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At least 307 records · Page 17

Full Multigrid Flow Solver

FMG3D (full multigrid 3 dimensions) is a pilot computer program that solves equations of fluid flow using a finite difference representation on a structured grid. Infrastructure exists for three dimensions but the current implementation treats only two dimensions. Written in Fortran 90, FMG3D takes advantage of the recursive subroutine feature, dynamic memory allocation, and structured-programming constructs of that language. FMG3D supports multi-block grids with three types of block-to-block interfaces: periodic, C-zero, and C-infinity. For all three types, grid points must match at interfaces. For periodic and C-infinity types, derivatives of grid metrics must be continuous at interfaces. The available equation sets are as follows: scalar elliptic equations, scalar convection equations, and the pressure-Poisson formulation of the Navier-Stokes equations for an incompressible fluid. All the equation sets are implemented with nonzero forcing functions to enable the use of user-specified solutions to assist in verification and validation. The equations are solved with a full multigrid scheme using a full approximation scheme to converge the solution on each succeeding grid level. Restriction to the next coarser mesh uses direct injection for variables and full weighting for residual quantities; prolongation of the coarse grid correction from the coarse mesh to the fine mesh uses bilinear interpolation; and prolongation of the coarse grid solution uses bicubic interpolation.

Mineck, Raymond E.↗

Implementation and Verification of Cable Bending Stiffness in MoorDyn: Preprint

Cable bending stiffness capabilities have been added to MoorDyn to enable modeling of dynamic power cables. The relatively large motions experienced by floating wind turbines and wave energy converters pose a challenge for power cables, whose internal components provide significant bending resistance and are sensitive to deformation. The behavior and associated design considerations of power cables in these highly dynamic applications make coupled analysis relevant for design. MoorDyn is a lumped-mass mooring dynamics model that is used for floating wind energy simulation (often coupled with OpenFAST) and floating wave energy converter simulation (often coupled with WEC-Sim). Its existing line elasticity formulation considers axial stiffness only. To properly capture the dynamics of power cables, a cable bending stiffness model has been added that approximates cable curvature based on the difference in tangent vectors of adjacent line elements. The resulting bending moment is realized by applying forces on adjacent nodes, leaving the underlying lumped-mass formulation unchanged. The bending stiffness implementation is verified in static conditions against analytical solutions and then in a dynamic power cable scenario in comparison with OrcaFlex. The dynamic scenario uses prescribed motions and includes wave loadings on the cable. Results indicate correct implementation of bending stiffness and show close agreement with OrcaFlex.

50 EE - Wind and Water Power Program - Water (EE-4↗

ExaWind: Predictive Wind Energy Simulations

This presentation describes the ExaWind project and the team's progress in creating a suite of performance-portable codes designed for predictive simulations of wind farms on next-generation exascale-class supercomputers. Such simulations will require the resolution of scales spanning many orders of magnitude, from blade boundary layers to wind farm flow structures. In the U.S., the first exascale systems will be GPU accelerated, and different GPU manufacturers have been chosen for the different systems. At the heart of the ExaWind software is a hybrid-solver approach based on the codes Nalu-Wind and AMR-Wind, which are computational fluid dynamics solvers for the incompressible Navier-Stokes equations. Nalu-Wind is an unstructured-grid code used to resolve wind turbine geometry and blade boundary layers, whereas AMR-Wind is a structured-grid background solver for atmospheric turbulent flow and turbine wake propagation. The models are coupled with overset meshes and global linear systems are approximated through a loose-coupling algorithm. Results will include validation-quality high-fidelity simulations and strong/weak scaling results from the Summit supercomputer.

49 EE - Wind and Water Power Program - Wind (EE-4W↗

Kalman Filtering with Inequality Constraints for Turbofan Engine Health Estimation

Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. This paper develops two analytic methods of incorporating state variable inequality constraints in the Kalman filter. The first method is a general technique of using hard constraints to enforce inequalities on the state variable estimates. The resultant filter is a combination of a standard Kalman filter and a quadratic programming problem. The second method uses soft constraints to estimate state variables that are known to vary slowly with time. (Soft constraints are constraints that are required to be approximately satisfied rather than exactly satisfied.) The incorporation of state variable constraints increases the computational effort of the filter but significantly improves its estimation accuracy. The improvement is proven theoretically and shown via simulation results. The use of the algorithm is demonstrated on a linearized simulation of a turbofan engine to estimate health parameters. The turbofan engine model contains 16 state variables, 12 measurements, and 8 component health parameters. It is shown that the new algorithms provide improved performance in this example over unconstrained Kalman filtering.

Simon, Dan↗

Characterization of the Scale Model Acoustic Test Overpressure Environment using Computational Fluid Dynamics

The Scale Model Acoustic Test (SMAT) is a 5% scale test of the Space Launch System (SLS), which is currently being designed at Marshall Space Flight Center (MSFC). The purpose of this test is to characterize and understand a variety of acoustic phenomena that occur during the early portions of lift off, one being the overpressure environment that develops shortly after booster ignition. The pressure waves that propagate from the mobile launcher (ML) exhaust hole are defined as the ignition overpressure (IOP), while the portion of the pressure waves that exit the duct or trench are the duct overpressure (DOP). Distinguishing the IOP and DOP in scale model test data has been difficult in past experiences and in early SMAT results, due to the effects of scaling the geometry. The speed of sound of the air and combustion gas constituents is not scaled, and therefore the SMAT pressure waves propagate at approximately the same speed as occurs in full scale. However, the SMAT geometry is twenty times smaller, allowing the pressure waves to move down the exhaust hole, through the trench and duct, and impact the vehicle model much faster than occurs at full scale. The DOP waves impact portions of the vehicle at the same time as the IOP waves, making it difficult to distinguish the different waves and fully understand the data. To better understand the SMAT data, a computational fluid dynamics (CFD) analysis was performed with a fictitious geometry that isolates the IOP and DOP. The upper and lower portions of the domain were segregated to accomplish the isolation in such a way that the flow physics were not significantly altered. The Loci/CHEM CFD software program was used to perform this analysis.

Nielsen, Tanner↗

Volume 35, AMT-1 Cruise Report and Preliminary Results

This report documents the scientific activities on board the Royal Research Ship (RRS) 'James Clark Ross' during the irst Atlantic Meridional Transect (AMT-1), 21 September to 24 October 1995. The ship sailed from Grimsby (England) for Montevideo (Uruguay) and then continued on to Stanley (Falkland Islands). The primary objective of the AMT program is to investigate basic biological processes in the open Atlantic Ocean over very broad spatial scales. For AMT-1, the meridional range covered was approximately 50 deg N to 50 deg S or nearly 8,000 nmi. The measurements to be taken during the AMT cruises are fundamental for the calibration, validation, and continuing understanding of remotely sensed observations of biological oceanography. They are also important for understanding plankton community structure over latitudinal scales and the role of the world ocean in global carbon cycles. During AMT-1 a variety of instruments were used to map the physical, chemical, and biological structure of the upper 200 m of the water column. Ocean color measurements were made using state-of-the-art sensors, whose calibration was traceable to the highest international standards. New advances in fluorometry were used to measure photosynthetic activity, which was then used to further interpret primary productivity. A unique set of samples and data were collected for the planktonic assemblages that vary throughout the range of the transect. These data will yield new interpretations on community composition and their role in carbon cycling. While the various provinces of the Atlantic Ocean were being crossed, the partial pressure of CO2 was related to biological productivity. This comparison revealed the areas of drawdown of atmospheric CO2 and how these areas relate to the surrounding biological productivity. These data, plus the measurements of light attenuation and phytoplankton optical properties, will be used as a primary input for basin-scale biological productivity models to help develop ecosystem dynamics models which will be important for improving the forecasting abilities of modelers. The AMT program is also attempting to meet the needs of international agencies in their implementation of Sensor Intercomparison and Merger for Biological and Interdisciplinary Ocean Studies (SIMBIOS), a program to develop a methodology and operational capability to combine data products from the various ocean color satellite missions.

Hooker, Stanford B.↗

Atomistic Simulations of Polydisperse Lignin Melts Using Simple Polydisperse Residue Input Generator

Understanding the physics of lignin will help rationalize its function in plant cell walls as well as aiding practical applications such as deriving biofuels and bioproducts. Here, in this work, we present SPRIG (Simple Polydisperse Residue Input Generator), a program for generating atomic-detail models of random polydisperse lignin copolymer melts i.e., the state most commonly found in nature. Using these models, we use all-atom molecular dynamics (MD) simulations to investigate the conformational and dynamic properties of polydisperse melts representative of switchgrass (Panicum virgatum L.) lignin. Polydispersity, branching and monolignol sequence are found to not affect the calculated glass transition temperature, T g . The Flory–Huggins scaling parameter for the segmental radius of gyration is 0.42 ± 0.02, indicating that the chains exhibit statistics that lie between a globular chain and an ideal Gaussian chain. Below T g the atomic mean squared displacements are independent of molecular weight. In contrast, above T g , they decrease with increasing molecular weight. Therefore, a monodisperse lignin melt is a good approximation to this polydisperse lignin when only static properties are probed, whereas the molecular weight distribution needs to be considered while analyzing lignin dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Propellant Slosh Analysis for the Solar Dynamics Observatory

The Solar Dynamics Observatory (SDO) mission, part of the Living With a Star program, is a geosynchronous satellite with tight pointing requirements. Due to a large amount of liquid propellant, a detailed slosh analysis is required to ensure the tight pointing budget can be satisfied. Much of the high fidelity slosh analysis and simulation has been performed via computational fluid dynamics. Even though this method of simulation is very accurate, it requires significant computational effort and specialized knowledge, limiting the ability of the SDO project to access fluid dynamics simulations at will. Furthermore, it is very difficult to incorporate most of these models into simulations of the overall spacecraft and its environment. Ultimately, the effects of the propellant slosh on the attitude stability and pointing performance of the entire spacecraft are of great interest to attitude control engineers. Equivalent mechanical models, such as models that approximate the fluid slosh effects by analogy to the movements of a point-mass pendulum, are important tools in simulating propellant slosh dynamics as part of the entire attitude determination and control system. This paper describes some of the current methods used to analyze and model slosh. It focuses on equivalent mechanical models and their incorporation into control-based analysis tools such as Simulink. The SDO mission is used as the case study for this work.

Mason, Paul A. C.↗

Unsteady transonic flow calculations for realistic aircraft configurations

A transonic unsteady aerodynamic and aeroelasticity code has been developed for application to realistic aircraft configurations. The new code is called CAP-TSD which is an acronym for Computational Aeroelasticity Program - Transonic Small Disturbance. The CAP-TSD code uses a time-accurate approximate factorization (AF) algorithm for solution of the unsteady transonic small-disturbance equation. The AF algorithm is very efficient for solution of steady and unsteady transonic flow problems. It can provide accurate solutions in only several hundred time steps yielding a significant computational cost savings when compared to alternative methods. The new code can treat complete aircraft geometries with multiple lifting surfaces and bodies including canard, wing, tail, control surfaces, launchers, pylons, fuselage, stores, and nacelles. Applications are presented for a series of five configurations of increasing complexity to demonstrate the wide range of geometrical applicability of CAP-TSD. These results are in good agreement with available experimental steady and unsteady pressure data. Calculations for the General Dynamics one-ninth scale F-16C aircraft model are presented to demonstrate application to a realistic configuration. Unsteady results for the entire F-16C aircraft undergoing a rigid pitching motion illustrated the capability required to perform transonic unsteady aerodynamic and aeroelastic analyses for such configurations.

Batina, John T.↗

Unsteady transonic flow calculations for realistic aircraft configurations

A transonic unsteady aerodynamic and aeroelasticity code has been developed for application to realistic aircraft configurations. The new code is called CAP-TSD which is an acronym for Computational Aeroelasticity Program - Transonic Small Disturbance. The CAP-TSD code uses a time-accurate approximate factorization (AF) algorithm for solution of the unsteady transonic small-disturbance equation. The AF algorithm is very efficient for solution of steady and unsteady transonic flow problems. It can provide accurate solutions in only several hundred time steps yielding a significant computational cost savings when compared to alternative methods. The new code can treat complete aircraft geometries with multiple lifting surfaces and bodies including canard, wing, tail, control surfaces, launchers, pylons, fuselage, stores, and nacelles. Applications are presented for a series of five configurations of increasing complexity to demonstrate the wide range of geometrical applicability of CAP-TSD. These results are in good agreement with available experimental steady and unsteady pressure data. Calculations for the General Dynamics one-ninth scale F-16C aircraft model are presented to demonstrate application to a realistic configuration. Unsteady results for the entire F-16C aircraft undergoing a rigid pitching motion illustrated the capability required to perform transonic unsteady aerodynamic and aeroelastic analyses for such configurations.

Batina, John T.↗

Small Radioisotope Power System at NASA Glenn Research Center

In April 2009, NASA Glenn Research Center (GRC) formed an integrated product team (IPT) to develop a Small Radioisotope Power System (SRPS) utilizing a single Advanced Stirling Convertor (ASC) with passive balancer for possible use by the International Lunar Network (ILN) program. The ILN program is studying the feasibility of implementing a multiple node seismometer network to investigate the internal lunar structure. A single ASC produces approximately 80 W(sub e) and could potentially supply sufficient power for that application. The IPT consists of Sunpower, Inc., to provide the single ASC with balancer, The Johns Hopkins University Applied Physics Laboratory (JHU/APL) to design an engineering model Single Convertor Controller (SCC) for an ASC with balancer, and NASA GRC to provide technical support to these tasks and to develop a simulated lunar lander test stand. A controller maintains stable operation of an ASC. It regulates the alternating current produced by the linear alternator of the convertor, provides a specified output voltage, and maintains operation at a steady piston amplitude and hot end temperature. JHU/APL also designed an ASC dynamic engine/alternator simulator to aid in the testing and troubleshooting of the SCC. This paper describes the requirements, design, and development of the SCC, including some of the key challenges and the solutions chosen to overcome those issues. In addition, it describes the plans to analyze the effectiveness of a passive balancer to minimize vibration from the ASC, characterize the effect of ASC vibration on a lunar lander, characterize the performance of the SCC, and integrate the single ASC, SCC, and lunar lander test stand to characterize performance of the overall system.

Dugala, Gina M.↗

Emergency in-flight egress opening for general aviation aircraft

In support of a stall/spin research program, an emergency in-flight egress system is being installed in a light general aviation airplane. To avoid a major structural redesign for a mechanical door, an add-on 11.2 kg pyrotechnic-actuated system was developed to create an opening in the existing structure. The airplane skin will be explosively severed around the side window, across a central stringer, and down to the floor, creating an opening of approximately 76 by 76 cm. The severed panel will be jettisoned at an initial velocity of approximately 13.7 m/sec. System development included a total of 68 explosive severance tests on aluminum material using small samples, small and full scale flat panel aircraft structural mock-ups, and an actual aircraft fuselage. These tests proved explosive sizing/severance margins, explosive initiation, explosive product containment, and system dynamics.

Bement, L. J.↗

Proposed data compression schemes for the Galileo S-band contingency mission

The Galileo spacecraft is currently on its way to Jupiter and its moons. In April 1991, the high gain antenna (HGA) failed to deploy as commanded. In case the current efforts to deploy the HGA fails, communications during the Jupiter encounters will be through one of two low gain antenna (LGA) on an S-band (2.3 GHz) carrier. A lot of effort has been and will be conducted to attempt to open the HGA. Also various options for improving Galileo's telemetry downlink performance are being evaluated in the event that the HGA will not open at Jupiter arrival. Among all viable options the most promising and powerful one is to perform image and non-image data compression in software onboard the spacecraft. This involves in-flight re-programming of the existing flight software of Galileo's Command and Data Subsystem processors and Attitude and Articulation Control System (AACS) processor, which have very limited computational and memory resources. In this article we describe the proposed data compression algorithms and give their respective compression performance. The planned image compression algorithm is a 4 x 4 or an 8 x 8 multiplication-free integer cosine transform (ICT) scheme, which can be viewed as an integer approximation of the popular discrete cosine transform (DCT) scheme. The implementation complexity of the ICT schemes is much lower than the DCT-based schemes, yet the performances of the two algorithms are indistinguishable. The proposed non-image compression algorith is a Lempel-Ziv-Welch (LZW) variant, which is a lossless universal compression algorithm based on a dynamic dictionary lookup table. We developed a simple and efficient hashing function to perform the string search.

Cheung, Kar-Ming↗

Collaborative Research: Explosive reconnection in relativistic magnetically-dominated plasmas (Final Report)

Magnetic fields can be the dominant component of astrophysical plasmas, so that the magnetic energy density might exceed even the rest-mass energy density of matter. In this extreme (and largely unexplored) regime the magnetic field controls the overall plasma evolution, dissipation, and acceleration of non-thermal particles. This plasma regime, applicable to a variety of astrophysical sources - magnetars, pulsars and pulsar wind nebulae (PWNe), jets of Active Galactic Nuclei (AGNs) and Gamma-Ray Bursters (GRBs) - is dramatically different from laboratory plasmas, the magnetospheres of planets, and the interplanetary plasma. Relativistic astrophysical sources then provide an unique opportunity to study the fundamental plasma physics of magnetically-dominated plasmas; a novel and fast-evolving field of theoretical research which, by investigating energy conversion and particle energization processes in plasmas, is of vital importance to the Fusion Energy Sciences DoE program. Data coming from astrophysical high-energy missions, especially the Crab Nebula flares recently observed by the Fermi and AGILE satellites, suggest that the acceleration of non-thermal particles to the highest energies occurs in magnetic reconnection events - a major change of paradigm in high-energy astrophysics. Most importantly, observations demand that particle acceleration should proceed extremely fast (with accelerating electric field of the order of the magnetic field) and on macroscopic scales (much larger, e.g., than the microscopic plasma skin depth). We are conducting studies of the microphysics of magnetically-dominated plasmas focussing in particular on the highly dynamic regime of explosive reconnection and associated particle acceleration in relativistic plasmas. We are studying the stability and explosive plasma dynamics, particle acceleration and radiation production in a number of idealized plasma configurations that approximate relevant astrophysical sources (like the magnetic ABC structures and interacting flux tubes, as well as generalizations of analytical models of X-point collapse to relativistic plasmas). The well-studied case of the Crab Nebula is taken as a prototypical example for the application of the model. We are combining analytical studies of explosive magnetic dynamics and dissipation in relativistic plasmas with particle-in-cell (PIC) simulations and fluid simulations. The theoretical model, fluid and particle-in-cell simulations are cross-checked for agreement and convergence.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Space Technology 5: Pathfinder for Future Micro-Sat Constellations

The Space Technology 5 (ST-5) Project, currently in the implementation phase, is part of the National Aeronautics and Space Administration (NASA) s New Millennium Program (NMP). ST-5 will consist of a constellation of three miniature satellites, each with mass less than 25 kg and size approximately 60 cm by 30 cm. ST-5 addresses technology challenges, as well as fabrication, assembly, test and operations strategies for future micro-satellite missions. ST-5 will be deployed into a highly eccentric, geo-transfer orbit (GTO). This will expose the spacecraft to a high radiation environment as well as provide a low level magnetic background. A three-month flight demonstration phase is planned to validate the technologies and demonstrate concepts for future missions. Each ST-5 spacecraft incorporates NMP competitively-selected breakthrough technologies. These include Cold Gas Micro-Thrusters for propulsion and attitude control, miniature X-band transponder for space-ground communications, Variable Emittance Coatings for dynamic thermal control, and CULPRiT ultra low power logic chip used for Reed-Solomon encoding. The ST-5 spacecraft itself is a technology that can be infused into future missions. It is a fully functional micro-spacecraft built within tight volume and mass constraints. It is built to withstand a high radiation environment, large thermal variations, and high launch loads. The spacecraft power system is low-power and low-voltage, and is designed to turn on after separation &om the launch vehicle. Some of the innovations that are included in the ST-5 design are a custom spacecraft deployment structure, magnetometer deployment boom, nutation damper, X-band antenna, miniature spinning sun sensor, solar array with triple junction solar cells, integral card cage assembly containing single card Command and Data Handling and Power System Electronics, miniature magnetometer, and lithium ion battery. ST-5 will demonstrate the ability of a micro satellite to perform research-quality science. Each ST-5 spacecraft will deploy a precision magnetometer to be used both for attitude determination and as a representative science instrument. The spacecraft has been developed with a low magnetic signature to avoid interference with the magnetometer. The spacecraft will be able to detect and respond autonomously to science events, i.e. significant changes in the magnetic field measurements. The three spacecraft will be a pathfinder for future constellation missions. They will be deployed to demonstrate an appropriate geometry for scientific measurements as a constellation. They will be operationally managed as a constellation, demonstrating automation and communication strategies that will be useful for future missions. The technologies and future mission concepts will be validated both on the ground and in space. Technologies will be validated on the ground by a combination of component level and system level testing of the flight hardware in a thermal vacuum environment. In flight, specific validation runs are planned for each of the technologies. Each validation run consists of one or more orbits with a specific validation objective. This paper will describe the ST-5 mission, and the applicability of the NMP technologies, spacecraft, and mission concepts to future missions. It will also discuss the validation approach for the ST-5 technologies and mission concepts.

Carlisle, Candace↗

Mars Reconnaissance Orbiter Uplink Analysis Tool

This software analyzes Mars Reconnaissance Orbiter (MRO) orbital geometry with respect to Mars Exploration Rover (MER) contact windows, and is the first tool of its kind designed specifically to support MRO-MER interface coordination. Prior to this automated tool, this analysis was done manually with Excel and the UNIX command line. In total, the process would take approximately 30 minutes for each analysis. The current automated analysis takes less than 30 seconds. This tool resides on the flight machine and uses a PHP interface that does the entire analysis of the input files and takes into account one-way light time from another input file. Input flies are copied over to the proper directories and are dynamically read into the tool s interface. The user can then choose the corresponding input files based on the time frame desired for analysis. After submission of the Web form, the tool merges the two files into a single, time-ordered listing of events for both spacecraft. The times are converted to the same reference time (Earth Transmit Time) by reading in a light time file and performing the calculations necessary to shift the time formats. The program also has the ability to vary the size of the keep-out window on the main page of the analysis tool by inputting a custom time for padding each MRO event time. The parameters on the form are read in and passed to the second page for analysis. Everything is fully coded in PHP and can be accessed by anyone with access to the machine via Web page. This uplink tool will continue to be used for the duration of the MER mission's needs for X-band uplinks. Future missions also can use the tools to check overflight times as well as potential site observation times. Adaptation of the input files to the proper format, and the window keep-out times, would allow for other analyses. Any operations task that uses the idea of keep-out windows will have a use for this program.

Khanampompan, Teerapat↗

Implementation and Verification of Cable Bending Stiffness in MoorDyn

The relatively large motions experienced by floating wind turbines and wave energy converters pose a challenge for power cables, whose internal components provide significant bending resistance and are sensitive to deformation. The behavior and associated design considerations of power cables in these highly dynamic applications make coupled analysis relevant for design. Bending stiffness capabilities have recently been added to the lumped-mass mooring dynamics model MoorDyn to enable simulation of dynamic power cables. MoorDyn is a common modeling choice for floating wind energy simulation (often coupled with OpenFAST) and floating wave energy converter simulation (often coupled with WEC-Sim) but the model’s previous line elasticity formulation only considered axial stiffness. To properly capture the dynamics of power cables, a bending stiffness model has been added that approximates cable curvature based on the difference in tangent vectors of adjacent elements. The resulting bending moment is realized by applying forces on adjacent nodes, enabling cable modeling while leaving the underlying lumped-mass formulation unchanged. In this paper, the new bending stiffness implementation is verified in static conditions against analytical solutions and then in a dynamic power cable scenario in comparison with the commercial simulator OrcaFlex. The dynamic scenario uses prescribed motions and includes wave loadings on the cable. Results indicate correct implementation of bending stiffness and show close agreement with OrcaFlex.

50 EE - Wind and Water Power Program - Water (EE-4↗

Algorithms for Efficient Reproducible Floating Point Summation

We define “reproducibility” as getting bitwise identical results from multiple runs of the same program, perhaps with different hardware resources or other changes that should not affect the answer. Many users depend on reproducibility for debugging or correctness. However, dynamic scheduling of parallel computing resources, combined with nonassociative floating point addition, makes reproducibility challenging even for summation, or operations like the BLAS. We describe a “reproducible accumulator” data structure (the “binned number”) and associated algorithms to reproducibly sum binary floating point numbers, independent of summation order. We use a subset of the IEEE Floating Point Standard 754-2008 and bitwise operations on the standard representations in memory. Our approach requires only one read-only pass over the data, and one reduction in parallel, using a 6-word reproducible accumulator (more words can be used for higher accuracy), enabling standard tiling optimization techniques. Summing n words with a 6-word reproducible accumulator requires approximately 9 n floating point operations (arithmetic, comparison, and absolute value) and approximately 3 n bitwise operations. The final error bound with a 6-word reproducible accumulator and our default settings can be up to 2 29 times smaller than the error bound for conventional (recursive) summation on ill-conditioned double-precision inputs.

Computer Science↗