Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “numerical algorithms”

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 1,765 records · Page 98
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

SIAM Conference on Parallel Processing for Scientific Computing, 4th, Chicago, IL, Dec. 11-13, 1989, Proceedings

Attention is given to such topics as an evaluation of block algorithm variants in LAPACK and presents a large-grain parallel sparse system solver, a multiprocessor method for the solution of the generalized Eigenvalue problem on an interval, and a parallel QR algorithm for iterative subspace methods on the CM2. A discussion of numerical methods includes the topics of asynchronous numerical solutions of PDEs on parallel computers, parallel homotopy curve tracking on a hypercube, and solving Navier-Stokes equations on the Cedar Multi-Cluster system. A section on differential equations includes a discussion of a six-color procedure for the parallel solution of elliptic systems using the finite quadtree structure, data parallel algorithms for the finite element method, and domain decomposition methods in aerodynamics. Topics dealing with massively parallel computing include hypercube vs. 2-dimensional meshes and massively parallel computation of conservation laws. Performance and tools are also discussed.

Dongarra, Jack↗
NASA NTRS1989

Stereo image visualization of numerically simulated turbulence

Stereo imaging techniques are used in the current study to analyze the results of a direct Navier-Stokes simulation of a turbulent boundary layer. Coherent structures embedded within the unsteady, highly three-dimensional turbulent flow fields are significantly enhanced through the use of stereo computer graphic renderings. In the paper, the geometrical foundations of two different methods for generating stereo images are reviewed. Sufficient detail is provided to enable readers to code stereo display algorithms from scratch. The effects of varying the geometric parameters of the stereo algorithm are demonstrated. Sample image pairs from animations of the turbulence numerical simulation are presented in color. Stereo imagery, especially when used with time-evolving data, provides new insight into the physical processes responsible for the generation an maintenance of turbulence within boundary layers.

Robinson, Stephen K.↗
NASA NTRS2002

New Attitude Sensor Alignment Calibration Algorithms

Accurate spacecraft attitudes may only be obtained if the primary attitude sensors are well calibrated. Launch shock, relaxation of gravitational stresses and similar effects often produce large enough alignment shifts so that on-orbit alignment calibration is necessary if attitude accuracy requirements are to be met. A variety of attitude sensor alignment algorithms have been developed to meet the need for on-orbit calibration. Two new algorithms are presented here: ALICAL and ALIQUEST. Each of these has advantages in particular circumstances. ALICAL is an attitude independent algorithm that uses near simultaneous measurements from two or more sensors to produce accurate sensor alignments. For each set of simultaneous observations the attitude is overdetermined. The information content of the extra degrees of freedom can be combined over numerous sets to provide the sensor alignments. ALIQUEST is an attitude dependent algorithm that combines sensor and attitude data into a loss function that has the same mathematical form as the Wahba problem. Alignments can then be determined using any of the algorithms (such as the QUEST quaternion estimator) that have been developed to solve the Wahba problem for attitude. Results from the use of these methods on active missions are presented.

Hashmall, Joseph A.↗
NASA NTRS1993

Progressive wave equations and algorithms for sonic boom propagation

Raspet, Bass, and others have carried out a number of studies of sonic boom propagation using algorithms that can be traced back to a 1973 doctoral thesis written by Pestorius at the University of Texas. The algorithm was originally set forth without a formal derivation from a governing set of partial differential equations. Perusal of Pestorius's report and of subsequent reports from the Texas nonlinear accoustics group suggests that such a derivation has not yet appeared in the archival literature. The author and his colleagues, on the other hand, have been working with an explicit set of approximate partial differential equations analogous to Burgers' equation. The present paper traces through the pertinent statements in the Pestorius reports and shows that the derived algorithm, at least in the limit of sufficiently short steps, is equivalent to the numerical solution of a similar (and nearly equivalent) explicit set of partial differential equations. The tying-together of the two approaches is important because it is possible that some of the basic ideas embodied in the Pestorius algorithm may be incorporated in other contexts where more nearly general models of sonic boom propagation through realistic atmospheres are to be solved numerically.

Pierce, Allan D.↗
DOE OSTI2021

Implicit highly-coupled single-ion Hall-MHD formulation for hybrid particle-in-cell codes

The rudiments of a particle-based single-fluid two-temperature magnetohydrodynamic (MHD) algorithm have been outlined in Thoma et al. (2013). The extension of this algorithm to include the effect of Hall physics is described in this paper. An implicit leapfrog version of the algorithm, which allows timesteps large compared to the resistive decay time and other relevant timescales, has recently been added to a hybrid particle-in-cell code. In standard MHD the Hall term in the generalized Ohm’s law can often be neglected when the Hall parameter is small. This term must, however, be retained in regimes where it is non-negligible. The retention of displacement current in Maxwell’s equations avoids the numerical difficulties associated with the whistler mode, which are encountered in standard explicit Hall-MHD codes, and allows the algorithm to be incorporated into hybrid particle-in-cell codes, for which particles may migrate from a kinetic to fluid to MHD description based upon local ambient plasma conditions. A highly-coupled implicit Hall-MHD formalism is presented, in which displacement current can either be retained or neglected. Even when displacement current is neglected, the highly-coupled implicit formalism avoids the restrictive timesteps for the whistler mode in explicit Hall-MHD codes. A comparison of numerical and analytic dispersion analysis demonstrates the feasibility of this approach and establishes relevant constraints to assure numerical stability. The implementation of the algorithm is described, and test simulation results in 1D and 2D in both linear and nonlinear regimes are presented.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1990

Flux-split algorithms for flows with non-equilibrium chemistry and vibrational relaxation

The present consideration of numerical computation methods for gas flows with nonequilibrium chemistry thermodynamics gives attention to an equilibrium model, a general nonequilibrium model, and a simplified model based on vibrational relaxation. Flux-splitting procedures are developed for the fully-coupled inviscid equations encompassing fluid dynamics and both chemical and internal energy-relaxation processes. A fully coupled and implicit large-block structure is presented which embodies novel forms of flux-vector split and flux-difference split algorithms valid for nonequilibrium flow; illustrative high-temperature shock tube and nozzle flow examples are given.

Grossman, B.↗
NASA NTRS1974

Transonic conical flow

The problem of inviscid, steady transonic conical flow, formulated in terms of the small disturbance theory, is studied. The small disturbance equation and similarity rules are presented, and a boundary value problem is formulated for the case of a supersonic freestream Mach number. The equation for the perturbation potential is solved numerically using an elliptic finite difference system. The difference equations are solved with a point relaxation algorithm that is also capable of capturing the shock wave during the iteration procedure by using the boundary conditions at the shock. Numerical calculations, for shock location, pressure distribution and drag coefficient, are presented for a family of nonlifting conical wings. The theory of slender wings is also presented and analytical results for pressure and drag coefficients are obtained.

Agopian, K. G.↗
DOE OSTI2026

Fast and Accurate Intersections on a Sphere

We introduce a fast, high-precision algorithm for calculating intersections between great circle arcs and lines of constant latitude on the unit sphere. We first propose a simplified intersection point formula with improved speed and numerical robustness over the ones traditionally implemented in geoscience software. We then show how algorithms based on the concept of error-free transformations (EFT) can be applied to evaluate this formula within a relative error bound that is on the order of machine precision. Here, we demonstrate that, with a vectorized and parallelized implementation, this enhanced accuracy is achieved with no compute time overhead compared to a direct calculation in hardware floating point, making our algorithm suitable for performance-sensitive applications like regridding of high-resolution climate data. In contrast, evaluating our formula using high-precision data types like quadruple precision and arbitrary precision, or using the robust intersection computation routines from the Computational Geometry Algorithms Library, leads to significant computational overhead, especially since these alternatives inhibit vectorization. More generally, our work demonstrates how EFT techniques can be combined and extended to implement nontrivial geometric calculations with high accuracy and speed.

Environmental sciences↗
DOE OSTI2021

Cyber Physical Grid-Interactive Distributed Energy Resources Control for VPP Dispatch and Regulation

This paper presents a cyber-physical algorithm for grid-interactive Distributed Energy Resource (DER) control to enable two features of Virtual Power Plants (VPPs) dispatch and grid voltage regulation, considering the communication and security impacts. We first formulate the DER dispatch problem as a real-time, iterative, and grid-interactive DER control problem. Thereafter, we consider a probabilistic traffic model to characterize 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 center that coordinately execute this dispatch algorithm. Finally, a strategy combining delay threshold and modified message update rules is proposed to immune the asynchrony resulting from the communications network traffic and it avoids possible numerical instabilities and sensitivities of the tracking and regulation capabilities of this DER control algorithm. By implementing the proposed cyber-physical algorithm on the modified IEEE 37-node system, our preliminary results exhibit that the uncertainties of the underlying communications infrastructure must be considered for the VPP tracking and regulation capabilities of any DER in a generic Cyber-Physical System (CPS), because the delayed voltage measurements in the uplink/bi-link cases result in the off-track in VPP dispatch and jittery in voltage regulation.

cyber-physical algorithm↗
DOE OSTI2021

Cholesky-based experimental design for Gaussian process and kernel-based emulation and calibration.

Gaussian processes and other kernel-based methods are used extensively to construct approximations of multivariate data sets. The accuracy of these approximations is dependent on the data used. This paper presents a computationally efficient algorithm to greedily select training samples that minimize the weighted L p error of kernel-based approximations for a given number of data. The method successively generates nested samples, with the goal of minimizing the error in high probability regions of densities specified by users. The algorithm presented is extremely simple and can be implemented using existing pivoted Cholesky factorization methods. Training samples are generated in batches which allows training data to be evaluated (labeled) in parallel. For smooth kernels, the algorithm performs comparably with the greedy integrated variance design but has significantly lower complexity. Numerical experiments demonstrate the efficacy of the approach for bounded, unbounded, multi-modal and non-tensor product densities. We also show how to use the proposed algorithm to efficiently generate surrogates for inferring unknown model parameters from data using Bayesian inference.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1974

Sequential square root filtering and smoothing of discrete linear systems

A square root information filter/smoother is derived using recursive least-squares arguments. The combined filter/smoother algorithm has the following attributes: (1) it has a square root structure, which enhances numerical accuracy; (2) filter and smoother mechanizations are identical in form, facilitating implementation of the smoother; and (3) storage and computation requirements are modest compared with other smoothing algorithms. Partitioning the results to separate bias parameters provides further computational economies and reduction of storage requirements.

Bierman, G. J.↗
NASA NTRS1982

Random element method for numerical modeling of diffusional processes

The random element method is a generalization of the random vortex method that was developed for the numerical modeling of momentum transport processes as expressed in terms of the Navier-Stokes equations. The method is based on the concept that random walk, as exemplified by Brownian motion, is the stochastic manifestation of diffusional processes. The algorithm based on this method is grid-free and does not require the diffusion equation to be discritized over a mesh, it is thus devoid of numerical diffusion associated with finite difference methods. Moreover, the algorithm is self-adaptive in space and explicit in time, resulting in an improved numerical resolution of gradients as well as a simple and efficient computational procedure. The method is applied here to an assortment of problems of diffusion of momentum and energy in one-dimension as well as heat conduction in two-dimensions in order to assess its validity and accuracy. The numerical solutions obtained are found to be in good agreement with exact solution except for a statistical error introduced by using a finite number of elements, the error can be reduced by increasing the number of elements or by using ensemble averaging over a number of solutions.

Ghoniem, A. F.↗
DOE OSTI2026

Machine Learning for Fairness-Aware Load Shedding: A Real-Time Solution via Identifying Binding Constraints: Preprint

Timely and effective load shedding in power systems is critical for maintaining supply-demand balance and preventing cascading blackouts. To eliminate load shedding bias against specific regions in the system, optimization-based methods are uniquely positioned to help balance between economic and fairness considerations. However, the resulting optimization problem involves complex constraints, which can be time-consuming to solve and thus cannot meet the real-time requirements of load shedding. To tackle this challenge, in this paper we present an efficient machine learning algorithm to enable millisecond-level computation for the optimization-based load shedding problem. Numerical studies on both a 3-bus toy example and a realistic RTS-GMLC system have demonstrated the validity and efficiency of the proposed algorithm for delivering fairness-aware and real-time load shedding decisions.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1987

Projection filters for modal parameter estimate for flexible structures

Single-mode projection filters are developed for eigensystem parameter estimates from both analytical results and test data. Explicit formulations of these projection filters are derived using the pseudoinverse matrices of the controllability and observability matrices in general use. A global minimum optimization algorithm is developed to update the filter parameters by using interval analysis method. Modal parameters can be attracted and updated in the global sense within a specific region by passing the experimental data through the projection filters. For illustration of this method, a numerical example is shown by using a one-dimensional global optimization algorithm to estimate model frequencies and dampings.

Huang, Jen-Kuang↗
DOE OSTI2021

A Range and Performance Optimized Version of the Computer-Aided Speckle Interferometry Algorithm for Real-Time Displacement-Strain Field Monitoring

Abstract This work presents an optimized implementation of the Computer-Aided Speckle Interferometry algorithm which enables full-field determination of displacements and strains on commodity Graphics Processing Units at high resolution and frame rates. By combining careful control of the average speckle size in a laser speckle pattern with a simple sampling rate conversion scheme, a compact representation of the optical speckle is achieved. This allows for optimal use of Graphics Processing Unit architecture with robust range extension. The optimal mapping of the Computer-Aided Speckle Interferometry algorithm to Graphics Processing Unit architecture is shown in detail, and a straightforward method for disambiguating large displacements is illustrated. Lastly, this paper demonstrates a two-step subimage-tapering modification to the original algorithm that enables robust range enhancement while maintaining resolution. Results from numerical simulations on synthetic speckle patterns are shown, and runtime performance metrics are provided, with performance ranging up to 60 frames per second in some cases. The method is suitable for interactive experimental mechanics research, process and testing or any application where real-time high-resolution displacement-strain monitoring is needed. A .NET Framework class library enabling the incorporation of the algorithm into 3rd -party applications is available for download.

42 ENGINEERING↗
DOE OSTI2022

Fast Solution of Fully Implicit Runge--Kutta and Discontinuous Galerkin in Time for Numerical PDEs, Part II: Nonlinearities and DAEs

Fully implicit Runge--Kutta (IRK) methods have many desirable accuracy and stability properties as time integration schemes, but high-order IRK methods are not commonly used in practice with large-scale numerical PDEs because of the difficulty of solving the stage equations. This paper introduces a theoretical and algorithmic framework for solving the nonlinear equations that arise from IRK methods (and discontinuous Galerkin discretizations in time) applied to nonlinear numerical PDEs, including PDEs with algebraic constraints. Several new linearizations of the nonlinear IRK equations are developed, offering faster and more robust convergence than the often-considered simplified Newton, as well as an effective preconditioner for the true Jacobian if exact Newton iterations are desired. Inverting these linearizations requires solving a set of block 2 x 2 systems. Under quite general assumptions, it is proven that the preconditioned 2 x 2 operator's condition number is bounded by a small constant close to one, independent of the spatial discretization, spatial mesh, and time step, and with only weak dependence on the number of stages or integration accuracy. Moreover, the new method is built using the same preconditioners needed for backward Euler-type time stepping schemes, so can be readily added to existing codes. The new methods are applied to several challenging fluid flow problems, including the compressible Euler and Navier--Stokes equations, and the vorticity-streamfunction formulation of the incompressible Euler and Navier--Stokes equations. Up to 10th-order accuracy is demonstrated using Gauss IRK, while in all cases fourth-order Gauss IRK requires roughly half the number of preconditioner applications as required by standard Singly diagonally implicit Runge--Kutta methods.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2003

A Stochastic Collocation Algorithm for Uncertainty Analysis

This report describes a stochastic collocation method to adequately handle a physically intrinsic uncertainty in the variables of a numerical simulation. For instance, while the standard Galerkin approach to Polynomial Chaos requires multi-dimensional summations over the stochastic basis functions, the stochastic collocation method enables to collapse those summations to a one-dimensional summation only. This report furnishes the essential algorithmic details of the new stochastic collocation method and provides as a numerical example the solution of the Riemann problem with the stochastic collocation method used for the discretization of the stochastic parameters.

Mathelin, Lionel↗
DOE OSTI2022

Adaptive experimental design for multi-fidelity surrogate modeling of multi-disciplinary systems

We present an adaptive algorithm for constructing surrogate models of multi-disciplinary systems composed of a set of coupled components. With this goal we introduce “coupling” variables with a priori unknown distributions that allow surrogates of each component to be built independently. Once built, the surrogates of the components are combined to form an integrated-surrogate that can be used to predict system-level quantities of interest at a fraction of the cost of the original model. The error in the integrated-surrogate is greedily minimized using an experimental design procedure that allocates the amount of training data, used to construct each component-surrogate, based on the contribution of those surrogates to the error of the integrated-surrogate. Here, the multi-fidelity procedure presented is a generalization of multi-index stochastic collocation that can leverage ensembles of models of varying cost and accuracy, for one or more components, to reduce the computational cost of constructing the integrated-surrogate. Extensive numerical results demonstrate that, for a fixed computational budget, our algorithm is able to produce surrogates that are orders of magnitude more accurate than methods that treat the integrated system as a black-box.

42 ENGINEERING↗