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Results for “Approximate 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.

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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS2014

Rapid State Space Modeling Tool for Rectangular Wing Aeroservoelastic Studies

This paper introduces a modeling and simulation tool for aeroservoelastic analysis of rectangular wings with trailing edge control surfaces. The inputs to the code are planform design parameters such as wing span, aspect ratio and number of control surfaces. A doublet lattice approach is taken to compute generalized forces. A rational function approximation is computed. The output, computed in a few seconds, is a state space aeroservoelastic model which can be used for analysis and control design. The tool is fully parameterized with default information so there is little required interaction with the model developer. Although, all parameters can be easily modified if desired.The focus of this paper is on tool presentation, verification and validation. This process is carried out in stages throughout the paper. The rational function approximation is verified against computed generalized forces for a plate model. A model composed of finite element plates is compared to a modal analysis from commercial software and an independently conducted experimental ground vibration test analysis. Aeroservoelastic analysis is the ultimate goal of this tool. Therefore the flutter speed and frequency for a clamped plate are computed using V-g and V-f analysis. The computational results are compared to a previously published computational analysis and wind tunnel results for the same structure. Finally a case study of a generic wing model with a single control surface is presented. Verification of the state space model is presented in comparison to V-g and V-f analysis. This also includes the analysis of the model in response to a 1-cos gust.

Modeling and Simulation↗
DOE OSTI2015

Size-dependent error of the density functional theory ionization potential in vacuum and solution

Density functional theory is often the method of choice for modeling the energetics of large molecules and including explicit solvation effects. It is preferable to use a method that treats systems of different sizes and with different amounts of explicit solvent on equal footing. However, recent work suggests that approximate density functional theory has a size-dependent error in the computation of the ionization potential. We here investigate the lack of size-intensivity of the ionization potential computed with approximate density functionals in vacuum and solution. We show that local and semi-local approximations to exchange do not yield a constant ionization potential for an increasing number of identical isolated molecules in vacuum. Instead, as the number of molecules increases, the total energy required to ionize the system decreases. Rather surprisingly, we find that this is still the case in solution, whether using a polarizable continuum model or with explicit solvent that breaks the degeneracy of each solute, and we find that explicit solvent in the calculation can exacerbate the size-dependent delocalization error. We demonstrate that increasing the amount of exact exchange changes the character of the polarization of the solvent molecules; for small amounts of exact exchange the solvent molecules contribute a fraction of their electron density to the ionized electron, but for larger amounts of exact exchange they properly polarize in response to the cationic solute. In vacuum and explicit solvent, the ionization potential can be made size-intensive by optimally tuning a long-range corrected hybrid functional.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1988

Approximate spatial reasoning

Much of human reasoning is approximate in nature. Formal models of reasoning traditionally try to be precise and reject the fuzziness of concepts in natural use and replace them with non-fuzzy scientific explicata by a process of precisiation. As an alternate to this approach, it has been suggested that rather than regard human reasoning processes as themselves approximating to some more refined and exact logical process that can be carried out with mathematical precision, the essence and power of human reasoning is in its capability to grasp and use inexact concepts directly. This view is supported by the widespread fuzziness of simple everyday terms (e.g., near tall) and the complexity of ordinary tasks (e.g., cleaning a room). Spatial reasoning is an area where humans consistently reason approximately with demonstrably good results. Consider the case of crossing a traffic intersection. We have only an approximate idea of the locations and speeds of various obstacles (e.g., persons and vehicles), but we nevertheless manage to cross such traffic intersections without any harm. The details of our mental processes which enable us to carry out such intricate tasks in such apparently simple manner are not well understood. However, it is that we try to incorporate such approximate reasoning techniques in our computer systems. Approximate spatial reasoning is very important for intelligent mobile agents (e.g., robots), specially for those operating in uncertain or unknown or dynamic domains.

Dutta, Soumitra↗
DOE OSTI2025

COBRA:COMPUTED-TOMOGRAPHY BASED RANDOM-FIELD APPROXIMATION

SF-25-115 COBRA (COmputed-tomography Based Random-field Approximation) is a Python application for generating statistically equivalent random fields from CT-scan imagery. It leverages Karhunen–Loève expansions to model microstructural variability, enabling users to: Preprocess CT scans (filtering and Gaussian transformation); Fit covariance kernels fromempirical data; Solve eigenproblems to obtain KL modes; Sample random fields onsistent with fitted statistics; Postprocess samples back into the physical domain.

Hu, Tianchen↗
NASA NTRS1997

On the Use of Statistics in Design and the Implications for Deterministic Computer Experiments

Perhaps the most prevalent use of statistics in engineering design is through Taguchi's parameter and robust design -- using orthogonal arrays to compute signal-to-noise ratios in a process of design improvement. In our view, however, there is an equally exciting use of statistics in design that could become just as prevalent: it is the concept of metamodeling whereby statistical models are built to approximate detailed computer analysis codes. Although computers continue to get faster, analysis codes always seem to keep pace so that their computational time remains non-trivial. Through metamodeling, approximations of these codes are built that are orders of magnitude cheaper to run. These metamodels can then be linked to optimization routines for fast analysis, or they can serve as a bridge for integrating analysis codes across different domains. In this paper we first review metamodeling techniques that encompass design of experiments, response surface methodology, Taguchi methods, neural networks, inductive learning, and kriging. We discuss their existing applications in engineering design and then address the dangers of applying traditional statistical techniques to approximate deterministic computer analysis codes. We conclude with recommendations for the appropriate use of metamodeling techniques in given situations and how common pitfalls can be avoided.

Simpson, Timothy W.↗
NASA NTRS2011

On the Accuracy of Double Scattering Approximation for Atmospheric Polarization Computations

Interpretation of multi-angle spectro-polarimetric data in remote sensing of atmospheric aerosols require fast and accurate methods of solving the vector radiative transfer equation (VRTE). The single and double scattering approximations could provide an analytical framework for the inversion algorithms and are relatively fast, however accuracy assessments of these approximations for the aerosol atmospheres in the atmospheric window channels have been missing. This paper provides such analysis for a vertically homogeneous aerosol atmosphere with weak and strong asymmetry of scattering. In both cases, the double scattering approximation gives a high accuracy result (relative error approximately 0.2%) only for the low optical path - 10(sup -2) As the error rapidly grows with optical thickness, a full VRTE solution is required for the practical remote sensing analysis. It is shown that the scattering anisotropy is not important at low optical thicknesses neither for reflected nor for transmitted polarization components of radiation.

Korkin, Sergey V.↗
DOE OSTI2018

Smoothness of Functions in Spaces of the Finite Element Method

We find necessary and sufficient conditions for the generalized smoothness of the coordinate functions obtained from the approximate relations. We show that for the coordinate functions the smoothness on their supports is equivalent to that on the boundaries of supports. We obtain conditions for the continuity of Courant type finite element approximations and conditions for the uniqueness of a linear space of such approximations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

The shifted boundary method for embedded domain computations. Part I: Poisson and Stokes problems

We propose a new finite element method for embedded domain computations, which falls in the category of surrogate/approximate boundary algorithms. The key feature of the proposed approach is the idea of shifting the location where boundary conditions are applied from the true to the surrogate boundary, and to appropriately modify the shifted boundary conditions, enforced weakly, in order to preserve optimal convergence rates of the numerical solution. This process yields a method which, in our view, is simple, efficient, and also robust, since it is not affected by the small-cut-cell problem. Although general in nature, here we apply this new concept to the Poisson and Stokes problems. We present in particular the full analysis of stability and convergence for the case of the Poisson operator, and numerical tests for both the Poisson and Stokes equations, for geometries of progressively higher complexity.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1984

Universal single level implicit algorithm for gasdynamics

A single level effectively explicit implicit algorithm for gasdynamics is presented. The method meets all the requirements for unconditionally stable global iteration over flows with mixed supersonic and supersonic zones including blunt body flow and boundary layer flows with strong interaction and streamwise separation. For hyperbolic (supersonic flow) regions the method is automatically equivalent to contemporary space marching methods. For elliptic (subsonic flow) regions, rapid convergence is facilitated by alternating direction solution sweeps which bring both sets of eigenvectors and the influence of both boundaries of a coordinate line equally into play. Point by point updating of the data with local iteration on the solution procedure at each spatial step as the sweeps progress not only renders the method single level in storage but, also, improves nonlinear accuracy to accelerate convergence by an order of magnitude over related two level linearized implicit methods. The method derives robust stability from the combination of an eigenvector split upwind difference method (CSCM) with diagonally dominant ADI(DDADI) approximate factorization and computed characteristic boundary approximations.

Lombard, C. K.↗
NASA NTRS2015

Rapid State Space Modeling Tool for Rectangular Wing Aeroservoelastic Studies

This paper introduces a modeling and simulation tool for aeroservoelastic analysis of rectangular wings with trailing-edge control surfaces. The inputs to the code are planform design parameters such as wing span, aspect ratio, and number of control surfaces. Using this information, the generalized forces are computed using the doublet-lattice method. Using Roger's approximation, a rational function approximation is computed. The output, computed in a few seconds, is a state space aeroservoelastic model which can be used for analysis and control design. The tool is fully parameterized with default information so there is little required interaction with the model developer. All parameters can be easily modified if desired. The focus of this paper is on tool presentation, verification, and validation. These processes are carried out in stages throughout the paper. The rational function approximation is verified against computed generalized forces for a plate model. A model composed of finite element plates is compared to a modal analysis from commercial software and an independently conducted experimental ground vibration test analysis. Aeroservoelastic analysis is the ultimate goal of this tool, therefore, the flutter speed and frequency for a clamped plate are computed using damping-versus-velocity and frequency-versus-velocity analysis. The computational results are compared to a previously published computational analysis and wind-tunnel results for the same structure. A case study of a generic wing model with a single control surface is presented. Verification of the state space model is presented in comparison to damping-versus-velocity and frequency-versus-velocity analysis, including the analysis of the model in response to a 1-cos gust.

Modeling and Simulation↗
NASA NTRS2015

Rapid State Space Modeling Tool for Rectangular Wing Aeroservoelastic Studies

This report introduces a modeling and simulation tool for aeroservoelastic analysis of rectangular wings with trailing-edge control surfaces. The inputs to the code are planform design parameters such as wing span, aspect ratio, and number of control surfaces. Using this information, the generalized forces are computed using the doublet-lattice method. Using Roger's approximation, a rational function approximation is computed. The output, computed in a few seconds, is a state space aeroservoelastic model which can be used for analysis and control design. The tool is fully parameterized with default information so there is little required interaction with the model developer. All parameters can be easily modified if desired. The focus of this report is on tool presentation, verification, and validation. These processes are carried out in stages throughout the report. The rational function approximation is verified against computed generalized forces for a plate model. A model composed of finite element plates is compared to a modal analysis from commercial software and an independently conducted experimental ground vibration test analysis. Aeroservoelastic analysis is the ultimate goal of this tool, therefore, the flutter speed and frequency for a clamped plate are computed using damping-versus-velocity and frequency-versus-velocity analysis. The computational results are compared to a previously published computational analysis and wind-tunnel results for the same structure. A case study of a generic wing model with a single control surface is presented. Verification of the state space model is presented in comparison to damping-versus-velocity and frequency-versus-velocity analysis, including the analysis of the model in response to a 1-cos gust.

Verification and Validation↗
DOE OSTI2014

Efficient on-the-fly ab initio semiclassical method for computing time-resolved nonadiabatic electronic spectra with surface hopping or Ehrenfest dynamics

We derive a somewhat crude, yet very efficient semiclassical approximation for computing nonadiabatic spectra. The resulting method, which is a generalization of the multiple-surface dephasing representation, includes quantum effects through interference of mixed quantum-classical trajectories and through quantum treatment of the collective electronic degree of freedom. The method requires very little computational effort beyond the fewest-switches surface hopping or Ehrenfest locally mean-field dynamics and is very easy to implement. The proposed approximation is tested by computing the absorption and time-resolved stimulated emission spectra of pyrazine using the four-dimensional three-surface model which allows for comparison with the numerically exact quantum spectra. As expected, the multiple-surface dephasing representation is not suitable for high-resolution linear spectra, yet it seems to capture all the important features of pump-probe spectra. Finally, the method is combined with on-the-fly ab initio evaluation of the electronic structure (i.e., energies, forces, electric-dipole, and nonadiabatic couplings) in order to compute fully dimensional nonadiabatic spectra of pyrazine without approximations inherent to analytical, including vibronic-coupling models. The Appendix provides derivations of perturbative expressions for linear and pump-probe spectra of arbitrary mixed states and for arbitrary laser pulse shapes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

A fast mollified impulse method for biomolecular atomistic simulations

Classical integration methods for molecular dynamics are inherently limited due to resonance phenomena occurring at certain time-step sizes. The mollified impulse method can partially avoid this problem by using appropriate filters based on averaging or projection techniques. However, existing filters are computationally expensive and tedious in implementation since they require either analytical Hessians or they need to solve nonlinear systems from constraints. In this work we follow a different approach based on corotation for the construction of a new filter for (flexible) biomolecular simulations. The main advantages of the proposed filter are its excellent stability properties and ease of implementation in standard softwares without Hessians or solving constraint systems. By simulating multiple realistic examples such as peptide, protein, ice equilibrium and ice–ice friction, the new filter is shown to speed up the computations of long-range interactions by approximately 20%. The proposed filtered integrators allow step sizes as large as 10 fs while keeping the energy drift less than 1% on a 50 ps simulation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Block Krylov Subspace Methods for Functions of Matrices II: Modified Block FOM

We analyze an expansion of the generalized block Krylov subspace framework of [Electron. Trans. Numer. Anal., 47 (2017), pp. 100--126]. This expansion allows the use of low-rank modifications of the matrix projected onto the block Krylov subspace and contains, as special cases, the block GMRES method and the new block Radau--Arnoldi method. Within this general setting, we present results that extend the interpolation property from the nonblock case to a matrix polynomial interpolation property for the block case, and we relate the eigenvalues of the projected matrix to the latent roots of these matrix polynomials. Some error bounds for these modified block FOM methods for solving linear systems are presented. We then show how cospatial residuals can be preserved in the case of families of shifted linear block systems. This result is used to derive computationally practical restarted algorithms for block Krylov approximations that compute the action of a matrix function on a set of several vectors simultaneously. Finally, we prove some error bounds and present numerical results showing that two modifications of FOM, the block harmonic and the block Radau--Arnoldi methods for matrix functions, can significantly improve the convergence behavior.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Relaxed Multibang Regularization for the Combinatorial Integral Approximation

Multibang regularization and combinatorial integral approximation decompositions are two actively researched techniques for integer optimal control. In this work, we consider a class of polyhedral functions that arise particularly as convex lower envelopes of multibang regularizers and show that they have beneficial properties with respect to regularization of relaxations of integer optimal control problems. We extend the algorithmic framework of the combinatorial integral approximation such that a subsequence of the computed discrete-valued controls converges to the infimum of the regularized integer control problem.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1985

Auto covariance computer

A laser velocimeter covariance processor which calculates the auto covariance and cross covariance functions for a turbulent flow field based on Poisson sampled measurements in time from a laser velocimeter is described. The device will process a block of data that is up to 4096 data points in length and return a 512 point covariance function with 48-bit resolution along with a 512 point histogram of the interarrival times which is used to normalize the covariance function. The device is designed to interface and be controlled by a minicomputer from which the data is received and the results returned. A typical 4096 point computation takes approximately 1.5 seconds to receive the data, compute the covariance function, and return the results to the computer.

Hepner, T. E.↗
DOE OSTI2024

Anderson acceleration with approximate calculations: Applications to scientific computing

Here we provide rigorous theoretical bounds for Anderson acceleration (AA) that allow for approximate calculations when applied to solve linear problems. We show that, when the approximate calculations satisfy the provided error bounds, the convergence of AA is maintained while the computational time could be reduced. We also provide computable heuristic quantities, guided by the theoretical error bounds, which can be used to automate the tuning of accuracy while performing approximate calculations. For linear problems, the use of heuristics to monitor the error introduced by approximate calculations, combined with the check on monotonicity of the residual, ensures the convergence of the numerical scheme within a prescribed residual tolerance. Motivated by the theoretical studies, we propose a reduced variant of AA, which consists in projecting the least-squares used to compute the Anderson mixing onto a subspace of reduced dimension. The dimensionality of this subspace adapts dynamically at each iteration as prescribed by the computable heuristic quantities. We numerically show and assess the performance of AA with approximate calculations on: (i) linear deterministic fixed-point iterations arising from the Richardson's scheme to solve linear systems with open-source benchmark matrices with various preconditioners and (ii) non-linear deterministic fixed-point iterations arising from non-linear time-dependent Boltzmann equations.

97 MATHEMATICS AND COMPUTING↗