Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “linear system”

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 685 records · Page 38
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Hydrodynamics of suspensions of passive and active rigid particles: a rigid multiblob approach

We develop a rigid multiblob method for numerically solving the mobility problem for suspensions of passive and active rigid particles of complex shape in Stokes flow in unconfined, partially confined, and fully confined geometries. As in a number of existing methods, we discretize rigid bodies using a collection of minimally resolved spherical blobs constrained to move as a rigid body, to arrive at a potentially large linear system of equations for the unknown Lagrange multipliers and rigid-body motions. Here we develop a block-diagonal preconditioner for this linear system and show that a standard Krylov solver converges in a modest number of iterations that is essentially independent of the number of particles. Key to the efficiency of the method is a technique for fast computation of the product of the blob-blob mobility matrix and a vector. For unbounded suspensions, we rely on existing analytical expressions for the Rotne-Prager-Yamakawa tensor combined with a fast multipole method (FMM) to obtain linear scaling in the number of particles. For suspensions sedimented against a single no-slip boundary, we use a direct summation on a graphical processing unit (GPU), which gives quadratic asymptotic scaling with the number of particles. For fully confined domains, such as periodic suspensions or suspensions confined in slit and square channels, we extend a recently developed rigid-body immersed boundary method by B. Kallemov, A. P. S. Bhalla, B. E. Griffith, and A. Donev (Commun. Appl. Math. Comput. Sci. 11 (2016), no. 1, 79-141) to suspensions of freely moving passive or active rigid particles at zero Reynolds number. We demonstrate that the iterative solver for the coupled fluid and rigid-body equations converges in a bounded number of iterations regardless of the system size. In our approach, each iteration only requires a few cycles of a geometric multigrid solver for the Poisson equation, and an application of the block-diagonal preconditioner, leading to linear scaling with the number of particles. We optimize a number of parameters in the iterative solvers and apply our method to a variety of benchmark problems to carefully assess the accuracy of the rigid multiblob approach as a function of the resolution. We also model the dynamics of colloidal particles studied in recent experiments, such as passive boomerangs in a slit channel, as well as a pair of non-Brownian active nanorods sedimented against a wall.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

GPU Accelerated Sparse Cholesky Factorization

The solution of sparse symmetric positive definite linear systems is an important computational kernel in large-scale scientific and engineering modeling and simulation. We will solve the linear systems using a direct method, in which a Cholesky factorization of the coefficient matrix is performed using a right-looking approach and the resulting triangular factors are used to compute the solution. Sparse Cholesky factorization is compute intensive. In this work we investigate techniques for reducing the factorization time in sparse Cholesky factorization by offloading some of the dense matrix operations on a GPU. We will describe the techniques we have considered. We achieved up to 4x speedup compared to the CPU-only version.

Karsavuran, M Ozan↗
DOE OSTI2015

Tailored multivariate analysis for modulated enhanced diffraction

Modulated enhanced diffraction (MED) is a technique allowing the dynamic structural characterization of crystalline materials subjected to an external stimulus, which is particularly suited for in situ and operando structural investigations at synchrotron sources. Contributions from the (active) part of the crystal system that varies synchronously with the stimulus can be extracted by an offline analysis, which can only be applied in the case of periodic stimuli and linear system responses. In this paper a new decomposition approach based on multivariate analysis is proposed. The standard principal component analysis (PCA) is adapted to treat MED data: specific figures of merit based on their scores and loadings are found, and the directions of the principal components obtained by PCA are modified to maximize such figures of merit. As a result, a general method to decompose MED data, called optimum constrained components rotation (OCCR), is developed, which produces very precise results on simulated data, even in the case of nonperiodic stimuli and/or nonlinear responses. The multivariate analysis approach is able to supply in one shot both the diffraction pattern related to the active atoms (through the OCCR loadings) and the time dependence of the system response (through the OCCR scores). When applied to real data, OCCR was able to supply only the latter information, as the former was hindered by changes in abundances of different crystal phases, which occurred besides structural variations in the specific case considered. To develop a decomposition procedure able to cope with this combined effect represents the next challenge in MED analysis.

Caliandro, Rocco↗
NASA NTRS1995

An approach to the development of numerical algorithms for first order linear hyperbolic systems in multiple space dimensions: The constant coefficient case

Two methods for developing high order single step explicit algorithms on symmetric stencils with data on only one time level are presented. Examples are given for the convection and linearized Euler equations with up to the eighth order accuracy in both space and time in one space dimension, and up to the sixth in two space dimensions. The method of characteristics is generalized to nondiagonalizable hyperbolic systems by using exact local polynominal solutions of the system, and the resulting exact propagator methods automatically incorporate the correct multidimensional wave propagation dynamics. Multivariate Taylor or Cauchy-Kowaleskaya expansions are also used to develop algorithms. Both of these methods can be applied to obtain algorithms of arbitrarily high order for hyperbolic systems in multiple space dimensions. Cross derivatives are included in the local approximations used to develop the algorithms in this paper in order to obtain high order accuracy, and improved isotropy and stability. Efficiency in meeting global error bounds is an important criterion for evaluating algorithms, and the higher order algorithms are shown to be up to several orders of magnitude more efficient even though they are more complex. Stable high order boundary conditions for the linearized Euler equations are developed in one space dimension, and demonstrated in two space dimensions.

Goodrich, John W.↗
DOE OSTI2019

An adjoint method for neoclassical stellarator optimization

Stellarators remain an enticing route to steady-state fusion power. However, to achieve the required confinement, the magnetic geometry must be highly optimized. This optimization requires navigating high-dimensional spaces, often necessitating the use of gradient-based methods. The gradient of the neoclassical fluxes is expensive to compute with classical methods, requiring $O(N)$ flux computations, where $N$ is the number of parameters. To reduce the cost of the gradient computation, we present an adjoint method for computing the derivatives of moments of the neoclassical distribution function for stellarator optimization. The linear adjoint method allows derivatives of quantities which depend on solutions of a linear system, such as moments of the distribution function, to be computed with respect to many parameters from the solution of only two linear systems. This reduces the cost of computing the gradient to the point that the finite-collisionality neoclassical fluxes can be used within an optimization loop. With the neoclassical adjoint method, we compute solutions of the drift kinetic equation and an adjoint drift kinetic equation to obtain derivatives of neoclassical quantities with respect to geometric parameters. When the number of parameters in the derivative is large ( $O(10^{2})$ ), this adjoint method provides up to a factor of 200 reduction in cost. We demonstrate adjoint-based optimization of the field strength to obtain minimal bootstrap current on a surface. With adjoint-based derivatives, we also compute the local sensitivity to magnetic perturbations on a flux surface and identify regions where tight tolerances on error fields are required for control of the bootstrap current or radial transport. Moreover, the solve for the ambipolar electric field is accelerated using a Newton method with derivatives obtained from the adjoint method.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Presentation: Sensor Anomaly Detection for Nuclear Reactor Systems Utilizing Linear Regression and K-Means Unsupervised Machine Learning: An overview of methods and results

This presentation is a culmination of work which has occurred over the course of a 10-week internship. Anomaly detection methods must be both robust enough to detect subtle anomalies yet not so sensitive to report false positives, which would result significant loss of revenue. Methods currently being developed for autonomous systems are often pursuing a Digital Twin method, which will look at the entire system and model it as a whole. This presentation, however, focuses less on direct application to an NPP, rather acting as a proof of concept for the methods developed. For the project, we look to develop methods to analyze steady-state data and report anomalies.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2017

Summer Proceedings 2016: The Center for Computing Research at Sandia National Laboratories

Solving sparse linear systems from the discretization of elliptic partial differential equations (PDEs) is an important building block in many engineering applications. Sparse direct solvers can solve general linear systems, but are usually slower and use much more memory than effective iterative solvers. To overcome these two disadvantages, a hierarchical solver (LoRaSp) based on H2-matrices was introduced in [22]. Here, we have developed a parallel version of the algorithm in LoRaSp to solve large sparse matrices on distributed memory machines. On a single processor, the factorization time of our parallel solver scales almost linearly with the problem size for three-dimensional problems, as opposed to the quadratic scalability of many existing sparse direct solvers. Moreover, our solver leads to almost constant numbers of iterations, when used as a preconditioner for Poisson problems. On more than one processor, our algorithm has significant speedups compared to sequential runs. With this parallel algorithm, we are able to solve large problems much faster than many existing packages as demonstrated by the numerical experiments.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1966

Minimax studies

Effect of nonzero initial conditions on selection of minimax controllers for large launch vehicles and extremal bounded amplitude bounded rate inputs to linear systems

CONTROL SYSTEM↗
NASA NTRS1978

DYGABCD: A program for calculating linear A, B, C, and D matrices from a nonlinear dynamic engine simulation

A digital computer program, DYGABCD, was developed that generates linearized, dynamic models of simulated turbofan and turbojet engines. DYGABCD is based on an earlier computer program, DYNGEN, that is capable of calculating simulated nonlinear steady-state and transient performance of one- and two-spool turbojet engines or two- and three-spool turbofan engines. Most control design techniques require linear system descriptions. For multiple-input/multiple-output systems such as turbine engines, state space matrix descriptions of the system are often desirable. DYGABCD computes the state space matrices commonly referred to as the A, B, C, and D matrices required for a linear system description. The report discusses the analytical approach and provides a users manual, FORTRAN listings, and a sample case.

Geyser, L. C.↗
DOE OSTI2019

Suppression of four-wave mixing in a 22 × 10 Gbps dense wavelength division multiplexed system by linearly chirped fiber Bragg gratings

A scheme comprising two linearly chirped fiber Bragg gratings (LCFBGs) is proposed to suppress four-wave mixing (FWM) effects in a 22×10 Gbps dense wavelength division multiplexed (DWDM) system employing dispersion shifted fiber with 0.2 nm channel spacing. The FWM reduction in our proposed scheme has been studied by varying the input signal power per channel from − 2 to + 10 dBm. The parameters of LCFBGs are optimized to obtain a maximum quality factor for all 22 channels. The proposed method is effective even at high input power (10 dBm) and provides a simple, cost effective way to improve the transmission performance in DWDM system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1997

A Study of Convergence of the PMARC Matrices Applicable to WICS Calculations

This report discusses some analytical procedures to enhance the real time solutions of PMARC matrices applicable to the Wall Interference Correction Scheme (WICS) currently being implemented at the 12 foot Pressure Tunell. WICS calculations involve solving large linear systems in a reasonably speedy manner necessitating exploring further improvement in solution time. This paper therefore presents some of the associated theory of the solution of linear systems. Then it discusses a geometrical interpretation of the residual correction schemes. Finally, some results of the current investigation are presented.

Ghosh, Amitabha↗
NASA NTRS1997

A Study of Convergence of the PMARC Matrices Applicable to WICS Calculations

This report discusses some analytical procedures to enhance the real time solutions of PMARC matrices applicable to the Wall Interference Correction Scheme (WICS) currently being implemented at the 12 foot Pressure Tunnel. WICS calculations involve solving large linear systems in a reasonably speedy manner necessitating exploring further improvement in solution time. This paper therefore presents some of the associated theory of the solution of linear systems. Then it discusses a geometrical interpretation of the residual correction schemes. Finally some results of the current investigation are presented.

Ghosh, Amitabha↗
NASA NTRS1983

Fractional representation theory - Robustness results with applications to finite dimensional control of a class of linear distributed systems

This paper reviews and extends the fractional representation theory. In particular, new and powerful robustness results are presented. This new theory is utilized to develop a preliminary design methodology for finite dimensional control of a class of linear evolution equations on a Banach space. The design is for stability in an input-output sense, but particular attention is paid to internal stability as well.

Nett, C. N.↗
DOE OSTI2017

SAM Process Heat Model Development and Validation: Liquid-HTF Trough and Direct Steam Generation Linear Focus Systems

Two new solar industrial process heat (SIPH) models have been added to the System Advisor Model (SAM) energy simulation tool. The two process heat models were: i) liquid-heat transfer fluid (HTF) parabolic troughs; and ii) direct steam generation (DSG) linear-focus collectors. The DSG model can simulate either DSG parabolic troughs (PT) or DSG Linear Fresnel (LF) fields, based on the optical characteristics supplied. These models help to meet the need for independent, validated tools that reliably simulate the effects of adding a solar field to provide heat for potential IPH applications. During the pre-validation of the liquid-HTF model, operational data was provided and preprocessed by SPF and evaluated at ZAE Bayern. The beta liquid-HTF model provided excellent agreement between the simulations and the operational data for the solar thermal yield generation on a yearly and monthly basis (4.4% difference). The final liquid-HTF process heat model has been further optimized with test users such as ZAE Bayern and SPF. Key improvements in the SIPH models to better model SIPH fields include the use of smaller piping systems and heat capacities, a single collector field, and a higher time-step resolution than for electricity generation (down to 10 minutes). Both the final liquid-HTF and DSG models were successfully validated against operational data for respective solar fields, and showed less than 5% deviation to actual results. A brief application where the liquid-HTF process heat model is used for a brewery in California and the value of reliably simulating a potential SIPH solar field are highlighted.

14 SOLAR ENERGY↗
DOE OSTI2014

SU-E-I-40: New Method for Measurement of Task-Specific, High-Resolution Detector System Performance

Purpose: Although generalized linear system analytic metrics such as GMTF and GDQE can evaluate performance of the whole imaging system including detector, scatter and focal-spot, a simplified task-specific measured metric may help to better compare detector systems. Methods: Low quantum-noise images of a neuro-vascular stent with a modified ANSI head phantom were obtained from the average of many exposures taken with the high-resolution Micro-Angiographic Fluoroscope (MAF) and with a Flat Panel Detector (FPD). The square of the Fourier Transform of each averaged image, equivalent to the measured product of the system GMTF and the object function in spatial-frequency space, was then divided by the normalized noise power spectra (NNPS) for each respective system to obtain a task-specific generalized signal-to-noise ratio. A generalized measured relative object detectability (GM-ROD) was obtained by taking the ratio of the integral of the resulting expressions for each detector system to give an overall metric that enables a realistic systems comparison for the given detection task. Results: The GM-ROD provides comparison of relative performance of detector systems from actual measurements of the object function as imaged by those detector systems. This metric includes noise correlations and spatial frequencies relevant to the specific object. Additionally, the integration bounds for the GM-ROD can be selected to emphasis the higher frequency band of each detector if high-resolution image details are to be evaluated. Examples of this new metric are discussed with a comparison of the MAF to the FPD for neuro-vascular interventional imaging. Conclusion: The GM-ROD is a new direct-measured task-specific metric that can provide clinically relevant comparison of the relative performance of imaging systems. Supported by NIH Grant: 2R01EB002873 and an equipment grant from Toshiba Medical Systems Corporation.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗