Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Arithmetic”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Robust trajectory-constrained frequency control for microgrids considering model linearization error

Grid supportive modes integrated within inverter-based resources can improve the frequency response of renewable-rich microgrids. The synthesis of grid supportive modes to guarantee frequency trajectory constraints under a predefined disturbance set is challenging but essential. To tackle this challenge, a numerical optimal control (NOC)-based control synthesis methodology is proposed. Without loss of generality, a wind-diesel fed microgrid is studied, where we aim to design grid supportive functions in the wind turbine. In the control design, linearized models are used, and the linearization-induced errors are quantitatively analyzed by reachability and interval arithmetics and represented in the form of interval uncertainties. Then, the NOC problem can be formulated into a robust mixed-integer linear program. The control structure is strategically configured into two levels to realize online deployment. The proposed control is verified on the modified 33-node microgrid with a full-order three-phase nonlinear model in Simulink. In conclusion, the simulation results show the effectiveness of the proposed control paradigm and the necessity of considering linearization-induced uncertainty.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2017

Parallel accelerated cyclic reduction preconditioner for three-dimensional elliptic PDEs with variable coefficients

We present a robust and scalable preconditioner for the solution of large-scale linear systems that arise from the discretization of elliptic PDEs amenable to rank compression. The preconditioner is based on hierarchical low-rank approximations and the cyclic reduction method. The setup and application phases of the preconditioner achieve log-linear complexity in memory footprint and number of operations, and numerical experiments exhibit good weak and strong scalability at large processor counts in a distributed memory environment. Numerical experiments with linear systems that feature symmetry and nonsymmetry, definiteness and indefiniteness, constant and variable coefficients demonstrate the preconditioner applicability and robustness. Furthermore, it is possible to control the number of iterations via the accuracy threshold of the hierarchical matrix approximations and their arithmetic operations, and the tuning of the admissibility condition parameter. Together, these parameters allow for optimization of the memory requirements and performance of the preconditioner.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Lightweight runtime checking of C programs with RTC

The C Programming Language is known for being an efficient language that can be compiled on almost any architecture and operating system. However the absence of dynamic safety checks and a relatively weak type system allows programmer oversights that are hard to spot. In this paper, we present RTC, a runtime monitoring tool that instruments unsafe code and monitors the program execution. RTC is built on top of the ROSE compiler infrastructure. RTC finds memory bugs and arithmetic overflows and underflows, and run-time type violations. Most of the instrumentations are directly added to the source file and only require a minimal runtime system. As a result, the instrumented code remains portable. In tests against known error detection benchmarks, RTC found 98% of all memory related bugs and had zero false positives. Finally, in performance tests conducted with well known algorithms, such as binary search and MD5, we determined that our tool has an average run-time overhead rate of 9.7× and memory overhead rate of 3.5×.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

An efficient and portable SIMD algorithm for charge/current deposition in Particle-In-Cell codes

In current computer architectures, data movement (from die to network) is by far the most energy consuming part of an algorithm (≈20pJ/word on-die to ≈10,000 pJ/word on the network). To increase memory locality at the hardware level and reduce energy consumption related to data movement, future exascale computers tend to use many-core processors on each compute nodes that will have a reduced clock speed to allow for efficient cooling. To compensate for frequency decrease, machine vendors are making use of long SIMD instruction registers that are able to process multiple data with one arithmetic operator in one clock cycle. SIMD register length is expected to double every four years. As a consequence, Particle-In-Cell (PIC) codes will have to achieve good vectorization to fully take advantage of these upcoming architectures. In this paper, we present a new algorithm that allows for efficient and portable SIMD vectorization of current/charge deposition routines that are, along with the field gathering routines, among the most time consuming parts of the PIC algorithm. Our new algorithm uses a particular data structure that takes into account memory alignment constraints and avoids gather/scat;ter instructions that can significantly affect vectorization performances on current CPUs. The new algorithm was successfully implemented in the 3D skeleton PIC code PICSAR and tested on Haswell Xeon processors (AVX2-256 bits wide data registers). Results show a factor of ×2 to ×2.5 speed-up in double precision for particle shape factor of orders 1–3. The new algorithm can be applied as is on future KNL (Knights Landing) architectures that will include AVX-512 instruction sets with 512 bits register lengths (8 doubles/16 singles). Program summary Program Title: vec_deposition Program Files doi:http://dx.doi.org/10.17632/nh77fv9k8c.1 Licensing provisions: BSD 3-Clause Programming language: Fortran 90 External routines/libraries: OpenMP > 4.0 Nature of problem: Exascale architectures will have many-core processors per node with long vector data registers capable of performing one single instruction on multiple data during one clock cycle. Data register lengths are expected to double every four years and this pushes for new portable solutions for efficiently vectorizing Particle-In-Cell codes on these future many-core architectures. One of the main hotspot routines of the PIC algorithm is the current/charge deposition for which there is no efficient and portable vector algorithm. Solution method: Here we provide an efficient and portable vector algorithm of current/charge deposition routines that uses a new data structure, which significantly reduces gather/scatter operations. Vectorization is controlled using OpenMP 4.0 compiler directives for vectorization which ensures portability across different architectures. Restrictions: Here we do not provide the full PIC algorithm with an executable but only vector routines for current/charge deposition. These scalar/vector routines can be used as library routines in your 3D Particle-In-Cell code. However, to get the best performances out of vector routines you have to satisfy the two following requirements: (1) Your code should implement particle tiling (as explained in the manuscript) to allow for maximized cache reuse and reduce memory accesses that can hinder vector performances. The routines can be used directly on each particle tile. (2) You should compile your code with a Fortran 90 compiler (e.g Intel, gnu or cray) and provide proper alignment flags and compiler alignment directives (more details in README file).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

GPU-accelerated Tersoff potentials for massively parallel Molecular Dynamics simulations

The Tersoff potential is one of the empirical many-body potentials that has been widely used in simulation studies at atomic scales. Unlike pair-wise potentials, the Tersoff potential involves three-body terms, which require much more arithmetic operations and data dependency. In this contribution, we have implemented the GPU-accelerated version of several variants of the Tersoff potential for LAMMPS, an open-source massively parallel Molecular Dynamics code. Compared to the existing MPI implementation in LAMMPS, the GPU implementation exhibits a better scalability and offers a speedup of 2.2X when run on 1000 compute nodes on the Titan supercomputer. On a single node, the speedup ranges from 2.0 to 8.0 times, depending on the number of atoms per GPU and hardware configurations. The most notable features of our GPU-accelerated version include its design for MPI/accelerator heterogeneous parallelism, its compatibility with other functionalities in LAMMPS, its ability to give deterministic results and to support both NVIDIA CUDA- and OpenCL-enabled accelerators. Our implementation is now part of the GPU package in LAMMPS and accessible for public use.

Computer Science↗
DOE OSTI2021

Caravel: A C++ framework for the computation of multi-loop amplitudes with numerical unitarity

We present the first public version of Caravel, a C++17 framework for the computation of multi-loop scattering amplitudes in quantum field theory, based on the numerical unitarity method. Caravel is composed of modules for the D-dimensional decomposition of integrands of scattering amplitudes into master and surface terms, the computation of tree-level amplitudes in floating point or finite-field arithmetic, the numerical computation of one- and two-loop amplitudes in QCD and Einstein gravity, and functional reconstruction tools. Here, we provide programs that showcase Caravel's main functionalities and allow to compute selected one- and two-loop amplitudes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Outdoor characterization of radio frequency electromagnetic fields in a Spanish birth cohort

There is considerable public concern in many countries about the possible adverse effects of exposure to non-ionizing radiation electromagnetic fields, especially in vulnerable populations such as children. The aim of this study was to characterize environmental exposure profiles within the frequency range 100 kHz–6 GHz in the immediate surrounds of the dwellings of 123 families from the INMA-Granada birth cohort in Southern Spain, using spot measurements. The arithmetic mean root mean-square electric field (E{sub RMS}) and power density (S{sub RMS}) values were, respectively, 195.79 mV/m (42.3% of data were above this mean) and 799.01 µW/m{sup 2} (30% of values were above this mean); median values were 148.80 mV/m and 285.94 µW/m{sup 2}, respectively. Exposure levels below the quantification limit were assigned a value of 0.01 V/m. Incident field strength levels varied widely among different areas or towns/villages, demonstrating spatial variability in the distribution of exposure values related to the surface area population size and also among seasons. Although recorded values were well below International Commission for Non-Ionizing Radiation Protection reference levels, there is a particular need to characterize incident field strength levels in vulnerable populations (e.g., children) because of their chronic and ever-increasing exposure. The effects of incident field strength have not been fully elucidated; however, it may be appropriate to apply the precautionary principle in order to reduce exposure in susceptible groups. - Highlights: • Spot measurements were performed in the immediate surrounds of children's dwellings. • Mean root mean-square electric field and power density values were calculated. • Most recorded values were far below international standard guideline limits. • Data demonstrate spatial variability in the distribution of exposure levels. • While adverse effects are proven, application of the precautionary principle may be appropriate.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

Thyroid antagonists and thyroid indicators in U.S. pregnant women in the Vanguard Study of the National Children's Study

The sodium iodide-symporter (NIS) mediates uptake of iodide into thyroid follicular cells. This key step in thyroid hormone synthesis is inhibited by perchlorate, thiocyanate (SCN) and nitrate (NO{sub 3}) anions. When these exposures occur during pregnancy the resulting decreases in thyroid hormones may adversely affect neurodevelopment of the human fetus. Our objectives were to describe and examine the relationship of these anions to the serum thyroid indicators, thyroid stimulating hormone (TSH) and free thyroxine (FT4), in third trimester women from the initial Vanguard Study of the National Children's Study (NCS); and to compare urine perchlorate results with those in pregnant women from the National Health and Nutritional Examination Survey (NHANES). Urinary perchlorate, SCN, NO{sub 3}, and iodine, serum TSH, FT4, and cotinine were measured and a food frequency questionnaire (FFQ) was administered to pregnant women enrolled in the initial Vanguard Study. We used multiple regression models of FT4 and TSH that included perchlorate equivalent concentration (PEC, which estimates combined inhibitory effects of the anions perchlorate, SCN, and NO{sub 3} on the NIS). We used multiple regression to model predictors of each urinary anion, using FFQ results, drinking water source, season of year, smoking status, and demographic characteristics. Descriptive statistics were calculated for pregnant women in NHANES 2001–2012. The geometric mean (GM) for urinary perchlorate was 4.04 µg/L, for TSH 1.46 mIU/L, and the arithmetic mean for FT4 1.11 ng/dL in 359 NCS women. In 330 women with completed FFQs, consumption of leafy greens, winter season, and Hispanic ethnicity were significant predictors of higher urinary perchlorate, which differed significantly by study site and primary drinking water source, and bottled water was associated with higher urinary perchlorate compared to filtered tap water. Leafy greens consumption was associated with higher urinary NO{sub 3} and higher urinary SCN. There was no association between urinary perchlorate or PEC and TSH or FT4, even for women with urinary iodine <100 µg/L. GM urinary perchlorate concentrations in the full sample (n=494) of third trimester NCS women (4.03 µg/L) were similar to pregnant women in NHANES (3.58 µg/L). - Highlights: • Limited biomonitoring data are available in pregnant women. • We found no effect of perchlorate and related anions on thyroid indicators in third trimester women. • Leafy green vegetables were a dietary source for perchlorate, nitrate, and thiocyanate.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

Soil contamination from lead battery manufacturing and recycling in seven African countries

Highlights: • Soil lead contamination was found at lead battery recycling facilities in Africa. • Mean lead concentrations were 2600 mg/kg in soil on the outside of plants. • Lead pollution at these sites poses significant health risks to the public. • Lead contamination at these plants suggest that extensive remediation is warranted. Lead battery recycling is a growing hazardous industry throughout Africa. We investigated potential soil contamination inside and outside formal sector recycling plants in seven countries. We collected 118 soil samples at 15 recycling plants and one battery manufacturing site and analyzed them for total lead. Lead levels in soils ranged from < 40–140,000 mg/kg. Overall mean lead concentrations were ~23,200 mg/kg but, average lead levels were 22-fold greater for soil samples from inside plant sites than from those collected outside these facilities. Arithmetic mean lead concentrations in soil samples from communities surrounding these plants were ~2600 mg/kg. As the lead battery industry in Africa continues to expand, it is expected that the number and size of lead battery recycling plants will grow to meet the forecasted demand. There is an immediate need to address ongoing exposures in surrounding communities, emissions from this industry and to regulate site closure financing procedures to ensure that we do not leave behind a legacy of lead contamination that will impact millions in communities throughout Africa.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Multipole interaction in spectral line broadening by plasmas

A long-standing ambiguity in spectral line broadening theory related to the electric field divergence in the quadrupole term of the screened Coulomb radiator-plasma interaction is examined. This is accomplished with multipole expansions from a Taylor series as well as a partial wave analysis of the screened Coulomb interaction. Here, it is explicitly shown that the two approaches agree up to the octupole term for an effective radiator size small compared to the plasma screening length. Furthermore, the ambigous corrections are confirmed appearing naturally in both methods. For higher multipoles the agreement is demonstrated numerically with a computer program using exact arithmetic.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Exposure of the Heart in Breast Cancer Radiation Therapy: A Systematic Review of Heart Doses Published During 2003 to 2013

Purpose: Breast cancer radiation therapy cures many women, but where the heart is exposed, it can cause heart disease. We report a systematic review of heart doses from breast cancer radiation therapy that were published during 2003 to 2013. Methods and Materials: Eligible studies were those reporting whole-heart dose (ie, dose averaged over the whole heart). Analyses considered the arithmetic mean of the whole-heart doses for the CT plans for each regimen in each study. We termed this “mean heart dose.” Results: In left-sided breast cancer, mean heart dose averaged over all 398 regimens reported in 149 studies from 28 countries was 5.4 Gy (range, <0.1-28.6 Gy). In regimens that did not include the internal mammary chain (IMC), average mean heart dose was 4.2 Gy and varied with the target tissues irradiated. The lowest average mean heart doses were from tangential radiation therapy with either breathing control (1.3 Gy; range, 0.4-2.5 Gy) or treatment in the lateral decubitus position (1.2 Gy; range, 0.8-1.7 Gy), or from proton radiation therapy (0.5 Gy; range, 0.1-0.8 Gy). For intensity modulated radiation therapy mean heart dose was 5.6 Gy (range, <0.1-23.0 Gy). Where the IMC was irradiated, average mean heart dose was around 8 Gy and varied little according to which other targets were irradiated. Proton radiation therapy delivered the lowest average mean heart dose (2.6 Gy, range, 1.0-6.0 Gy), and tangential radiation therapy with a separate IMC field the highest (9.2 Gy, range, 1.9-21.0 Gy). In right-sided breast cancer, the average mean heart dose was 3.3 Gy based on 45 regimens in 23 studies. Conclusions: Recent estimates of typical heart doses from left breast cancer radiation therapy vary widely between studies, even for apparently similar regimens. Maneuvers to reduce heart dose in left tangential radiation therapy were successful. Proton radiation therapy delivered the lowest doses. Inclusion of the IMC doubled typical heart dose.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2013

Obtaining identical results with double precision global accuracy on different numbers of processors in parallel particle Monte Carlo simulations

We describe and compare different approaches for achieving numerical reproducibility in photon Monte Carlo simulations. Reproducibility is desirable for code verification, testing, and debugging. Parallelism creates a unique problem for achieving reproducibility in Monte Carlo simulations because it changes the order in which values are summed. This is a numerical problem because double precision arithmetic is not associative. Parallel Monte Carlo, both domain replicated and decomposed simulations, will run their particles in a different order during different runs of the same simulation because the non-reproducibility of communication between processors. In addition, runs of the same simulation using different domain decompositions will also result in particles being simulated in a different order. In [1], a way of eliminating non-associative accumulations using integer tallies was described. This approach successfully achieves reproducibility at the cost of lost accuracy by rounding double precision numbers to fewer significant digits. This integer approach, and other extended and reduced precision reproducibility techniques, are described and compared in this work. Increased precision alone is not enough to ensure reproducibility of photon Monte Carlo simulations. Non-arbitrary precision approaches require a varying degree of rounding to achieve reproducibility. For the problems investigated in this work double precision global accuracy was achievable by using 100 bits of precision or greater on all unordered sums which where subsequently rounded to double precision at the end of every time-step.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Accelerating solidification process simulation for large-sized system of liquid metal atoms using GPU with CUDA

Molecular dynamics simulation is a powerful tool to simulate and analyze complex physical processes and phenomena at atomic characteristic for predicting the natural time-evolution of a system of atoms. Precise simulation of physical processes has strong requirements both in the simulation size and computing timescale. Therefore, finding available computing resources is crucial to accelerate computation. However, a tremendous computational resource (GPGPU) are recently being utilized for general purpose computing due to its high performance of floating-point arithmetic operation, wide memory bandwidth and enhanced programmability. As for the most time-consuming component in MD simulation calculation during the case of studying liquid metal solidification processes, this paper presents a fine-grained spatial decomposition method to accelerate the computation of update of neighbor lists and interaction force calculation by take advantage of modern graphics processors units (GPU), enlarging the scale of the simulation system to a simulation system involving 10 000 000 atoms. In addition, a number of evaluations and tests, ranging from executions on different precision enabled-CUDA versions, over various types of GPU (NVIDIA 480GTX, 580GTX and M2050) to CPU clusters with different number of CPU cores are discussed. The experimental results demonstrate that GPU-based calculations are typically 9∼11 times faster than the corresponding sequential execution and approximately 1.5∼2 times faster than 16 CPU cores clusters implementations. On the basis of the simulated results, the comparisons between the theoretical results and the experimental ones are executed, and the good agreement between the two and more complete and larger cluster structures in the actual macroscopic materials are observed. Moreover, different nucleation and evolution mechanism of nano-clusters and nano-crystals formed in the processes of metal solidification is observed with large-sized system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Stable evaluation of Green's functions in cylindrically stratified regions with uniaxial anisotropic layers

We present a robust algorithm for the computation of electromagnetic fields radiated by point sources (Hertzian dipoles) in cylindrically stratified media where each layer may exhibit material properties (permittivity, permeability, and conductivity) with uniaxial anisotropy. Analytical expressions are obtained based on the spectral representation of the tensor Green's function based on cylindrical Bessel and Hankel eigenfunctions, and extended for layered uniaxial media. Due to the poor scaling of these eigenfunctions for extreme arguments and/or orders, direct numerical evaluation of such expressions can produce numerical instability, i.e., underflow, overflow, and/or round-off errors under finite precision arithmetic. To circumvent these problems, we develop a numerically stable formulation through suitable rescaling of various expressions involved in the computational chain, to yield a robust algorithm for all parameter ranges. Numerical results are presented to illustrate the robustness of the formulation including cases of practical interest.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Exploiting data representation for fault tolerance

Incorrect computer hardware behavior may corrupt intermediate computations in numerical algorithms, possibly resulting in incorrect answers. Prior work models misbehaving hardware by randomly flipping bits in memory. We start by accepting this premise, and present an analytic model for the error introduced by a bit flip in an IEEE 754 floating-point number. We then relate this finding to the linear algebra concepts of normalization and matrix equilibration. In particular, we present a case study illustrating that normalizing both vector inputs of a dot product minimizes the probability of a single bit flip causing a large error in the dot product's result. Moreover, the absolute error is either less than one or very large, which allows detection of large errors. Then, we apply this to the GMRES iterative solver. We count all possible errors that can be introduced through faults in arithmetic in the computationally intensive orthogonalization phase of GMRES, and show that when the matrix is equilibrated, the absolute error is bounded above by one.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

On the classification of weakly integral modular categories

In this paper we classify all modular categories of dimension 4m, where m is an odd square-free integer, and all rank 6 and rank 7 weakly integral modular categories. This completes the classification of weakly integral modular categories through rank 7. In particular, our results imply that all integral modular categories of rank at most 7 are pointed (that is, every simple object has dimension 1). All the non-integral (but weakly integral) modular categories of ranks 6 and 7 have dimension 4m, with m an odd square free integer, so their classification is an application of our main result. The classification of rank 7 integral modular categories is facilitated by an analysis of the two group actions on modular categories: the Galois group of the field generated by the entries of the S-matrix and the group of invertible isomorphism classes of objects. We derive some valuable arithmetic consequences from these actions.

modular categories↗
DOE OSTI2018

Computational framework for modeling membrane processes without process and solution property simplifications

Accurately modeling membrane processes is critical to evaluating novel process configurations, designing scalable membrane systems, informing process cost estimates, and directing future research. Most membrane process models trade accuracy for computational efficiency by employing simplified approximations of the process (i.e. no salt flux, no pressure drop) and solution properties (i.e. ideal solution, and constant density, viscosity, and diffusivity). Our report introduces a detailed one-dimensional finite difference model for evaluating membrane processes that avoids these common simplifications. We apply this model to quantify the error introduced by these simplifications for case studies of reverse osmosis, osmotically assisted reverse osmosis, forward osmosis, and pressure retarded osmosis. While the magnitude of error introduced by these simplifications is reliant on the case study parameters and specifications, we find that existing model formulations can underestimate or overestimate average water flux by nearly 50% for some membrane processes operating under standard conditions. Lastly we investigate the error introduced by simplified inlet-outlet models that do not solve the governing system of differential equations, and we assess the accuracy of novel inlet-outlet formulations that use a log and geometric mean, instead of the typical arithmetic mean, to represent non-linear water flux profiles.

42 ENGINEERING↗
DOE OSTI2022

Characterization of multi-material 316L-Hastelloy X fabricated via laser powder-bed fusion

The aim of this work is to provide firsthand knowledge of 316 L stainless steel (316 L) and Hastelloy X (HX) multi-material processing via laser powder bed fusion (PBF). Specifically, microstructure of the interface is studied using scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDS), and X-ray diffraction (XRD). Surface metrology is performed to characterize the resulting surface roughness at the interface followed by tensile and flexural testing of multi-material samples to characterize the mechanical properties of the interfaces. Results showed that use of proper process parameters for each individual material led to formation of a compositional gradient at the interface that stretched for 240 μm (10–12 layers) with no evidence of cracking or porosity. The interface exhibited higher surface roughness compared to 316 L or HX as measured by arithmetic mean height, Sa, and maximum valley depth, Sv, parameters. During tensile testing, samples failed in the 316 L region away from the interface, with comparable yield strength, ultimate strength, and ductility. Finally, it was concluded that the “naturally” formed interface created a compositional gradient which was defect free due to similar values of coefficient of thermal expansion, input energy density, and different Marangoni numbers of the materials.

316L stainless Steel↗