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 649 records · Page 36
All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

Towards Formalization of Advanced Linear Algebra with Applications to Dynamical Systems using PVS

Linear Algebra is essential for numerous aerospace problems of interest. Formal reasoning about hybrid systems that contain variables modeled by differential equations rely on concepts from Linear Algebra such as eigenvalues, matrix decompositions, and matrix valued functions. For example, the long-term dynamics of a system of differential equations depend on the stability/instability of its equilibrium points, which often reduces to an eigenvalue problem. This talk will embark on a quest to formalize theorems and results about eigenvalues and eigenvectors using PVS. We shall start our journey with 2 x 2 complex matrices, where we will apply our PVS code to a simple example of a dynamical system. Since it can be difficult or impossible to give simple expressions of eigenvalues for larger matrices (i.e. 5 x 5 or higher), we then move towards specifying the power method for verified computation of eigenvalue approximations in PVS. This effort requires development of multivariate complex arithmetic. At the end of the day, having such additions to the PVS NASA libraries will help move towards the use of formal methods to verify concepts of control theory and system level verification.

Linear Algebra↗
NASA NTRSDate not supplied

Memory Optimizations for Sparse Linear Algebra on GPU Hardware

An effort to maximize memory bandwidth utilization for a sparse linear algebra kernel executing on NVIDIA® Tesla V100 and A100 Graphics Processing Units (GPUs) is described. The kernel consists of a block-sparse matrix-vector product and a series of forward/backward triangular solves. The computation is memory-bound and exhibits low arithmetic intensity. Along with a relatively small block size, the data layout poses a challenge to effectively utilize the available memory bandwidth on common GPU architectures. An earlier implementation using a warp to process a single row of the matrix was found to yield good memory performance on the V100 architecture. However, anew approach, which assigns a warp to six rows of the matrix, is proposed for the A100. In addition, two new features offered by the A100 architecture are explored.L2residency control enables a portion of theL2cache to be used for persistent data access, and the asynchronous copy instruction allows data to be loaded directly from main memory into shared memory. Demonstrations show that the new implementation improves memory bandwidth utilization from 71.5% to 81.2% of the peak available on theA100 architecture.

GPU↗
NASA NTRS2022

Retraction Note: A 10 per cent increase in global land evapotranspiration from 2003 to 2019

In this article, we calculated global land evapotranspiration for 2003 to 2019 using a massbalance approach. To do this, we calculated evapotranspiration as the residual of the water balance, using an ensemble of datasets for precipitation, discharge and total water storage change. We made an error in calculating the global mean precipitation: we used arithmetic averaging to calculate the mean, instead of calculating a spatially weighted mean to account for the changing grid box size with latitude. As a result, the magnitudes of the global mean precipitation time series were underestimated. This impacted the subsequent calculation of global mean evapotranspiration, resulting in the mean evapotranspiration values being underestimated and altering some results. We are therefore retracting this article. We thank Ning Ma and others for bringing this error to our attention.

Madeleine Pascolini-Campbell↗
NASA NTRS2022

The Harmonic Linearized Navier-Stokes Equations for Transition Prediction in Three-Dimensional Flows

The conventional method to predict the onset of laminar-turbulent transition in convectively unstable boundary-layer flows is based on the logarithmic amplification ratio, the so-called N-factor, of the linear instability waves. To calculate the N-factor, the flow variables are decomposed into a laminar basic state solution and the linear disturbances, which are assumed to be harmonic in time. The most commonly used linear stability analysis approaches include the locally parallel linear stability theory (LST) and the nonlocal, weakly nonparallel parabolized stability equations (PSE). However, these methods do not account for strong streamwise gradients that are encountered in several configurations of interest, such as those in the vicinity of roughness elements, steps, gaps, or corners. To compute the linear evolution of disturbances along such strongly nonparallel regions, the harmonic linearized Navier-Stokes equations (HLNSE) need to be solved. The discretization of the HLNSE for spanwise/azimuthally inhomogeneous laminar basic states yields a linear system of complex arithmetic with a leading dimension of the order of 10^(7) to 10^(8) even in relatively simple flows. A combined multithread and multiprocessor algorithm is implemented for the direct solution of such linear systems. Results for a supersonic boundary layer over a three-dimensional roughness patch show good agreement with experimental measurements when the evolution of the instability waves over the roughness patch is included via the HLNSE. Additionally, inflow-resolvent analysis based on the HLNSE for discrete-roughness-induced disturbances in the nose tip of a blunt cone at Mach 6 demonstrates the importance of including the disturbance amplification along the near vicinity of the roughness element and separation region.

Boundary Layer Stability↗
NASA NTRS2022

The Harmonic Linearized Navier-Stokes Equations for Transition Prediction in Three-Dimensional Flows

The conventional method to predict the onset of laminar-turbulent transition in convectively unstable boundary-layer flows is based on the logarithmic amplification ratio, the so-called N-factor, of the linear instability waves. To calculate the N-factor, the flow variables are decomposed into a laminar basic state solution and the linear disturbances, which are assumed to be harmonic in time. The most commonly used linear stability analysis approaches include the locally parallel linear stability theory (LST) and the non-local, weakly nonparallel parabolized stability equations (PSE). However, these methods do not account for strong streamwise gradients that are encountered in several configurations of interest, as roughness elements, steps, gaps, or corners. To solve the linear evolution of disturbances along such strongly nonparallel regions, the harmonic linearized Navier-Stokes equations (HLNSE) need to be solved. The discretization of the HLNSE for spanwise/azimuthally inhomogeneous laminar basic states yields a linear system of complex arithmetic with a leading dimension of the order of 107 to 108. A combined multithread and multiprocessor algorithm is implemented for the direct solution of such linear system. Results for a supersonic boundary layer over a three-dimensional roughness patch show good agreement with experimental measurements when the evolution of the instability waves over the roughness patch is included via the HLNSE.

Boundary Layer Stability↗
NASA NTRS2022

Structural and chemical complexity of minerals: An update

The complexities of chemical composition and crystal structure are fundamental characteristics of minerals that have high relevance to the understanding of their stability, occurrence and evolution. This review summarises recent developments in the field of mineral complexity and outlines possible directions for its future elaboration. The database of structural and chemical complexity parameters of minerals is updated by H-correction of structures with unknown H positions and the inclusion of new data. The revised average complexity values (arithmetic means) for all minerals are 3.54(2) bits/atom and 345(10) bits/cell (based upon 4443 structure reports). The distributions of atomic information amounts, chemIG and strIG, versus the number of mineral species fit the normal modes, whereas the distributions of total complexities, chemIG,total and strIG,total, along with numbers of atoms per formula and per unit cell are log normal. The three most complex mineral species known today are ewingite, morrisonite and ilmajokite, all either discovered or structurally characterised within the last five years. The most important complexity-generating mechanisms in minerals are: (1) the presence of isolated large clusters; (2) the presence of large clusters linked together to form three-dimensional frameworks; (3) formation of complex three-dimensional modular frameworks; (4) formation of complex modular layers; (5) high hydration state in salts with complex heteropolyhedral units; and (6) formation of ordered superstructures of relatively simple structure types. The relations between symmetry and complexity are considered. The analysis of temporal dynamics of mineralogical discoveries since 1875 with the step of 25 years show the increasing chemical and structural complexities of human knowledge of the mineral kingdom in the history of mineralogy. In the Earth’s history, both diversity and complexity of minerals experience dramatic increases associated with the formation of Earth’s continental crust, initiation of plate tectonics and the Great Oxidation event.

complexity↗
NASA NTRSDate not supplied

A Provably Correct Floating-Point Implementation of Well Clear Avionics Concepts

The NASA DAIDALUS library provides formal definitions for Detect-and-Avoid avionics concepts such as when an aircraft is well-clear with respect to the surrounding air traffic, i.e., it does not operate in such proximity to create a collision hazard. While several properties are proven correct for DAIDALUS assuming ideal real number arithmetic, an actual implementation that uses floating-point numbers may behave unexpectedly because of round-off errors and run-time exceptions. This paper presents an experience report on the application of a formal methods toolchain to extract and verify floating-point C code from a real-valued specification of the well-clear module of DAIDALUS. This toolchain comprises the PVS theorem prover, the PRECiSA floating-point analyzer and code generator, and the Frama-C analysis suite. The generated code is automatically instrumented to detect when the control flow of the floating-point program may diverge from the ideal real number specification, and it is annotated with contracts that state the maximum accumulated round-off error. The absence of overflows is also formally verified for the generated code. In order to apply the toolchain to an industrial case study such as DAIDALUS, a formally verified pre-processing of the input specification is performed, which includes a program slicing and several semantic-preserving simplifications.

Program verification↗
NASA NTRSDate not supplied

Perturbations in Brain Functional Connectivity Patterns After Waking From Slow Wave Sleep Under Different Cognitive States

Sleep inertia refers to the state of transition between sleep and wake characterized by impaired alertness, confusion, and reduced cognitive and behavioral performance. While the behavioral symptoms of sleep inertia are well described, the neurological changes that lead to this state remain elusive. Here, to understand the state of sleep inertia and the reorganization that the brain undergoes, we took a graph theoretical approach and compared the EEG derived brain connectivity patterns before sleep and after waking up while participants (n = 10) performed multiple tasks that differed in cognitive complexities. We focused on how the degree and the clustering coefficient of brain regions (EEG sensors) change immediately after participants wake up from slow wave sleep. During a psychomotor vigilance task (PVT), designed to assess vigilant attention, we find that the brain regions with strong network connectivity (degree) before sleep show a reduction in connectivity after waking. In contrast, those with low connectivity before sleep have greater connectivity after waking. The regions that undergo these changes are specific to each participant and these findings are unique to the beta frequency range, which plays a key role in sensorimotor functioning and preserving the current state of the brain. Moreover, in tasks that required inhibitory control and arithmetic reasoning, we found that only regions with weak connectivity before sleep exhibited more connections after waking, but regions with high connectivity prior to sleeping remained unchanged, highlighting task specific effects. Furthermore, we find that during the PVT, the clustering coefficient within low frequency oscillations of the brain is reduced upon waking while it remains unchanged during other tasks. These results suggest that the connections between regions that are lost after abrupt awakening can be reallocated to other regions in order to renormalize the brain. However, this response may only be evident during specific cognitive states and may be more nuanced during complex task performance.

sleep inertia↗
DOE OSTI2015

Failure detection in high-performance clusters and computers using chaotic map computations

A programmable media includes a processing unit capable of independent operation in a machine that is capable of executing 10.sup.18 floating point operations per second. The processing unit is in communication with a memory element and an interconnect that couples computing nodes. The programmable media includes a logical unit configured to execute arithmetic functions, comparative functions, and/or logical functions. The processing unit is configured to detect computing component failures, memory element failures and/or interconnect failures by executing programming threads that generate one or more chaotic map trajectories. The central processing unit or graphical processing unit is configured to detect a computing component failure, memory element failure and/or an interconnect failure through an automated comparison of signal trajectories generated by the chaotic maps.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Parameter Estimation of Gaussian-Damped Sinusoids from a Geometric Perspective

The five parameter gaussian damped sinusoid equation is a reasonable model for betatron motion with chromatic decoherence of the proton bunch centroid signal in the ring at the Spallation Neutron Source. A geometric method for efficiently fitting this equation to the turn by turn signals to extract the betatron tune and damping constant will be presented. This method separates the parameters into global and local parameters and allows the use of vector arithmetic to eliminate the local parameters from the parameter search space. Furthermore, this method is easily generalized to reduce the parameter search space for a larger class of problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

A source-attractor approach to network detection of radiation sources

Radiation source detection using a network of detectors is an active field of research for homeland security and defense applications. We propose Source-attractor Radiation Detection (SRD) method to aggregate measurements from a network of detectors for radiation source detection. SRD method models a potential radiation source as a magnet -like attractor that pulls in pre-computed virtual points from the detector locations. A detection decision is made if a sufficient level of attraction, quantified by the increase in the clustering of the shifted virtual points, is observed. Compared with traditional methods, SRD has the following advantages: i) it does not require an accurate estimate of the source location from limited and noise-corrupted sensor readings, unlike the localizationbased methods, and ii) its virtual point shifting and clustering calculation involve simple arithmetic operations based on the number of detectors, avoiding the high computational complexity of grid-based likelihood estimation methods. We evaluate its detection performance using canonical datasets from Domestic Nuclear Detection Office s (DNDO) Intelligence Radiation Sensors Systems (IRSS) tests. SRD achieves both lower false alarm rate and false negative rate compared to three existing algorithms for network source detection.

Wu, Qishi↗
DOE OSTI2016

Universal Number Library

This floating-point arithmetic library contains a software implementation of Universal Numbers (unums) as described by John Gustafson [1]. The unum format is a superset of IEEE 754 floating point with several advantages. Computing with unums provides more accurate answers without rounding errors, underflow or overflow. In contrast to fixed-sized IEEE numbers, a variable number of bits can be used to encode unums. This all allows number with only a few significant digits or with a small dynamic range to be represented more compactly.

Lloyd, G. Scott↗
DOE OSTI2016

Math processing by detection of elementary valued operands

One embodiment of the present invention includes a method for simplifying arithmetic operations by detecting operands with elementary values such as zero or 1.0. Computer and graphics processing systems perform a great number of multiply-add operations. In a significant portion of these operations, the values of one or more of the operands are zero or 1.0. By detecting the occurrence of these elementary values, math operations can be greatly simplified, for example by eliminating multiply operations when one multiplicand is zero or 1.0 or eliminating add operations when one addend is zero. The simplified math operations resulting from detecting elementary valued operands provide significant savings in overhead power, dynamic processing power, and cycle time.

Finchelstein, Daniel Frederic↗
DOE OSTI2019

GraphBLAST: A High-Performance Linear Algebra-based Graph Framework on the GPU

High-performance implementations of graph algorithms are challenging to implement on new parallel hardware such as GPUs, because of three challenges: (1) difficulty of coming up with graph building blocks, (2) load imbalance on parallel hardware, and (3) graph problems having low arithmetic intensity. To address these challenges, GraphBLAS is an innovative, on-going effort by the graph analytics community to propose building blocks based in sparse linear algebra, which will allow graph algorithms to be expressed in a performant, succinct, composable and portable manner. In this paper, we examine the performance challenges of a linear algebra-based approach to building graph frameworks and describe new design principles for overcoming these bottlenecks. Among the new design principles is exploiting input sparsity, which allows users to write graph algorithms without specifying push and pull direction. Exploiting output sparsity allows users to tell the backend which values of the output in a single vectorized computation they do not want computed. Load-balancing is an important feature for balancing work amongst parallel workers. We describe the important load-balancing features for handling graphs with different characteristics. The design principles described in this paper have been implemented in "GraphBLAST", the first open-source linear algebra-based graph framework on GPU targeting high-performance computing. The results show that on a single GPU, GraphBLAST has on average at least an order of magnitude speedup over previous GraphBLAS implementations SuiteSparse and GBTL, comparable performance to the fastest GPU hardwired primitives and shared-memory graph frameworks Ligra and Gunrock, and better performance than any other GPU graph framework, while offering a simpler and more concise programming model.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Heterogeneous graphics processing unit for scheduling thread groups for execution on variable width SIMD units

A compute unit configured to execute multiple threads in parallel is presented. The compute unit includes one or more single instruction multiple data (SIMD) units and a fetch and decode logic. The SIMD units have differing numbers of arithmetic logic units (ALUs), such that each SIMD unit can execute a different number of threads. The fetch and decode logic is in communication with each of the SIMD units, and is configured to assign the threads to the SIMD units for execution based on such differing numbers of ALUs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Computational processor-in-memory with enhanced strided memory access

A computational memory for a computer. The memory includes a memory bank having a selected-row buffer and being configured to store records up to a number, K. The memory also includes an accumulator connected to the memory bank, the accumulator configured to store up to K records. The memory also includes an arithmetic and logic unit (ALU) connected to the accumulator and to the selected row buffer of the memory bank, the ALU having an indirect network of 2K ports for reading and writing records in the memory bank and the accumulator, and the ALU further physically configured to operate as a sorting network. The memory also includes a controller connected to the memory bank, the ALU, and the accumulator, the controller being hardware configured to direct operation of the ALU.

DeBenedictis, Erik↗
DOE OSTI2021

Method and apparatus for asynchronous scheduling

A method and apparatus of asynchronous scheduling in a graphics device includes sending one or more instructions from an instruction scheduler to one or more instruction first-in/first-out (FIFO) devices. An instruction in the one or more FIFO devices is selected for execution by a single-instruction/multiple-data (SIMD) pipeline unit. It is determined whether all operands for the selected instruction are available for execution of the instruction, and if all the operands are available, the selected instruction is executed on the SIMD pipeline unit. The self-timed arithmetic pipeline unit (SIMD pipeline unit) is effectively encapsulated in a synchronous, (e.g., clocked by global clock), scheduler and register file environment.

Kalamatianos, John↗
DOE OSTI2019

Toward Simulating Turbulent Wall-Bounded Flows at High Reynolds Numbers on Exascale Platforms

Given that wall resolved LES (WRLES) of high Reynolds number flows will continue to be intractable on even exascale computing platforms, there is considerable effort to make hybrid RANS/LES (HRLES) methods the tool of choice for predictive simulations of high-Re separated flows. The fidelity of HRLES depends on the ability of the subgrid model to account for the effects of the filtered scales on the resolved scales, and on the numerical schemes that are used to evolve the Navier-Stokes equations. While higher-order numerical schemes, with low dissipation/dispersion errors (and higher arithmetic intensity), are commonly used for canonical flow simulations (on simpler geometries), the bulk of the high-Re flow simulations on complex geometry still employ nominally second-order accurate schemes in structured/unstructured flow solvers. Hence, there is a need for better sub-grid models that can improve the predictive capability of both the higher-order flow solvers and existing second-order accurate flow solvers, for simulating turbulent separated flows. This talk is about ongoing efforts to develop HRLES subgrid models from DNS/WRLES simulations of canonical flows over curved and sharply discontinuous surfaces and their ability to predict high-Re flows on current petascale platforms.

Balakrishnan, Ramesh↗