Search NASA⌕ Search

SEARCH · Search NASA

Results for “numerical algorithm computing”

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 703 records · Page 39
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

A high-order vertex-based central ENO finite-volume scheme for three-dimensional compressible flows

High-order discretization methods offer the potential to reduce the computational cost associated with modeling compressible flows. However, it is difficult to obtain accurate high-order discretizations of conservation laws that do not produce spurious oscillations near discontinuities, especially on multi-dimensional unstructured meshes. A novel, high-order, central essentially non-oscillatory (CENO) finite-volume method that does not have these difficulties is proposed for tetrahedral meshes. The proposed unstructured method is vertex-based, which differs from existing cell-based CENO formulations, and uses a hybrid reconstruction procedure that switches between two different solution representations. It applies a high-order k-exact reconstruction in smooth regions and a limited linear reconstruction when discontinuities are encountered. Both reconstructions use a single, central stencil for all variables, making the application of CENO to arbitrary unstructured meshes relatively straightforward. The new approach was applied to the conservation equations governing compressible flows and assessed in terms of accuracy and computational cost. For all problems considered, which included various function reconstructions and idealized flows, CENO demonstrated excellent reliability and robustness. Up to fifth-order accuracy was achieved in smooth regions and essentially non-oscillatory solutions were obtained near discontinuities. The high-order schemes were also more computationally efficient for high-accuracy solutions, i.e., they took less wall time than the lower-order schemes to achieve a desired level of error. In one particular case, it took a factor of 24 less wall-time to obtain a given level of error with the fourth-order CENO scheme than to obtain the same error with the second-order scheme.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Optimal Attack Strategies Subject to Detection Constraints Against Cyber-Physical Systems

This paper studies an attacker against a cyberphysical system (CPS) whose goal is to move the state of a CPS to a target state while ensuring that his or her probability of being detected does not exceed a given bound. The attacker’s probability of being detected is related to the nonnegative bias induced by his or her attack on the CPS’s detection statistic. We formulate a linear quadratic cost function that captures the attacker’s control goal and establish constraints on the induced bias that reflect the attacker’s detection-avoidance objectives. When the attacker is constrained to be detected at the false-alarm rate of the detector, we show that the optimal attack strategy reduces to a linear feedback of the attacker’s state estimate. In the case that the attacker’s bias is upper bounded by a positive constant, we provide two algorithms – an optimal algorithm and a sub-optimal, less computationally intensive algorithm – to find suitable attack sequences. Lastly, we illustrate our attack strategies in numerical examples based on a remotely-controlled helicopter under attack.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
NASA NTRS1978

User interface concerns

Three possible goals for the Numerical Aerodynamic Simulation Facility (NASF) are: (1) a computational fluid dynamics (as opposed to aerodynamics) algorithm development tool; (2) a specialized research laboratory facility for nearly intractable aerodynamics problems that industry encounters; and (3) a facility for industry to use in its normal aerodynamics design work that requires high computing rates. The central system issue for industry use of such a computer is the quality of the user interface as implemented in some kind of a front end to the vector processor.

Redhed, D. D.↗
NASA NTRS1980

An analysis of GDOP in global positioning system navigation

The accuracy of user navigation fix based on the NAVSTAR global positioning system is described. The trace of this matrix serves as a convenient navigation performance index and the square root of the trace is called geometric dilution of precision (GDOP). Certain theoretical results concerning the general properties of the navigation performance are derived. An efficient algorithm for the computation of GDOP is given. Applications of the results are illustrated by numerical examples.

Fang, B. T.↗
NASA NTRS1986

Automated Design Synthesis

Automated Design Synthesis (ADS) program is general-purpose numerical optimization program containing wide variety of algorithms. Assumed user prepares analysis problem capable of computing objective function and constraints. Program able to accept as part of input design variable quantities. Optimization process carried out by ADS coupled with user's program. ADS used for constrained and unconstrained function minimization. Solution of general problem separated into three basic levels: Strategy, Optimizer, and One-Dimensional Search. Already significant applications in area of structural synthesis (minimum-weight design).

Vanderplaats, G. N.↗
NASA NTRS1992

CFD lends the government a hand

The present survey of important and novel CFD applications being developed and implemented by U.S. Government contractors gives attention to naval vessel flow-modeling, Army ballistic and rotary wing aerodynamics, and NASA hypersonic vehicle related applications of CFD. CFD-generated knowledge of numerical algorithms, fluid motion, and supercomputer use is being incorporated into such additional areas as computational electromagnetics and acoustics. Attention is presently given to CFD methods' development status in such fields as submarine boundary layers, hypersonic kinetic energy projectile shock structures, helicopter main rotor tip flows, and National Aerospace Plane aerothermodynamics.

Lekoudis, Spiro↗
NASA NTRS1995

High-order essentially non-oscillatory methods for computational aeroacoustics

The desire to obtain acoustic information from the numerical solution of a nonlinear system of equations is a demanding proposition for a computational algorithm. High-order accuracy is required for the propagation of high-frequency, low-amplitude waves. In addition, it is desirable to highly resolve discontinuities that can develop in the solutions of the Euler or Navier-Stokes equations. The class of essentially non-oscillatory (ENO) shock-capturing schemes has been designed to have both of these properties. The dual capacity of ENO schemes for high-order accuracy and non-oscillatory shock-capturing is achieved through the use of adaptive stenciling, which makes these schemes highly nonlinear. These schemes are briefly described and referenced herein. A fourth-order algorithm is then applied to the solution of an acoustic wave in a quasi-one-dimensional converging-diverging nozzle.

Casper, Jay↗
NASA NTRS1997

Using High-Order Methods on Lower-Order Geometries

The desire to obtain acoustic information from the numerical solution of a nonlinear system of equations is a demanding proposition for a computational algorithm. High-order accuracy is required for the propagation of high-frequency, low-amplitude waves. The accuracy of an algorithm can be compromised by low-order errors that naturally occur in the solution of a particular problem. Such errors arise from two sources: the presence of discontinuities in the flow field or because the geometry on which the problem is defined is not everywhere smooth to the order of the scheme. The performance of high-order accurate essentially non-oscillatory (ENO) schemes on piecewise smooth solutions is well documented. Herein, the performance of these methods on smooth solutions defined on piecewise smooth geometries is investigated. The propagation of sound in a quasi-one-dimensional nozzle is considered as a test case. Some of the issues involved in the extension to two spatial dimensions are discussed.

Casper, Jay↗
NASA NTRS1988

Analysis of long term heart rate variability: methods, 1/f scaling and implications

The use of spectral techniques to quantify short term heart rate fluctuations on the order of seconds to minutes has helped define the autonomic contributions to beat-to-beat control of heart rate. We used similar techniques to quantify the entire spectrum (0.00003-1.0 Hz) of heart rate variability during 24 hour ambulatory ECG monitoring. The ECG from standard Holter monitor recordings from normal subjects was sampled with the use of a phase locked loop, and a heart rate time series was constructed at 3 Hz. Frequency analysis of the heart rate signal was performed after a nonlinear filtering algorithm was used to eliminate artifacts. A power spectrum of the entire 24 hour record revealed power that was inversely proportional to frequency, 1/f, over 4 decades from 0.00003 to 0.1 Hz (period approximately 10 hours to 10 seconds). Displaying consecutive spectra calculated at 5 minute intervals revealed marked variability in the peaks at all frequencies throughout the 24 hours, probably accounting for the lack of distinct peaks in the spectra of the entire records.

Non-NASA Center↗
NASA NTRS2018

A Higher-Order Space-Time Finite-Element Method for Moving-Body and Fluid-Structure Interaction Problems

We present a high-order finite-element method for moving body and fluid/structure interaction problems. Our solution strategy is based on a space-time discontinuous Galerkin (DG) spectral-element discretization which extends to arbitrary order of accuracy. The space-time DG discretization is a natural choice for moving body and fluid-structure interaction problems as moving surfaces are incorporated simply by considering curved space-time elements whose space-time faces align with the moving body. We present a discontinuous-Galerkin in time discretization for six-degree of motion modeling of rigid bodies, and a continuous-Galerkin discretization for equations of linear elasticity to generate curved space-time meshes. Numerical results for several simple 2D test cases are presented in order to verify the implementation of the different models. Finally we present a preliminary dynamic simulation of a parachute.

High-Order↗
DOE OSTI2017

Numerical approach of the quantum circuit theory

In this paper we develop a numerical method based on the quantum circuit theory to approach the coherent electronic transport in a network of quantum dots connected with arbitrary topology. The algorithm was employed in a circuit formed by quantum dots connected each other in a shape of a linear chain (associations in series), and of a ring (associations in series, and in parallel). For both systems we compute two current observables: conductance and shot noise power. We find an excellent agreement between our numerical results and the ones found in the literature. Moreover, we analyze the algorithm efficiency for a chain of quantum dots, where the mean processing time exhibits a linear dependence with the number of quantum dots in the array.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Randomized Algorithms for Scientific Computing (RASC)

Randomized algorithms have propelled advances in artificial intelligence (AI) and represent a foundational research area in advancing AI for Science. Future advancements in DOE Office of Science priority areas such as climate science, astrophysics, fusion, advanced materials, combustion, and quantum computing all require randomized algorithms for surmounting challenges of complexity, robustness, and scalability. Advances in data collection and numerical simulation have changed the dynamics of scientific research and motivate the need for randomized algorithms. For instance, advances in imaging technologies such as X-ray ptychography, electron microscopy, electron energy loss spectroscopy, or adaptive optics lattice light-sheet microscopy collect hyperspectral imaging and scattering data in terabytes, at breakneck speed enabled by state-of-the-art detectors. The data collection is exceptionally fast compared with its analysis. Likewise, advances in high-performance architectures have made exascale computing a reality and changed the economies of scientific computing in the process. Floating-point operations that create data are essentially free in comparison with data movement. Thus far, most approaches have focused on creating faster hardware. Ironically, this faster hardware has exacerbated the problem by making data still easier to create. Under such an onslaught, scientists often resort to heuristic deterministic sampling schemes (e.g., low-precision arithmetic, sampling every nth element) and sacrifice potentially valuable accuracy. Dramatically better results can be achieved via randomized algorithms, reducing the data size as much as or more than naive deterministic subsampling can achieve, while retaining the high accuracy of computing on the full data set. By randomized algorithms we mean those algorithms that employ some form of randomness in internal algorithmic decisions to accelerate time to solution, increase scalability, or improve reliability. Examples include matrix sketching for solving large-scale least-squares problems (see Figure 1) and stochastic gradient descent for training machine learning models. We are not recommending heuristic methods but rather randomized algorithms that have certificates of correctness and probabilistic guarantees of optimality and near-optimality. Such approaches can be useful beyond acceleration, for example, in understanding how to avoid measure zero worst-case scenarios that plague methods such as QR matrix factorization.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Parallel replica dynamics method for bistable stochastic reaction networks: Simulation and sensitivity analysis

Stochastic reaction networks that exhibit bistable behavior are common in systems biology, materials science, and catalysis. Sampling of stationary distributions is crucial for understanding and characterizing the long-time dynamics of bistable stochastic dynamical systems. However, simulations are often hindered by the insufficient sampling of rare transitions between the two metastable regions. In this paper, we apply the parallel replica method for a continuous time Markov chain in order to improve sampling of the stationary distribution in bistable stochastic reaction networks. The proposed method uses parallel computing to accelerate the sampling of rare transitions. Furthermore, it can be combined with the path-space information bounds for parametric sensitivity analysis. With the proposed methodology, we study three bistable biological networks: the Schlögl model, the genetic switch network, and the enzymatic futile cycle network. We demonstrate the algorithmic speedup achieved in these numerical benchmarks. More significant acceleration is expected when multi-core or graphics processing unit computer architectures and programming tools such as CUDA are employed

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

An algorithm for computing the 2D structure of fast rotating stars

Stars may be understood as self-gravitating masses of a compressible fluid whose radiative cooling is compensated by nuclear reactions or gravitational contraction. The understanding of their time evolution requires the use of detailed models that account for a complex microphysics including that of opacities, equation of state and nuclear reactions. The present stellar models are essentially one-dimensional, namely spherically symmetric. However, the interpretation of recent data like the surface abundances of elements or the distribution of internal rotation have reached the limits of validity of one-dimensional models because of their very simplified representation of large-scale fluid flows. In this article, we describe the ESTER code, which is the first code able to compute in a consistent way a two-dimensional model of a fast rotating star including its large-scale flows. Compared to classical 1D stellar evolution codes, many numerical innovations have been introduced to deal with this complex problem. First, the spectral discretization based on spherical harmonics and Chebyshev polynomials is used to represent the 2D axisymmetric fields. A nonlinear mapping maps the spheroidal star and allows a smooth spectral representation of the fields. The properties of Picard and Newton iterations for solving the nonlinear partial differential equations of the problem are discussed. It turns out that the Picard scheme is efficient on the computation of the simple polytropic stars, but Newton algorithm is unsurpassed when stellar models include complex microphysics. Finally, we discuss the numerical efficiency of our solver of Newton iterations. This linear solver combines the iterative Conjugate Gradient Squared algorithm together with an LU-factorization serving as a preconditioner of the Jacobian matrix.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Progress with the COGENT Edge Kinetic Code: Implementing the Fokker-Plank Collision Operator

Here, COGENT is a continuum gyrokinetic code for edge plasma simulations being developed by the Edge Simulation Laboratory collaboration. The code is distinguished by application of a fourth-order finite-volume (conservative) discretization, and mapped multiblock grid technology to handle the geometric complexity of the tokamak edge. The distribution function F is discretized in v∥ – μ (parallel velocity – magnetic moment) velocity coordinates, and the code presently solves an axisymmetric full-f gyro-kinetic equation coupled to the long-wavelength limit of the gyro-Poisson equation. COGENT capabilities are extended by implementing the fully nonlinear Fokker-Plank operator to model Coulomb collisions in magnetized edge plasmas. The corresponding Rosenbluth potentials are computed by making use of a finite-difference scheme and multipole-expansion boundary conditions. Details of the numerical algorithms and results of the initial verification studies are discussed. (© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1995

Reliability enhancement of Navier-Stokes codes through convergence acceleration

Methods for enhancing the reliability of Navier-Stokes computer codes through improving convergence characteristics are presented. The improving of these characteristics decreases the likelihood of code unreliability and user interventions in a design environment. The problem referred to as a 'stiffness' in the governing equations for propulsion-related flowfields is investigated, particularly in regard to common sources of equation stiffness that lead to convergence degradation of CFD algorithms. Von Neumann stability theory is employed as a tool to study the convergence difficulties involved. Based on the stability results, improved algorithms are devised to ensure efficient convergence in different situations. A number of test cases are considered to confirm a correlation between stability theory and numerical convergence. The examples of turbulent and reacting flow are presented, and a generalized form of the preconditioning matrix is derived to handle these problems, i.e., the problems involving additional differential equations for describing the transport of turbulent kinetic energy, dissipation rate and chemical species. Algorithms for unsteady computations are considered. The extension of the preconditioning techniques and algorithms derived for Navier-Stokes computations to three-dimensional flow problems is discussed. New methods to accelerate the convergence of iterative schemes for the numerical integration of systems of partial differential equtions are developed, with a special emphasis on the acceleration of convergence on highly clustered grids.

Merkle, Charles L.↗