Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Decomposition algorithm”

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 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
NASA NTRS1998

Three-Dimensional High-Lift Analysis Using a Parallel Unstructured Multigrid Solver

A directional implicit unstructured agglomeration multigrid solver is ported to shared and distributed memory massively parallel machines using the explicit domain-decomposition and message-passing approach. Because the algorithm operates on local implicit lines in the unstructured mesh, special care is required in partitioning the problem for parallel computing. A weighted partitioning strategy is described which avoids breaking the implicit lines across processor boundaries, while incurring minimal additional communication overhead. Good scalability is demonstrated on a 128 processor SGI Origin 2000 machine and on a 512 processor CRAY T3E machine for reasonably fine grids. The feasibility of performing large-scale unstructured grid calculations with the parallel multigrid algorithm is demonstrated by computing the flow over a partial-span flap wing high-lift geometry on a highly resolved grid of 13.5 million points in approximately 4 hours of wall clock time on the CRAY T3E.

Mavriplis, Dimitri J.↗
NASA NTRS1998

Observation and Modeling of Single Wall Carbon Nanotube Bend Junctions

Single wall carbon nanotube (SWNT) bends, with diameters from approx. 1.0 to 2.5 nm and bend angles from 18 deg. to 34 deg., are observed in catalytic decomposition of hydrocarbons at 600 - 1200 C. An algorithm using molecular dynamics simulation (MD) techniques is developed to model these structures that are considered to be SWNT junctions formed by topological defects (i.e. pentagon-heptagon pairs). The algorithm is used to predict the tube helicities and defect configurations for bend junctions using the observed tube diameters and bend angles. The number and arrangement of the defects at the junction interfaces are found to depend on the tube helicities and bend angle. The structural and energetic calculations using the Brenner potential show a number of stable junction configurations for each bend angle with the 34 deg. bends being more stable than the others. Tight binding calculations for local density of state (LDOS) and transmission coefficients are carried out to investigate electrical properties of the bend junctions.

Han, Jie↗
NASA NTRS2007

An NAFP Project: Use of Object Oriented Methodologies and Design Patterns to Refactor Software Design

In the early problem-solution era of software programming, functional decompositions were mainly used to design and implement software solutions. In functional decompositions, functions and data are introduced as two separate entities during the design phase, and are followed as such in the implementation phase. Functional decompositions make use of refactoring through optimizing the algorithms, grouping similar functionalities into common reusable functions, and using abstract representations of data where possible; all these are done during the implementation phase. This paper advocates the usage of object-oriented methodologies and design patterns as the centerpieces of refactoring software solutions. Refactoring software is a method of changing software design while explicitly preserving its external functionalities. The combined usage of object-oriented methodologies and design patterns to refactor should also benefit the overall software life cycle cost with improved software.

Shaykhian, Gholam Ali↗
NASA NTRS2017

A Space-Based Observational Strategy for Characterizing the First Stars and Galaxies Using the Redshifted 21cm Global Spectrum

The redshifted 21 cm monopole is expected to be a powerful probe of the epoch of the first stars and galaxies(10 less than z less than 35). The global 21 cm signal is sensitive to the thermal and ionization state of hydrogen gas and thusprovides a tracer of sources of energetic photonsprimarily hot stars and accreting black holeswhich ionize andheat the high redshift intergalactic medium (IGM). This paper presents a strategy for observations of the globalspectrum with a realizable instrument placed in a low-altitude lunar orbit, performing night-time 40120 MHzspectral observations, while on the farside to avoid terrestrial radio frequency interference, ionospheric corruption,and solar radio emissions. The frequency structure, uniformity over large scales, and unpolarized state of theredshifted 21 cm spectrum are distinct from the spectrally featureless, spatially varying, and polarized emissionfrom the bright foregrounds. This allows a clean separation between the primordial signal and foregrounds. Forsignal extraction, we model the foreground, instrument, and 21 cm spectrum with eigenmodes calculated viaSingular Value Decomposition analyses. Using a Markov Chain Monte Carlo algorithm to explore the parameterspace defined by the coefficients associated with these modes, we illustrate how the spectrum can be measured andhow astrophysical parameters (e.g., IGM properties, first star characteristics) can be constrained in the presence offoregrounds using the Dark Ages Radio Explorer (DARE).

Burns, Jack O.↗
NASA NTRS1994

Operations for Learning with Graphical Models

This paper is a multidisciplinary review of empirical, statistical learning from a graphical model perspective. Well-known examples of graphical models include Bayesian net- works, directed graphs representing a Markov chain, and undirected networks representing a Markov field. These graphical models are extended to model data analysis and empirical learning using the notation of plates. Graphical operations for simplifying and manipulating a problem are provided including decomposition, differentiation, and the manipulation of probability models from the exponential family. These operations adapt existing techniques from statistics and automatic differentiation to graphs. Two standard algorithm schemes for learning are reviewed in a graphical framework: Gibbs sampling and the expectation maximization algorithm. Some algorithms are developed in this graphical framework including a generalized version of linear regression, techniques for feed-forward networks, and learning Gaussian and discrete Bayesian networks from data. The paper concludes by sketching some implications for data analysis and summarizing some popular algorithms that fall within the framework presented. The main original contributions here are the decomposition techniques and the demonstration that graphical models provide a framework for understanding and developing complex learning algorithms.

Buntine, Wray L.↗
DOE OSTI2021

Electric vehicle fast charging infrastructure planning in urban networks considering daily travel and charging behavior

Electric vehicles are a sustainable substitution to conventional vehicles. This work introduces an integrated framework for urban fast charging infrastructure to address the range anxiety issue. A mesoscopic simulation tool is developed to generate trip trajectories, and simulate charging behavior based on various trip attributes. The resulting charging demand is the key input to a mixed-integer nonlinear program that seeks charging station configuration. The model minimizes the total system cost including charging station and charger installation costs, and charging, queuing, and detouring delays. The problem is solved using a decomposition technique incorporating a commercial solver for small networks, and a heuristic algorithm for large-scale networks, in addition to the Golden Section method. The solution quality and significant superiority in the computational efficiency of the decomposition approach are confirmed in comparison with the implicit enumeration approach. Furthermore, the required infrastructure to support urban trips is explored for future market shares and technologies.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2021

Experimental quantum learning of a spectral decomposition

Currently available quantum hardware allows for small-scale implementations of quantum machine learning algorithms. Such experiments aid the search for applications of quantum computers by benchmarking the near-term feasibility of candidate algorithms. Here we demonstrate the quantum learning of a two-qubit unitary by a sequence of three parameterized quantum circuits containing a total of 21 variational parameters. Moreover, we variationally diagonalize the unitary to learn its spectral decomposition, i.e., its eigenvalues and eigenvectors. We illustrate how this can be used as a subroutine to compress the depth of dynamical quantum simulations. One can view our implementation as a demonstration of entanglement-enhanced machine learning, as only a single (entangled) training data pair is required to learn a 4 × 4 unitary matrix.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Domain Decomposition for Integer Optimal Control with Total Variation Regularization

Total variation integer optimal control problems admit solutions and necessary optimality conditions via geometric variational analysis. In spite of the existence of said solutions, algorithms which solve the discretized objective suffer from high numerical cost associated with the combinatorial nature of integer programming. Hence, such methods are often limited to small and medium-sized problems. We propose a globally convergent, coordinate descent–inspired algorithm that allows tractable subproblem solutions restricted to a partition of the domain. Our decomposition method solves relatively small trust-region subproblems that modify the control variable on a subdomain only. Given nontrivial subdomain overlap, we prove that a global first-order necessary optimality condition is equivalent to a first-order necessary optimality condition per subdomain. We additionally show that a sufficient decrease is achieved on a single subdomain by way of a trust-region subproblem solver using geometric measure–theoretic arguments, which we integrate with a greedy patch selection to prove convergence of our algorithm. In conclusion, we demonstrate the practicality of our algorithm on a benchmark large-scale, PDE-constrained integer optimal control problem and find that our method is faster than the state of the art.

domain decomposition↗
NASA NTRS1993

Parametric binary dissection

Binary dissection is widely used to partition non-uniform domains over parallel computers. This algorithm does not consider the perimeter, surface area, or aspect ratio of the regions being generated and can yield decompositions that have poor communication to computation ratio. Parametric Binary Dissection (PBD) is a new algorithm in which each cut is chosen to minimize load + lambda x(shape). In a 2 (or 3) dimensional problem, load is the amount of computation to be performed in a subregion and shape could refer to the perimeter (respectively surface) of that subregion. Shape is a measure of communication overhead and the parameter permits us to trade off load imbalance against communication overhead. When A is zero, the algorithm reduces to plain binary dissection. This algorithm can be used to partition graphs embedded in 2 or 3-d. Load is the number of nodes in a subregion, shape the number of edges that leave that subregion, and lambda the ratio of time to communicate over an edge to the time to compute at a node. An algorithm is presented that finds the depth d parametric dissection of an embedded graph with n vertices and e edges in O(max(n log n, de)) time, which is an improvement over the O(dn log n) time of plain binary dissection. Parallel versions of this algorithm are also presented; the best of these requires O((n/p) log(sup 3)p) time on a p processor hypercube, assuming graphs of bounded degree. How PBD is applied to 3-d unstructured meshes and yields partitions that are better than those obtained by plain dissection is described. Its application to the color image quantization problem is also discussed, in which samples in a high-resolution color space are mapped onto a lower resolution space in a way that minimizes the color error.

Bokhari, Shahid H.↗
NASA NTRS1989

Parallel algorithms and architecture for computation of manipulator forward dynamics

Parallel computation of manipulator forward dynamics is investigated. Considering three classes of algorithms for the solution of the problem, that is, the O(n), the O(n exp 2), and the O(n exp 3) algorithms, parallelism in the problem is analyzed. It is shown that the problem belongs to the class of NC and that the time and processors bounds are of O(log2/2n) and O(n exp 4), respectively. However, the fastest stable parallel algorithms achieve the computation time of O(n) and can be derived by parallelization of the O(n exp 3) serial algorithms. Parallel computation of the O(n exp 3) algorithms requires the development of parallel algorithms for a set of fundamentally different problems, that is, the Newton-Euler formulation, the computation of the inertia matrix, decomposition of the symmetric, positive definite matrix, and the solution of triangular systems. Parallel algorithms for this set of problems are developed which can be efficiently implemented on a unique architecture, a triangular array of n(n+2)/2 processors with a simple nearest-neighbor interconnection. This architecture is particularly suitable for VLSI and WSI implementations. The developed parallel algorithm, compared to the best serial O(n) algorithm, achieves an asymptotic speedup of more than two orders-of-magnitude in the computation the forward dynamics.

Fijany, Amir↗
NASA NTRS1990

Counterrotating prop-fan simulations which feature a relative-motion multiblock grid decomposition enabling arbitrary time-steps

Improvements are presented of a computer algorithm developed for the time-accurate flow analysis of rotating machines. The flow model is a finite volume method utilizing a high-resolution approximate Riemann solver for interface flux definitions. The numerical scheme is a block LU implicit iterative-refinement method which possesses apparent unconditional stability. Multiblock composite gridding is used to orderly partition the field into a specified arrangement of blocks exhibiting varying degrees of similarity. Block-block relative motion is achieved using local grid distortion to reduce grid skewness and accommodate arbitrary time step selection. A general high-order numerical scheme is applied to satisfy the geometric conservation law. An even-blade-count counterrotating unducted fan configuration is chosen for a computational study comparing solutions resulting from altering parameters such as time step size and iteration count. The solutions are compared with measured data.

Janus, J. Mark↗
NASA NTRS1999

Automated Development of Accurate Algorithms and Efficient Codes for Computational Aeroacoustics

The simulation of sound generation and propagation in three space dimensions with realistic aircraft components is a very large time dependent computation with fine details. Simulations in open domains with embedded objects require accurate and robust algorithms for propagation, for artificial inflow and outflow boundaries, and for the definition of geometrically complex objects. The development, implementation, and validation of methods for solving these demanding problems is being done to support the NASA pillar goals for reducing aircraft noise levels. Our goal is to provide algorithms which are sufficiently accurate and efficient to produce usable results rapidly enough to allow design engineers to study the effects on sound levels of design changes in propulsion systems, and in the integration of propulsion systems with airframes. There is a lack of design tools for these purposes at this time. Our technical approach to this problem combines the development of new, algorithms with the use of Mathematica and Unix utilities to automate the algorithm development, code implementation, and validation. We use explicit methods to ensure effective implementation by domain decomposition for SPMD parallel computing. There are several orders of magnitude difference in the computational efficiencies of the algorithms which we have considered. We currently have new artificial inflow and outflow boundary conditions that are stable, accurate, and unobtrusive, with implementations that match the accuracy and efficiency of the propagation methods. The artificial numerical boundary treatments have been proven to have solutions which converge to the full open domain problems, so that the error from the boundary treatments can be driven as low as is required. The purpose of this paper is to briefly present a method for developing highly accurate algorithms for computational aeroacoustics, the use of computer automation in this process, and a brief survey of the algorithms that have resulted from this work. A review of computational aeroacoustics has recently been given by Lele.

Goodrich, John W.↗
NASA NTRS1988

Optical matrix-vector processing for computational fluid dynamics

An optical processor to solve partial differential equations for computational fluid dynamics applications is considered. This application is new and original for optical processors. The algorithms that are used are optical realizations of the Newton-Raphson method for nonlinear equations and a new optical LU direct decomposition and Gauss-Seidel iterative solution to the resultant linear algebraic equations. These algorithms are used to solve Burger's equation (a specific form of the momentum equation in fluid dynamics). The nonlinear equations provide 1-D velocity data at each time step. Simulation results of optical processing with these algorithms on computational fluid dynamics data is included.

Perlee, Caroline J.↗
NASA NTRS1993

Parallel execution of a three-dimensional, chemically reacting, Navier-Stokes code on distributed-memory machines

This paper describes the parallel version of the three-dimensional, chemically reacting, computational fluid dynamics (CFD) code, SPARK. This work was performed on the Intel iPSC/860-based parallel computers. The SPARK code utilizes relatively simple explicit numerical algorithms, but models complex chemical reactions. The code solves the equations over a regular structured mesh so a simple dam decomposition is used to assign work to the individual processors. The explicit nature of the algorithm, combined with the computational intensity of the chemistry calculations, results in a very low communication-to-computation ratio when compared to typical CFD codes. The efficiency of the parallel code is examined and shown to be about 65 percent when the problem size is scaled with the number of processors. Two low-angle wall-jet injection cases are solved to demonstrate the capability of the parallel code for solving large problems efficiently.

Otto, John C.↗
DOE OSTI2026

Efficient CP Rounding Using Alternating Least Squares with QR Decomposition

The CANDECOMP/PARAFAC (CP) decomposition is widely used for analyzing multidimensional data, and the alternating least squares (CP-ALS) algorithm is a common method for its computation. CP rounding is the problem of computing a lower-rank CP decomposition of an input already in a higher-rank CP format. While the normal equations (NE) approach in CP-ALS is efficient for the CP rounding problem and frequently used, it becomes unstable in the presence of ill-conditioned subproblems. This paper presents a new QR-based CP-ALS method for CP rounding that preserves both numerical stability and computational efficiency. Here, our experiments show that the proposed method offers significant speedup over a previous QR-based approach and the Tensor Toolbox's NE-based implementation, particularly for higher-order tensors. Furthermore, our approach demonstrates a marked reduction in error for ill-conditioned problems, with error reductions several orders of magnitude smaller compared to the NE-based method, while achieving faster convergence and more accurate solutions. By using a more numerically stable approach, we can solve more problems in reduced working precision, which enables further reduction in time to solution.

CANDECOMP/PARAFAC↗
DOE OSTI2022

Superconvergence of Online Optimization for Model Predictive Control

We develop a one-Newton-step-per-horizon, online, lag-L, model predictive control (MPC) algorithm for solving discrete-time, equality-constrained, nonlinear dynamic programs. Based on recent sensitivity analysis results for the target problems class, we prove that the approach exhibits a behavior that we call superconvergence; that is, the tracking error with respect to the full horizon solution is not only stable for successive horizon shifts, but also decreases with increasing shift order to a minimum value that decays exponentially in the length of the receding horizon. The key analytical step is the decomposition of the one-step error recursion of our algorithm into algorithmic error and perturbation error. We show that the perturbation error decays exponentially with the lag between two consecutive receding horizons, while the algorithmic error, determined by Newton’s method, achieves quadratic convergence instead. Overall this approach induces our local exponential convergence result in terms of the receding horizon length for suitable values of L. In conclusion, numerical experiments validate our theoretical findings.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A quantum algorithm for evolving open quantum dynamics on quantum computing devices

Abstract Designing quantum algorithms for simulating quantum systems has seen enormous progress, yet few studies have been done to develop quantum algorithms for open quantum dynamics despite its importance in modeling the system-environment interaction found in most realistic physical models. In this work we propose and demonstrate a general quantum algorithm to evolve open quantum dynamics on quantum computing devices. The Kraus operators governing the time evolution can be converted into unitary matrices with minimal dilation guaranteed by the Sz.-Nagy theorem. This allows the evolution of the initial state through unitary quantum gates, while using significantly less resource than required by the conventional Stinespring dilation. We demonstrate the algorithm on an amplitude damping channel using the IBM Qiskit quantum simulator and the IBM Q 5 Tenerife quantum device. The proposed algorithm does not require particular models of dynamics or decomposition of the quantum channel, and thus can be easily generalized to other open quantum dynamical models.

42 ENGINEERING↗
NASA NTRS1992

An efficient solution procedure for the thermoelastic analysis of truss space structures

A solution procedure is proposed for the thermal and thermoelastic analysis of truss space structures in periodic motion. In this method, the spatial domain is first descretized using a consistent finite element formulation. Then the resulting semi-discrete equations in time are solved analytically by using Fourier decomposition. Geometrical symmetry is taken advantage of completely. An algorithm is presented for the calculation of heat flux distribution. The method is demonstrated via a numerical example of a cylindrically shaped space structure.

Givoli, D.↗