Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Algorithms and Theoretical Developments”

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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Parallel O(log n) algorithms for open- and closed-chain rigid multibody systems based on a new mass matrix factorization technique

In this paper, parallel O(log n) algorithms for computation of rigid multibody dynamics are developed. These parallel algorithms are derived by parallelization of new O(n) algorithms for the problem. The underlying feature of these O(n) algorithms is a drastically different strategy for decomposition of interbody force which leads to a new factorization of the mass matrix (M). Specifically, it is shown that a factorization of the inverse of the mass matrix in the form of the Schur Complement is derived as M(exp -1) = C - B(exp *)A(exp -1)B, wherein matrices C, A, and B are block tridiagonal matrices. The new O(n) algorithm is then derived as a recursive implementation of this factorization of M(exp -1). For the closed-chain systems, similar factorizations and O(n) algorithms for computation of Operational Space Mass Matrix lambda and its inverse lambda(exp -1) are also derived. It is shown that these O(n) algorithms are strictly parallel, that is, they are less efficient than other algorithms for serial computation of the problem. But, to our knowledge, they are the only known algorithms that can be parallelized and that lead to both time- and processor-optimal parallel algorithms for the problem, i.e., parallel O(log n) algorithms with O(n) processors. The developed parallel algorithms, in addition to their theoretical significance, are also practical from an implementation point of view due to their simple architectural requirements.

Fijany, Amir↗
NASA NTRS2010

Hazard Detection Analysis for a Forward-Looking Interferometer

The Forward-Looking Interferometer (FLI) is a new instrument concept for obtaining the measurements required to alert flight crews to potential weather hazards to safe flight. To meet the needs of the commercial fleet, such a sensor should address multiple hazards to warrant the costs of development, certification, installation, training, and maintenance. The FLI concept is based on high-resolution Infrared Fourier Transform Spectrometry (FTS) technologies that have been developed for satellite remote sensing. These technologies have also been applied to the detection of aerosols and gases for other purposes. The FLI concept is being evaluated for its potential to address multiple hazards including clear air turbulence (CAT), volcanic ash, wake vortices, low slant range visibility, dry wind shear, and icing during all phases of flight (takeoff, cruise, and landing). The research accomplished in this second phase of the FLI project was in three major areas: further sensitivity studies to better understand the potential capabilities and requirements for an airborne FLI instrument, field measurements that were conducted in an effort to provide empirical demonstrations of radiometric hazard detection, and theoretical work to support the development of algorithms to determine the severity of detected hazards

West, Leanne↗
NASA NTRS1987

Strategies for concurrent processing of complex algorithms in data driven architectures

The results of ongoing research directed at developing a graph theoretical model for describing data and control flow associated with the execution of large grained algorithms in a spatial distributed computer environment is presented. This model is identified by the acronym ATAMM (Algorithm/Architecture Mapping Model). The purpose of such a model is to provide a basis for establishing rules for relating an algorithm to its execution in a multiprocessor environment. Specifications derived from the model lead directly to the description of a data flow architecture which is a consequence of the inherent behavior of the data and control flow described by the model. The purpose of the ATAMM based architecture is to optimize computational concurrency in the multiprocessor environment and to provide an analytical basis for performance evaluation. The ATAMM model and architecture specifications are demonstrated on a prototype system for concept validation.

Stoughton, John W.↗
DOE OSTI2025

Real-space Kohn–Sham density functional theory for complex energy applications

Real-space Kohn-Sham density functional theory (real-space KS-DFT) enables large-scale electronic structure simulations that is particularly well-suited for the modern high-performance computing (HPC) architectures. This feature article reviews its theoretical foundations, highlights the algorithmic advances and recent developments, and showcases applications in complex nano systems. We aim to provide a perspective on the trajectory of real-space KS-DFT as an emerging tool for computational chemistry and materials science in the exascale era.

Zhang, Zeyi↗
NASA NTRS1993

Resource utilization model for the algorithm to architecture mapping model

The analytical model for resource utilization and the variable node time and conditional node model for the enhanced ATAMM model for a real-time data flow architecture are presented in this research. The Algorithm To Architecture Mapping Model, ATAMM, is a Petri net based graph theoretic model developed at Old Dominion University, and is capable of modeling the execution of large-grained algorithms on a real-time data flow architecture. Using the resource utilization model, the resource envelope may be obtained directly from a given graph and, consequently, the maximum number of required resources may be evaluated. The node timing diagram for one iteration period may be obtained using the analytical resource envelope. The variable node time model, which describes the change in resource requirement for the execution of an algorithm under node time variation, is useful to expand the applicability of the ATAMM model to heterogeneous architectures. The model also describes a method of detecting the presence of resource limited mode and its subsequent prevention. Graphs with conditional nodes are shown to be reduced to equivalent graphs with time varying nodes and, subsequently, may be analyzed using the variable node time model to determine resource requirements. Case studies are performed on three graphs for the illustration of applicability of the analytical theories.

Stoughton, John W.↗
DOE OSTI2026

Leveraging Qubit Loss Detection in Fault-Tolerant Quantum Algorithms

Qubit loss errors constitute a dominant source of noise in many quantum hardware systems, particularly in neutral-atom quantum computers. We develop a theoretical framework to effectively detect and correct loss errors in logical algorithms and leverage such loss information in decoding. Considering general quantum error correction codes and logical circuits, we introduce a delayed-erasure decoder for experimentally motivated error models which leverages information from delayed loss detection to accurately correct loss errors, even when the precise moment of the error is unknown. Using this decoder, we identify strategies for detecting and correcting loss errors based on the logical circuit structure. For deep circuits prior to logical measurement, we explore methods to integrate loss detection into syndrome extraction with minimal overhead, identifying optimal strategies depending on the qubit loss fraction in the noise and hardware capabilities. In contrast, we find that many key algorithmic subroutines involve frequent gate teleportation, shortening the circuit depth before logical measurement and naturally replacing qubits with no additional experimental overhead. We simulate this setting using a toy model algorithm for small-angle synthesis and find a significant performance improvement as the loss fraction increases. These results provide a path forward for advancing large-scale fault-tolerant quantum computation in systems with loss error detection.

atoms↗
NASA NTRS1989

Modeling of high speed chemically reacting flow-fields

The SPARK3D and SPARK3D-PNS computer programs were developed to model 3-D supersonic, chemically reacting flow-fields. The SPARK3D code is a full Navier-Stokes solver, and is suitable for use in scramjet combustors and other regions where recirculation may be present. The SPARK3D-PNS is a parabolized Navier-Stokes solver and provides an efficient means of calculating steady-state combustor far-fields and nozzles. Each code has a generalized chemistry package, making modeling of any chemically reacting flow possible. Research activities by the Langley group range from addressing fundamental theoretical issues to simulating problems of practical importance. Algorithmic development includes work on higher order and upwind spatial difference schemes. Direct numerical simulations employ these algorithms to address the fundamental issues of flow stability and transition, and the chemical reaction of supersonic mixing layers and jets. It is believed that this work will lend greater insight into phenomenological model development for simulating supersonic chemically reacting flows in practical combustors. Currently, the SPARK3D and SPARK3D-PNS codes are used to study problems of engineering interest, including various injector designs and 3-D combustor-nozzle configurations. Examples, which demonstrate the capabilities of each code are presented.

Drummond, J. P.↗
NASA NTRS1995

Robust integration schemes for generalized viscoplasticity with internal-state variables. Part 2: Algorithmic developments and implementation

This two-part report is concerned with the development of a general framework for the implicit time-stepping integrators for the flow and evolution equations in generalized viscoplastic models. The primary goal is to present a complete theoretical formulation, and to address in detail the algorithmic and numerical analysis aspects involved in its finite element implementation, as well as to critically assess the numerical performance of the developed schemes in a comprehensive set of test cases. On the theoretical side, the general framework is developed on the basis of the unconditionally-stable, backward-Euler difference scheme as a starting point. Its mathematical structure is of sufficient generality to allow a unified treatment of different classes of viscoplastic models with internal variables. In particular, two specific models of this type, which are representative of the present start-of-art in metal viscoplasticity, are considered in applications reported here; i.e., fully associative (GVIPS) and non-associative (NAV) models. The matrix forms developed for both these models are directly applicable for both initially isotropic and anisotropic materials, in general (three-dimensional) situations as well as subspace applications (i.e., plane stress/strain, axisymmetric, generalized plane stress in shells). On the computational side, issues related to efficiency and robustness are emphasized in developing the (local) interative algorithm. In particular, closed-form expressions for residual vectors and (consistent) material tangent stiffness arrays are given explicitly for both GVIPS and NAV models, with their maximum sizes 'optimized' to depend only on the number of independent stress components (but independent of the number of viscoplastic internal state parameters). Significant robustness of the local iterative solution is provided by complementing the basic Newton-Raphson scheme with a line-search strategy for convergence. In the present second part of the report, we focus on the specific details of the numerical schemes, and associated computer algorithms, for the finite-element implementation of GVIPS and NAV models.

Li, Wei↗
NASA NTRS1984

Atmospheric Effects on Remote Sensing of the Earth's Surface

The main causes and magnitude of the atmospheric effects on remote sensing of the Earth's surface are determined. Theoretical study as well as measurements are included. The knowledge gained from this study will be used to develop atmospheric correction algorithms and to test them with satellite data. In a theoretical investigation of the relative effects of the aerosol optical thickness, absorption, and size distribution on remote sensing, it was found that aerosol absorption has a significant effect on satellite measurements of surface reflectivity. The absorption effect is stronger for high than for low surface reflectances. The aerosol optical thickness is dominant for small surface reflectances. The accuracy of clustering algorithms depends on both parameters. The vegetation index, however, is affected by the optical thickness but only weakly affected by the absorption. A laboratory simulation of the atmospheric effect on the radiance of sunlight scattered from the Earth's surface-atmosphere system was performed. This experiment verified the existence of the adjacency effect (the effect of a bright field on the radiance detected above a dark field) and was used to test 3-D radiative transfer models. In a theoretical study it was found that atmospheric scattering resulting from the adjacency effect reduces the separability between surface classes.

Fraser, R. E.↗
NASA NTRS1990

Computational enhancement of an unsymmetric block Lanczos algorithm

An unsymmetric block Lanczos algorithm has been employed for the dynamic analysis of a large system which has arbitrary damping and/or repeated (or closely spaced) eigenvalues. In the algorithm development, the right and left Lanczos vectors are all theoretically biorthogonal to each other. However, these vectors may lose the biorthogonality owing to cancellation and roundoff errors. For the unsymmetric case there can be a breakdown, even without numerical errors. This paper describes computational techniques which have led to a robust unsymmetric block Lanczos algorithm.

Kim, Hyoung M.↗
DOE OSTI2025

Cyber‐Resilient Distributed Energy Resource Control Algorithms for Smart Distribution Grids

ABSTRACT This paper focuses on the development of cyber‐resilient gradient‐based optimisation algorithms and theoretical proof for grid‐interactive distributed energy resource (DER) control to enable two grid services of virtual power plants (VPPs) dispatch and grid voltage regulation, considering the communication and security impacts. Firstly, the combined DER dispatch and voltage regulation as a real‐time gradient‐based optimisation problem is recapped. Thereafter, we consider a probabilistic traffic model to characterise packet delays and loss in a communication network, and study how the delays enter the process of information exchange among the grid measurement units, local DER controllers and the grid control centre that execute this control algorithm in a coordinated manner. Then, a strategy combining delay thresholds and message update rules is proposed to immunity the asynchrony resulting from the communications traffic and it avoids possible numerical instabilities and sensitivities of the power tracking and voltage regulation capabilities, resulting as cyber‐resilient DER control algorithms. Additionally, their convergence is theoretically proved. Effectiveness of proposed cyber‐resilient algorithms has been validated on the IEEE 37‐bus system in terms of convergence, VPP tracking and voltage regulation performance for smart distribution systems with high penetration of DERs.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1973

An historical survey of computational methods in optimal control.

Review of some of the salient theoretical developments in the specific area of optimal control algorithms. The first algorithms for optimal control were aimed at unconstrained problems and were derived by using first- and second-variation methods of the calculus of variations. These methods have subsequently been recognized as gradient, Newton-Raphson, or Gauss-Newton methods in function space. A much more recent addition to the arsenal of unconstrained optimal control algorithms are several variations of conjugate-gradient methods. At first, constrained optimal control problems could only be solved by exterior penalty function methods. Later algorithms specifically designed for constrained problems have appeared. Among these are methods for solving the unconstrained linear quadratic regulator problem, as well as certain constrained minimum-time and minimum-energy problems. Differential-dynamic programming was developed from dynamic programming considerations. The conditional-gradient method, the gradient-projection method, and a couple of feasible directions methods were obtained as extensions or adaptations of related algorithms for finite-dimensional problems. Finally, the so-called epsilon-methods combine the Ritz method with penalty function techniques.

Polak, E.↗
NASA NTRS1992

Towards a theory of automated elliptic mesh generation

The theory of elliptic mesh generation is reviewed and the fundamental problem of constructing computational space is discussed. It is argued that the construction of computational space is an NP-Complete problem and therefore requires a nonstandard approach for its solution. This leads to the development of graph-theoretic, combinatorial optimization and integer programming algorithms. Methods for the construction of two dimensional computational space are presented.

Cordova, J. Q.↗
NASA NTRS2012

TRMM Latent Heating Retrieval and Comparisons with Field Campaigns and Large-Scale Analyses

Rainfall production is a fundamental process within the Earth's hydrological cycle because it represents both a principal forcing term in surface water budgets, and its energetics corollary, latent heating (LH), is one of the principal sources of atmospheric diabatic heating. Latent heat release itself is a consequence of phase changes between the vapor, liquid, and frozen states of water. The vertical distribution of LH has a strong influence on the atmosphere, controlling large-scale tropical circulations, exciting and modulating tropical waves, maintaining the intensities of tropical cyclones, and even providing the energetics of midlatitude cyclones and other mobile midlatitude weather systems. Moreover, the processes associated with LH result in significant non-linear changes in atmospheric radiation through the creation, dissipation and modulation of clouds and precipitation. Yanai et al. (1973) utilized the meteorological data collected from a sounding network to present a pioneering work on thermodynamic budgets, which are referred to as the apparent heat source (Q1) and apparent moisture sink (Q2). Yanai's paper motivated the development of satellite-based LH algorithms and provided a theoretical background for imposing large-scale advective forcing into cloud-resolving models (CRMs). These CRM-simulated LH and Q1 data have been used to generate the look-up tables used in LH algorithms. This paper examines the retrieval, validation, and application of LH estimates based on rain rate quantities acquired from the Tropical Rainfall Measuring Mission satellite (TRMM). TRMM was launched in November 1997 as a joint enterprise between the American and Japanese space agencies -- with overriding goals of providing accurate four-dimensional estimates of rainfall and LH over the global Tropics and subtropics equatorward of 35o. Other literature has acknowledged the achievement of the first goal of obtaining an accurate rainfall climatology. This paper describes the second major goal of obtaining credible LH estimates as well as their applications within TRMM's zone of coverage, the standard TRMM LH products, and areas for further improvement.

latent heating↗
NASA NTRSDate not supplied

Newly Available Single Field-of-view Sounder Atmospheric Product (SiFSAP) and Its Derivative Product

The Single Field-of-view Sounder Atmospheric product (SiFSAP) has been developed and delivered to NASA GES DISC. The SiFSAP Algorithm Theoretical Basis Documents (ATBD) and users manuals are ready to be released to public. This novel data product supplements other operational products such as AIRS version 7 and the Community Long-term Infrared Microwave Combined Atmospheric Product System (CLIMCAPS) from two main perspectives: 1) improving the spatial resolution of sounder Level-2 data to extend its usage in weather and dynamics focus area; 2) establishing radiance closure between Level-2 data and directly measured Level-1 radiances to facilitate the climate trend analysis. SiFSAP has 3-times higher spatial resolution and 9-times denser data products comparing to current NASA and NOAA operational IR sounder products. SiFSAP is derived using the optimal estimation method based physical retrieval algorithm. The Principal Component-based Radiative Transfer Model (PCRTM) which includes the cloud scattering simulation is used for the forward model so that the solution can fit the spectral radiances under all-sky conditions for individual single field-of-view (SFOV) measurements. A general introduction of the SiFSAP algorithm and corresponding validation work will be presented. Also introduced here is the Climate Fingerprinting Sounder product (ClimFiSP) that is the derivative product of SiFSAP and will be released in the near future. The ClimFiSP algorithm uses pre-constructed fingerprinting relationship to achieve a low-latency Level-3 data production and facilitate the fusion of data of different sounders.

Wan Wu↗
NASA NTRS1991

Redundancy management for efficient fault recovery in NASA's distributed computing system

The management of redundancy in computer systems was studied and guidelines were provided for the development of NASA's fault-tolerant distributed systems. Fault recovery and reconfiguration mechanisms were examined. A theoretical foundation was laid for redundancy management by efficient reconfiguration methods and algorithmic diversity. Algorithms were developed to optimize the resources for embedding of computational graphs of tasks in the system architecture and reconfiguration of these tasks after a failure has occurred. The computational structure represented by a path and the complete binary tree was considered and the mesh and hypercube architectures were targeted for their embeddings. The innovative concept of Hybrid Algorithm Technique was introduced. This new technique provides a mechanism for obtaining fault tolerance while exhibiting improved performance.

Malek, Miroslaw↗
NASA NTRS1997

Implicit Kalman filtering

For an implicitly defined discrete system, a new algorithm for Kalman filtering is developed and an efficient numerical implementation scheme is proposed. Unlike the traditional explicit approach, the implicit filter can be readily applied to ill-conditioned systems and allows for generalization to descriptor systems. The implementation of the implicit filter depends on the solution of the congruence matrix equation (A1)(Px)(AT1) = Py. We develop a general iterative method for the solution of this equation, and prove necessary and sufficient conditions for convergence. It is shown that when the system matrices of an implicit system are sparse, the implicit Kalman filter requires significantly less computer time and storage to implement as compared to the traditional explicit Kalman filter. Simulation results are presented to illustrate and substantiate the theoretical developments.

Non-NASA Center↗
DOE OSTI2024

Generalized boost transformations in finite volumes and application to Hamiltonian methods

The investigation of hadron interactions within lattice QCD has been facilitated by the well-known quantisation condition, linking scattering phase shifts to finite-volume energies. Additionally, the ability to utilise systems at finite total boosts has been pivotal in smoothly charting the energy-dependent behaviour of these phase shifts. The existing implementations of the quantization condition at finite boosts rely on momentum transformations between rest and moving frames, defined directly in terms of the energy eigenvalues. This energy dependence is unsuitable in the formulation of a Hamiltonian. In this work, we introduce a novel approach to generalise the three-momentum boost prescription, enabling the incorporation of energy-independent finite-volume Hamiltonians within moving frames. We demonstrate the application of our method through numerical comparisons, employing a phenomenological ππ scattering example.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗