In FYs 2016–2017, INL developed two additional subsystems in the Modelica framework: (1) a high-temperature steam electrolysis plant as a high priority industrial plant to be integrated with a light water reactor within an N-R HES and (2) a gas turbine power plant as a secondary energy supply. In FY 2018, the RO desalination system model developed in FY 2015 has been updated such that the model is compatible with the most recent version of the ThermoPower library. Special attention has been given to the controller settings based on process models, aiming to improve process dynamics and controllability. A dynamic performance analysis of the updated RO desalination plant was carried out to evaluate the technical feasibility (load-following capability) of such a system operating under highly variable conditions requiring flexible output. Simulation results involving several case studies show that the suggested control scheme could maintain the controlled variables (including the variable electrical load and RO feed pressure) within desired limits under various plant operating conditions. The results also indicate that the proposed RO plant could provide operational flexibility to participate in energy management at the utility scale by dynamically optimizing the use of excess plant capacity within an N-R HES. For a small-scale energy storage system, a sensible Thermal Energy Storage (TES) model has been developed in the Modelica Framework in FY 2018.

25 ENERGY STORAGE↗

ARENA: Asynchronous Reconfigurable Accelerator Ring to Enable Data-Centric Parallel Computing

The next generation HPC and data centers are likely to be reconfigurable and data-centric due to the trend of hardware specialization and the emergence of data-driven applications. In this work, we propose ARENA – an asynchronous reconfigurable accelerator ring architecture as a potential scenario on how the future HPC and data centers will be like. Despite using the coarse-grained reconfigurable arrays (CGRAs) as the substrate platform, our key contribution is not only the CGRA-cluster design itself, but also the ensemble of a new architecture and programming model that enables asynchronous tasking across a cluster of reconfigurable nodes, so as to bring specialized computation to the data rather than the reverse. We presume distributed data storage without asserting any prior knowledge on the data distribution. Hardware specialization occurs at runtime when a task finds the majority of data it requires are available at the present node. In other words, we dynamically generate specialized CGRA accelerators where the data reside. The asynchronous tasking for bringing computation to data is achieved by circulating the task token, which describes the dataflow graphs to be executed for a task, among the CGRA cluster connected by a fast ring network. Evaluations on a set of HPC and data-driven applications across different domains show that ARENA can provide better parallel scalability with reduced data movement (53.9 percent). Compared with contemporary compute-centric parallel models, ARENA can bring on average 4.37× speedup. The synthesized CGRAs and their task-dispatchers only occupy 2.93mm 2 chip area under 45nm process technology and can run at 800MHz with on average 759.8mW power consumption. ARENA also supports the concurrent execution of multi-applications, offering ideal architectural support for future high-performance parallel computing and data analytics systems.

97 MATHEMATICS AND COMPUTING↗

Imaging Complex Subsurface Structures for Geothermal Exploration at Pirouette Mountain and Eleven-Mile Canyon in Nevada

Accurate imaging of subsurface complex structures with faults is crucial for geothermal exploration because faults are generally the primary conduit of hydrothermal flow. It is very challenging to image geothermal exploration areas because of complex geologic structures with various faults and noisy surface seismic data with strong and coherent ground-roll noise. In addition, fracture zones and most geologic formations behave as anisotropic media for seismic-wave propagation. Properly suppressing ground-roll noise and accounting for subsurface anisotropic properties are essential for high-resolution imaging of subsurface structures and faults for geothermal exploration. We develop a novel wavenumber-adaptive bandpass filter to suppress the ground-roll noise without affecting useful seismic signals. This filter adaptively exploits both characteristics of the lower frequency and the smaller velocity of the ground-roll noise than those of the signals. Consequently, this filter can effectively differentiate the ground-roll noise from the signal. We use our novel filter to attenuate the ground-roll noise in seismic data along five survey lines acquired by the U.S. Navy Geothermal Program Office at Pirouette Mountain and Eleven-Mile Canyon in Nevada, United States. We then apply our novel anisotropic least-squares reverse-time migration algorithm to the resulting data for imaging subsurface structures at the Pirouette Mountain and Eleven-Mile Canyon geothermal exploration areas. The migration method employs an efficient implicit wavefield-separation scheme to reduce image artifacts and improve the image quality. Our results demonstrate that our wavenumber-adaptive bandpass filtering method successfully suppresses the strong and coherent ground-roll noise in the land seismic data, and our anisotropic least-squares reverse-time migration produces high-resolution subsurface images of Pirouette Mountain and Eleven-Mile Canyon, facilitating accurate fault interpretation for geothermal exploration.

15 GEOTHERMAL ENERGY↗

Twist again: Dynamically and reversibly controllable chirality in liquid crystalline elastomer microposts

Photoresponsive liquid crystalline elastomers (LCEs) constitute ideal actuators for soft robots because their light-induced macroscopic shape changes can be harnessed to perform specific articulated motions. Conventional LCEs, however, do not typically exhibit complex modes of bending and twisting necessary to perform sophisticated maneuvers. Here, we model LCE microposts encompassing side-chain mesogens oriented along a magnetically programmed nematic director, and azobenzene cross-linkers, which determine the deformations of illuminated posts. On altering the nematic director orientation from vertical to horizontal, the post’s bending respectively changes from light-seeking to light-avoiding. Moreover, both modeling and subsequent experiments show that with the director tilted at 45°, the initially achiral post reversibly twists into a right- or left-handed chiral structure, controlled by the angle of incident light. We exploit this photoinduced chirality to design “chimera” posts (encompassing two regions with distinct director orientations) that exhibit simultaneous bending and twisting, mimicking motions exhibited by the human musculoskeletal system.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Northern Arabian Sea Circulation-Autonomous Research (NASCar): A Research Initiative Based on Autonomous Sensors

The Arabian Sea circulation is forced by strong monsoonal winds and is characterized by vigorous seasonally reversing currents, extreme differences in sea surface salinity, localized substantial upwelling, and widespread submesoscale thermohaline structures. Its complicated sea surface temperature patterns are important for the onset and evolution of the Asian monsoon. This article describes a program that aims to elucidate the role of upper-ocean processes and atmospheric feedbacks in setting the sea surface temperature properties of the region. The wide range of spatial and temporal scales and the difficulty of accessing much of the region with ships due to piracy motivated a novel approach based on state-of-the-art autonomous ocean sensors and platforms. The extensive data set that is being collected, combined with numerical models and remote sensing data, confirms the role of planetary waves in the reversal of the Somali Current system. These data also document the fast response of the upper equatorial ocean to monsoon winds through changes in temperature and salinity and the connectivity of the surface currents across the northern Indian Ocean. New observations of thermohaline interleaving structures and mixing in setting the surface temperature properties of the northern Arabian Sea are also discussed.

54 ENVIRONMENTAL SCIENCES↗

Global reverse supply chain design for solid waste recycling under uncertainties and carbon emission constraint

Highlights: • We propose a robust model for global reverse supply chain design. • The uncertain waste collection rate, currency exchange rate, and the maritime cost are incorporated. • The total emission and cost are affected by both the uncertainties and the global carbon cap. • The waste products flows between countries vary with the levels of uncertainties and the global carbon cap. • There is an opportunity to reduce the maritime emission. - Abstract: The emergence of concerns over environmental protection, resource conservation as well as the development of logistics operations and manufacturing technology has led several countries to implement formal collection and recycling systems of solid waste. Such recycling system has the benefits of reducing environmental pollution, boosting the economy by creating new jobs, and generating income from trading the recyclable materials. This leads to the formation of a global reverse supply chain (GRSC) of solid waste. In this paper, we investigate the design of such a GRSC with a special emphasis on three aspects; (1) uncertainty of waste collection levels, (2) associated carbon emissions, and (3) challenges posed by the supply chain’s global aspect, particularly the maritime transportation costs and currency exchange rates. To the best of our knowledge, this paper is the first attempt to integrate the three above-mentioned important aspects in the design of a GRSC. We have used mixed integer-linear programming method along with robust optimization to develop the model which is validated using a sample case study of e-waste management. Our results show that using a robust model by taking the complex interactions characterizing global reverse supply chain networks into account, we can create a better GRSC. The effect of uncertainties and carbon constraints on decisions to reduce costs and emissions are also shown.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Strategies for Constructing and Operating DNA Origami Linear Actuators

Abstract Linear actuators are ubiquitous components at all scales of engineering. DNA nanotechnology offers a unique opportunity for bottom‐up assembly at the molecular scale, providing nanoscale precision with multiple methods for constructing and operating devices. In this paper, DNA origami linear actuators with up to 200 nm travel, based on a rail threading a topologically locked slider, are demonstrated. Two strategies, one‐ and two‐pot assembly, are demonstrated whereby the two components are folded from one or two DNA scaffold strands, respectively. In order to control the position of the slider on the rail, the rail and the inside of the slider are decorated with single‐stranded oligonucleotides with distinct sequences. Two positioning strategies, based on diffusion and capture of signaling strands, are used to link the slider reversibly to determined positions on the rail with high yield and precision. These machine components provide a basis for applications in molecular machinery and nanoscale manufacture including programmed chemical synthesis.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Final Scientific/Technical Report for Program Title: Solar Powered Dewvaporation Desalination System

Desalination technologies have been used increasingly throughout the world to produce the drinking water from the brackish ground and sea water for the past few decades. Among the commercially available desalination technologies, reverse osmosis (RO) and multi-stage flash distillation are the most widely used technologies globally. However, these technologies are difficult to be directly integrated with green energies without converting them to electricity. Dewvaporation, a desalination process, uses saturated steam as a carrier-gas to evaporate water from saline feeds and form pure condensate. It has the major technical benefit of reusing energy, released from vapor condensation, multiple times. The current proposal has been planned to address this issue. In Phase I, we have successfully demonstrated the feasibility of a new plasmonic nanoparticle based approach through fabrication and evaluation of a solar powered water vapor generation module. The water vapor generation module allows generation of high temperature plasmon on a fiber bundle end, where strong water and plasmon interaction occurs generating water vapor. Plasmon enhanced water evaporation has been realized on plasmonic nanoparticle immobilized substrate with an energy conversion efficiency of over 50%.

14 SOLAR ENERGY↗

Interpreting the Operando X-ray Absorption Near-Edge Structure of Supported Cu and CuPd Clusters in Conditions of Oxidative Dehydrogenation of Propane: Dynamic Changes in Composition and Size

Supported subnano-cluster catalysts are highly dynamic, developing true active sites only under the pressures and temperatures of reaction conditions. Operando X-ray absorption near-edge structure (XANES) spectroscopy can track changes in the oxidation state and the local environment of cluster atoms, providing insight into the development of these active sites. While bulk metal, oxide, and hydroxide standards are often used for fitting experimental XANES spectra to obtain average oxidation states, we recently showed that computed cluster standards of relevant compositions are a more suitable basis, producing more accurate fits. Here, we theoretically interpret the operando XANES of supported Cu 3 Pd and Cu 4 clusters during temperature-programmed reaction (TPRx) of oxidative dehydrogenation of propane. We use an expanded basis set including both globally optimized computed clusters and bulk standards. Not only can we track reversible composition/oxidation state change with temperature, but also the irreversible growth of the bulk fraction upon heating, which we attribute to cluster sintering. This has important implications for the mechanism of the catalyzed reaction and the nature of the available active sites. Here, we propose that operando XANES provides most significant insight into the nature of supported cluster catalysts in reaction conditions when interpreted using mixed computed cluster and bulk standards.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Alignment switching in 3D-printed smectic liquid crystal elastomers

Extrusion-based additive manufacturing has emerged as a powerful platform for designing shape-morphing materials through controlled orientation. However, existing approaches primarily rely on a single mode of flow-induced alignment, limiting orientation programmability. Herein, we present a direct-ink-writing approach for smectic liquid crystal elastics that exploits two distinct alignment modes within a single ink. The smectic ink exhibits shear- and temperature-dependent orientation switching, enabling molecular alignment either perpendicular or parallel to the print direction. Combined rheological, X-ray, and molecular dynamics analyses reveal that this alignment inversion arises from the preservation or collapse of smectic layers under flow. This reversible switching encodes both contractile and elongational actuation within individual filaments, greatly expanding the design freedom of printed liquid crystal elastomers. We demonstrate 2D and 3D structures with diverse programmed shape transformations, highlighting the potential of this platform for adaptive soft actuators and architected functional materials.

Lee, Jin Hyeong [Pusan National University, Busan,↗

Search for Time Reversal Symmetry Violation with TREK at J-PARC (Closeout Report)

This DOE Early Career Award has enabled Dr. Michael Kohl to take on and expand his leadership roles in several projects such as TREK@J-PARC, OLYMPUS@DESY, MUSE@PSI, and in the experimental program in Hall C at Jefferson Lab. Dr. Kohl has successfully accomplished several items: (i) Preliminary results from SANE (E08-003) at Jefferson Lab: Former HU graduate student Anusha Liyanage has pursued her PhD research on SANE. Her analysis of the elastic ep scattering data has resulted in the extraction of the proton electric-to-magnetic form factor ratio from double spin asymmetries at the highest momentum transfer to date. The results are almost final and a publication is in preparation. (ii) Approval of TREK/E36 for running, preparation of simulation and analysis: the TREK experiment has been stage-II approved in fall 2013, has been mounted on the hall floor from November 2014 to April 2015, has been commissioned in April-June 2015 and is scheduled to run in fall 2015. The group has contributed significantly with simulations and magnetic field map calculations, has investigated the sensitivity of TREK to new light neutral particles, and contributed substantially to the mounting and commissioning of the experiment. (iii) Running of OLYMPUS and analysis: Under Dr. Kohl's leadership as spokesman, the OLYMPUS experiment has completed data taking beginning of 2013; calibrations and analysis have been well underway, with results to be expected in the course of 2015. (iv) Operation of GEM detectors at OLYMPUS and MUSE: The GEM telescopes built for OLYMPUS luminosity monitoring with forward-angle ep elastic scattering have been operated successfully, have meanwhile been relocated to PSI, and have been re-commissioned as beam particle trackers for the PSI secondary beams for MUSE. (v) Trained and prepared postdocs and graduate students for their future careers. Two postdocs from Dr. Kohl's group (Dr. Juergen Diefenbach and Dr. Peter Monaghan) have found permanent academic positions. Two former graduate students of the group have graduated and received their PhD degrees in nuclear physics (Dr. Anusha Liyanage and Dr. Ozgur Ates). In particular, this award has enabled Dr. Kohl to pursue the TREK project (Time Reversal Experiment with Kaons) at J-PARC, which he has been leading and advancing as International Spokesperson. Originally proposed as a search for time reversal symmetry violation, the project has evolved into a precision test of lepton flavor universality in the Standard Model along with sensitive searches for physics beyond the Standard Model through a possible discovery of new particles such as a sterile neutrino or a neutral gauge boson from the hidden sector in the mass region up to 300 MeV/c2. Experiment TREK/E36, first proposed in 2010, has been mounted between November 2014 and April 2015, and commissioning with beam has been started in April 2015, with production running anticipated in early summer and late fall 2015. It uses the apparatus from the previous KEK/E-246 experiment with partial upgrades to measure the ratio of decay widths of leptonic two-body decays of the charged kaon to µν and eν, respectively, which is highly sensitive to the ratio of electromagnetic charged lepton couplings and possible new physics processes that could differentiate between μ and e, hence breaking lepton flavor universality of the Standard Model. Through the searches for neutral massive particles, TREK/E36 can severely constrain any new physics scenarios designed to explain the proton radius puzzle.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Three component vibrational time reversal communication

Time reversal provides an optimal prefilter matched signal to apply to a communication signal before signal transmission. Time reversal allows compensation for wave speed dispersion and can function well in reverberant environments. Time reversal can be used to focus elastic energy to each of the three components of motion independently. A pipe encased in concrete was used to demonstrate the ability to conduct communications of information using three component time reversal. Furthermore, the ability of time reversal to compensate for multi-path distortion (overcoming reverberation) will be demonstrated and the rate of signal communication will be presented. [The U.S. Department of Energy, through the LANL/LDRD Program, is gratefully acknowledged for supporting this work.]

42 ENGINEERING↗

Fullrmc, a rigid body reverse monte carlo modeling package enabled with machine learning and artificial intelligence

Here, a new Reverse Monte Carlo (RMC) package ‘fullrmc’ for atomic or rigid body and molecular, amorphous or crystalline materials is presented. fullrmc main purpose is to provide a fully modular, fast and flexible software, thoroughly documented, complex molecules enabled, written in a modern programming language (python, cython ,C and C++ when performance is needed) and complying to modern programming practices. fullrmc approach in solving an atomic or molecular structure is different from existing RMC algorithms and software. In a nutshell, traditional RMC methods and software randomly adjust atom positions until the whole system has the greatest consistency with a set of experimental data. In contrast, fullrmc applies smart moves endorsed with reinforcement machine learning to groups of atoms. While fullrmc allows running traditional RMC modelling, the uniqueness of this approach resides in its ability to customize grouping atoms in any convenient way with no additional programming efforts and to apply smart and more physically meaningful moves to the defined groups of atoms. Also fullrmc provides a unique way with almost no additional computational cost to recur a group’s selection, allowing the system to go out of local minimas by refining a group’s position or exploring through and beyond not allowed positions and energy barriers the unrestricted three dimensional space around a group.

97 MATHEMATICS AND COMPUTING↗

Detection and quantitation of right ventricular reversible perfusion defects by stress SPECT myocardial perfusion imaging: A proof-of-principle study

Background: In patients with right dominant coronary circulation, the right ventricular (RV) myocardium and the inferior region of the left ventricular (LV) myocardium share a common source of blood flow. We hypothesized that stress/rest SPECT myocardial perfusion imaging (MPI) could detect reversible perfusion defects in the RV in some patients with LV inferior wall perfusion abnormalities. Material and Methods: We identified 2 groups of patients with LV inferior wall perfusion defects (with or without defects in other regions of LV myocardium) from our database. Patients in group 1 (n = 17) had reversible perfusion defects in the RV free wall by visual analysis, while patients in group 2 (n = 17) did not. The images were processed with filtered back projection and, separately, with iterative reconstruction. The images were then re-processed using an automated quantitative software that is specifically designed to include the RV in the region of interest. Results: There were 76% men in group 1 and 94% in group 2 (P <0.05). The mean age was 65±20 in group 1 vs. 63±18 years in group 2 (P < 0.05). The stress type was exercise in 30% in group 1 and 35% in group 2, with the remaining patients studied with pharmacological stress testing (P = NS). The presence of RV reversible perfusion defects using filtered back projection was more evident in 13 patients (75%), while it was better seen with iterative reconstruction in 4 patients (25%). By automated analysis, the RV reversible perfusion defect size was 19 ± 14% of RV myocardium. Conclusion: This proof-of-principle study demonstrates that reversible RV perfusion defects suggestive of ischemia can be detected by SPECT myocardial perfusion imaging in some patients with LV inferior ischemia by visual analysis and can be quantitated by automated programs. Further studies on the diagnostic and prognostic relevance of assessing RV ischemia on SPECT MPI are needed.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Effects of Water Vapor on the Reactivity of Aluminosilicates in Vapor-Phase Propanal Aldol Condensation

Aluminosilicate materials have been extensively studied as efficient aldol catalysts for C-C coupling reactions due to their acidic nature, high surface area, thermal stability, and porous structure. This work investigated the impact of water vapor pressure on the catalytic reactivity of aluminosilicates for the aldol condensation of propanal to 2-methyl-2-pentenal (MP). The catalytic performance of amorphous SiO2-Al2O3 (A-Si-Al) and aluminated MCM-41 (Al-MCM-41) for the vapor-phase aldol condensation of propanal was evaluated at 200 degrees C as a function of vapor-phase water content at atmospheric pressure. Our findings demonstrate that co-feeding low water vapor pressures (1-18 kPa) with propanal enhances the rates of MP production at 200 degrees C on A-Si-Al. Conversely, water vapor pressures of 25 kPa result in a decrease in aldol dimer formation rates. The rate of MP production evaluated on Al-MCM-41 also increased in the presence of 5 kPa water compared to anhydrous conditions. Propylamine temperature-programmed desorption analyses revealed an increase in Bronsted acid site density when both catalysts were exposed to water, which likely accounts for the observed enhancement in aldol condensation reactivity under hydrous conditions. Reversibility testing of the water vapor effect under reaction conditions, combined with X-ray diffraction analysis of fresh, spent, and regenerated catalysts, revealed no structural changes in either aluminosilicate upon exposure to water or reaction conditions. The rates of aldol condensation and the impact of water vapor were highly consistent across both materials, suggesting that zeolite crystallinity has minimal influence on the catalytic performance.

acid catalysts↗

Towards reverse mode automatic differentiation of Kokkos-based codes

Derivative computation is a key component of optimization, sensitivity analysis, uncertainty quantification, and the solving of nonlinear problems. Automatic differentiation (AD) is a powerful technique for evaluating such derivatives, and in recent years, has been integrated into programming environments such as Jax, PyTorch, and TensorFlow to support derivative computations needed for training of machine learning models, facilitating wide-spread use of these technologies. The C++ language has become the de facto standard for scientific computing due to numerous factors, yet language complexity has made the wide-spread adoption of AD technologies for C++ difficult, hampering the incorporation of powerful differentiable programming approaches into C++ scientific simulations. This is exacerbated by the increasing emergence of architectures, such as GPUs, with limited memory capabilities and requiring massive thread-level concurrency. C++ AD tools must effectively use these environments to bring novel scientific simulations to next-generation DOE experimental and observational facilities. In this project, we investigated source transformation-based automatic differentiation using LLVM compiler infrastructure to automatically generate portable and efficient gradient computations of Kokkos-based code. We have demonstrated that our proposed strategy is feasible by investigating the usage of a prototype LLVM-based source transformation tool to generate gradients of simple functions made of sequences of simple Kokkos parallel regions. Speedups of up to 500x compared to Sacado were observed on NVIDIA V100 GPU.

97 MATHEMATICS AND COMPUTING↗