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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.

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At least 469 records · Page 26
All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

Experimental, Theoretical, and Computational Investigation of Separated Nozzle Flows

A detailed experimental, theoretical, and computational study of separated nozzle flows has been conducted. Experimental testing was performed at the NASA Langley 16-Foot Transonic Tunnel Complex. As part of a comprehensive static performance investigation, force, moment, and pressure measurements were made and schlieren flow visualization was obtained for a sub-scale, non-axisymmetric, two-dimensional, convergent- divergent nozzle. In addition, two-dimensional numerical simulations were run using the computational fluid dynamics code PAB3D with two-equation turbulence closure and algebraic Reynolds stress modeling. For reference, experimental and computational results were compared with theoretical predictions based on one-dimensional gas dynamics and an approximate integral momentum boundary layer method. Experimental results from this study indicate that off-design overexpanded nozzle flow was dominated by shock induced boundary layer separation, which was divided into two distinct flow regimes; three- dimensional separation with partial reattachment, and fully detached two-dimensional separation. The test nozzle was observed to go through a marked transition in passing from one regime to the other. In all cases, separation provided a significant increase in static thrust efficiency compared to the ideal prediction. Results indicate that with controlled separation, the entire overexpanded range of nozzle performance would be within 10% of the peak thrust efficiency. By offering savings in weight and complexity over a conventional mechanical exhaust system, this may allow a fixed geometry nozzle to cover an entire flight envelope. The computational simulation was in excellent agreement with experimental data over most of the test range, and did a good job of modeling internal flow and thrust performance. An exception occurred at low nozzle pressure ratios, where the two-dimensional computational model was inconsistent with the three-dimensional separation observed in the experiment. In general, the computation captured the physics of the shock boundary layer interaction and shock induced boundary layer separation in the nozzle, though there were some differences in shock structure compared to experiment. Though minor, these differences could be important for studies involving flow control or thrust vectoring of separated nozzles. Combined with other observations, this indicates that more detailed, three-dimensional computational modeling needs to be conducted to more realistically simulate shock-separated nozzle flows.

Hunter, Craig A.↗
DOE OSTI2023

Tensor Decompositions for Count Data that Leverage Stochastic and Deterministic Optimization

There is growing interest to extend low-rank matrix decompositions to multi-way arrays, or tensors. One fundamental low-rank tensor decomposition is the canonical polyadic decomposition (CPD). The challenge of fitting a low-rank, nonnegative CPD model to Poisson-distributed count data is of particular interest. Several popular algorithms use local search methods to approximate the global maximum likelihood estimator from local minima. Simultaneously, a recent trend in theoretical computer science and numerical linear algebra leverages randomization to solve very large, hard problems. The typical approach is to use randomization for a fast approximation and determinism for refinement to yield effective algorithms with theoretical guarantees. Two popular algorithms for Poisson CPD reflect that emergent dichotomy: CP Alternating Poisson Regression is a deterministic algorithm and Generalized Canonical Polyadic decomposition makes use of stochastic algorithms in several variants. This work extends recent work to develop two new methods that leverage randomized and deterministic algorithms for improved accuracy and performance.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Intrusive Uncertainty Quantification and Optimal Experiment Design in the Open-Source Pyomo Ecosystem

This contribution describes ParmEst and Pyomo.DoE, two pillars of the open-source Python-based Pyomo ecosystem for computational optimization with (partial differential) algebraic equation mathematical models. Specifically, ParmEst facilitates intrusive frequentist parameter estimation (PE) and uncertainty quantification (UQ) through built-in features, such as covariance matrix estimation, bootstrapping, and likelihood ratio tests. Complementary, Pyomo.DoE enables optimal experiment design by maximizing various metrics of the Fisher information matrix, such as A-optimality (trace), D-optimality (determinant), E-optimality (minimum eigenvalue), and ME-optimality (condition number). ParmEst and Pyomo.DoE can solve high-dimensional optimization problems by leveraging the model structure and exact derivative information. Finally, we will discuss future opportunities to integrate PE and UQ capabilities with optimization under uncertainty, including robust optimization with non-convex models via PyROS.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1993

Structured adaptive grid generation using algebraic methods

The accuracy of the numerical algorithm depends not only on the formal order of approximation but also on the distribution of grid points in the computational domain. Grid adaptation is a procedure which allows optimal grid redistribution as the solution progresses. It offers the prospect of accurate flow field simulations without the use of an excessively timely, computationally expensive, grid. Grid adaptive schemes are divided into two basic categories: differential and algebraic. The differential method is based on a variational approach where a function which contains a measure of grid smoothness, orthogonality and volume variation is minimized by using a variational principle. This approach provided a solid mathematical basis for the adaptive method, but the Euler-Lagrange equations must be solved in addition to the original governing equations. On the other hand, the algebraic method requires much less computational effort, but the grid may not be smooth. The algebraic techniques are based on devising an algorithm where the grid movement is governed by estimates of the local error in the numerical solution. This is achieved by requiring the points in the large error regions to attract other points and points in the low error region to repel other points. The development of a fast, efficient, and robust algebraic adaptive algorithm for structured flow simulation applications is presented. This development is accomplished in a three step process. The first step is to define an adaptive weighting mesh (distribution mesh) on the basis of the equidistribution law applied to the flow field solution. The second, and probably the most crucial step, is to redistribute grid points in the computational domain according to the aforementioned weighting mesh. The third and the last step is to reevaluate the flow property by an appropriate search/interpolate scheme at the new grid locations. The adaptive weighting mesh provides the information on the desired concentration of points to the grid redistribution scheme. The evaluation of the weighting mesh is accomplished by utilizing the weight function representing the solution variation and the equidistribution law. The selection of the weight function plays a key role in grid adaptation. A new weight function utilizing a properly weighted boolean sum of various flowfield characteristics is defined. The redistribution scheme is developed utilizing Non-Uniform Rational B-Splines (NURBS) representation. The application of NURBS representation results in a well distributed smooth grid by maintaining the fidelity of the geometry associated with boundary curves. Several algebraic methods are applied to smooth and/or nearly orthogonalize the grid lines. An elliptic solver is utilized to smooth the grid lines if there are grid crossings. Various computational examples of practical interest are presented to demonstrate the success of these methods.

Yang, Jiann-Cherng↗
NASA NTRS1991

Algebraic grid generation for complex geometries

An efficient computer program called GRID2D/3D has been developed to generate single and composite grid systems within geometrically complex two- and three-dimensional (2D and 3D) spatial domains that can deform with time. GRID2D/3D generates single grid systems by using algebraic grid generation methods based on transfinite interpolation. The distribution of grid points within the spatial domain is controlled by stretching functions and grid lines can intersect boundaries of the spatial domain orthogonally. GRID2D/3D generates composite grid systems by patching together two or more single grid systems. The patching can be discontinuous or continuous. For 2D spatial domains the boundary curves are constructed by using either cubic or tension spline interpolation. For 3D spatial domains the boundary surfaces are constructed by using a new technique, developed in this study, referred to as 3D bidirectional Hermite interpolation.

Shih, T. I.-P.↗
DOE OSTI2014

A scalable approach to solving dense linear algebra problems on hybrid CPU-GPU systems

Aiming to fully exploit the computing power of all CPUs and all graphics processing units (GPUs) on hybrid CPU-GPU systems to solve dense linear algebra problems, in this paper we design a class of heterogeneous tile algorithms to maximize the degree of parallelism, to minimize the communication volume, and to accommodate the heterogeneity between CPUs and GPUs. The new heterogeneous tile algorithms are executed upon our decentralized dynamic scheduling runtime system, which schedules a task graph dynamically and transfers data between compute nodes automatically. The runtime system uses a new distributed task assignment protocol to solve data dependencies between tasks without any coordination between processing units. By overlapping computation and communication through dynamic scheduling, we are able to attain scalable performance for the double-precision Cholesky factorization and QR factorization. Finally, our approach demonstrates a performance comparable to Intel MKL on shared-memory multicore systems and better performance than both vendor (e.g., Intel MKL) and open source libraries (e.g., StarPU) in the following three environments: heterogeneous clusters with GPUs, conventional clusters without GPUs, and shared-memory systems with multiple GPUs.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2017

Color Algebras

A color algebra refers to a system for computing sums and products of colors, analogous to additive and subtractive color mixtures. The difficulty addressed here is the fact that, because of metamerism, we cannot know with certainty the spectrum that produced a particular color solely on the basis of sensory data. Knowledge of the spectrum is not required to compute additive mixture of colors, but is critical for subtractive (multiplicative) mixture. Therefore, we cannot predict with certainty the multiplicative interactions between colors based solely on sensory data. There are two potential applications of a color algebra: first, to aid modeling phenomena of human visual perception, such as color constancy and transparency; and, second, to provide better models of the interactions of lights and surfaces for computer graphics rendering.

color rendering↗
DOE OSTI2019

Constant depth, near constant depth, and subcubic size threshold circuits for linear algebraic calculations

A method of increasing an efficiency at which a plurality of threshold gates arranged as neuromorphic hardware is able to perform a linear algebraic calculation having a dominant size of N. The computer-implemented method includes using the plurality of threshold gates to perform the linear algebraic calculation in a manner that is simultaneously efficient and at a near constant depth. “Efficient” is defined as a calculation algorithm that uses fewer of the plurality of threshold gates than a naïve algorithm. The naïve algorithm is a straightforward algorithm for solving the linear algebraic calculation. “Constant depth” is defined as an algorithm that has an execution time that is independent of a size of an input to the linear algebraic calculation. The near constant depth comprises a computing depth equal to or between O(log(log(N)) and the constant depth.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Efficient electronic structure theory via hierarchical scale-adaptive coupled-cluster formalism: I. Theory and computational complexity analysis

In this work, a novel reduced-scaling, general-order coupled-cluster approach is formulated by exploiting hierarchical representations of many-body tensors, combined with the recently suggested formalism of scale-adaptive tensor algebra. Inspired by the hierarchical techniques from the renormalization group approach, H/H 2 -matrix algebra and fast multipole method, the computational scaling reduction in our formalism is achieved via coarsening of quantum many-body interactions at larger interaction scales, thus imposing a hierarchical structure on many-body tensors of coupled-cluster theory. In our approach, the interaction scale can be defined on any appropriate Euclidean domain (spatial domain, momentum-space domain, energy domain, etc.). Additionally, we show that the hierarchically resolved many-body tensors reduce the storage requirements to O(N), where N is the number of simulated quantum particles. Subsequently, we prove that any connected many-body diagram with arbitrary-order tensors, e.g., an arbitrary coupled-cluster diagram, can be evaluated in O(NlogN) floating-point operations. On top of that, we elaborate an additional approximation to further reduce the computational complexity of higher-order coupled-cluster equations, i.e., equations involving higher than double excitations, which otherwise would introduce a large prefactor into formal O(NlogN) scaling.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

A High Performance Sparse Tensor Algebra Compiler in MLIR

Sparse tensor algebra is widely used in many applications, including scientific computing, machine learning, and data analytics. The performance of sparse tensor algebra kernels strongly depends on the intrinsic characteristics of the input tensors, hence many storage formats are designed for tensors to achieve optimal performance for particular applications/architectures, which makes it challenging to implement and optimize every tensor operation of interest on a given architecture. We propose a tensor algebra domain-specific language (DSL) and compiler framework to automatically generate kernels for mixed sparse-dense tensor algebra operations. The proposed DSL provides high-level programming abstractions that resemble the familiar Einstein notation to represent tensor algebra operations. The compiler introduces a new Sparse Tensor Algebra dialect built on top of LLVM's extensible MLIR compiler infrastructure for efficient code generation while covering a wide range of tensor storage formats. Our compiler also leverages input-dependent code optimization to enhance data locality for better performance. Our results show that the performance of automatically generated kernels outperforms the state-of-the-art sparse tensor algebra compiler, with up to 20.92x, 6.39x, and 13.9x performance improvement over state-of-the-art tensor algebra compilers, for parallel SpMV, SpMM, and TTM, respectively.

Tian, Ruiqin↗
NASA NTRS1990

On the numerical simulation of spatial disturbances in blunt-nose flat plate flow

The feasibility of the simulation of the evolution of spatially amplified disturbances in realistic airfoil flows using a standard Navier-Stokes airfoil code is considered for a blunt-nose flat plate flow. A basic stationary flow and its linear-stability-theory characteristics are analyzed. A computational C-grid is generated using an algebraic grid-generation technique. It is concluded that further improvements to the computational grid and to the code are necessary to make the proposed simulations economical.

Laurien, Eckart↗
DOE OSTI2023

Accelerating the density-functional tight-binding method using graphical processing units

Acceleration of the density-functional tight-binding (DFTB) method on single and multiple graphical processing units (GPUs) was accomplished using the MAGMA linear algebra library. Herein two major computational bottlenecks of DFTB ground-state calculations were addressed in our implementation: the Hamiltonian matrix diagonalization and the density matrix construction. The code was implemented and benchmarked on two different computer systems: (1) the SUMMIT IBM Power9 supercomputer at the Oak Ridge National Laboratory Leadership Computing Facility with 1–6 NVIDIA Volta V100 GPUs per computer node and (2) an in-house Intel Xeon computer with 1–2 NVIDIA Tesla P100 GPUs. The performance and parallel scalability were measured for three molecular models of 1-, 2-, and 3-dimensional chemical systems, represented by carbon nanotubes, covalent organic frameworks, and water clusters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

New Effective Multithreaded Matching Algorithms

Matching is an important combinatorial problem with a number of applications in areas such as community detection, sparse linear algebra, and network alignment. Since computing optimal matchings can be very time consuming, several fast approximation algorithms, both sequential and parallel, have been suggested. Common to the algorithms giving the best solutions is that they tend to be sequential by nature, while algorithms more suitable for parallel computation give solutions of less quality. We present a new simple 1 2 -approximation algorithm for the weighted matching problem. This algorithm is both faster than any other suggested sequential 1 2 -approximation algorithm on almost all inputs and also scales better than previous multithreaded algorithms. We further extend this to a general scalable multithreaded algorithm that computes matchings of weight comparable with the best sequential algorithms. The performance of the suggested algorithms is documented through extensive experiments on different multithreaded architectures.

matching, parallel algorithms↗
DOE OSTI2016

TuckerCompressMPI v. 1.0

As parallel computing trends towards the exascale, scientific data produced by high-fidelity simulations are growing increasingly massive. For instance, a simulation on a three-dimensional spatial grid with 512 points per dimension that tracks 64 variables per grid point for 128 time steps yields 8 TB of data. By viewing the data as a dense five-way tensor, we can compute a Tucker decomposition to find inherent low-dimensional multilinear structure, achieving compression ratios of up to 10000 on real-world data sets with negligible loss in accuracy. So that we can operate on such massive data, we present the first-ever distributed-memory parallel implementation for the Tucker decomposition, whose key computations correspond to parallel linear algebra operations, albeit with nonstandard data layouts. Our approach specifies a data distribution for tensors that avoids any tensor data redistribution, either locally or in parallel. This software provides a method for compressing large-scale multiway data.

Austin, Woody↗
NASA NTRS1966

Computer program determines chemical equilibria in complex systems

Computer program numerically solves nonlinear algebraic equations for chemical equilibrium based on iteration equations independent of choice of components. This program calculates theoretical performance for frozen and equilibrium composition during expansion and Chapman-Jouguet flame properties, studies combustion, and designs hardware.

Gordon, S.↗