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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 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

A reaction–diffusion model for phenotypic evolution

We present a reaction–diffusion mathematical model for the evolutionary dynamics of phenotypic evolution. A detailed deduction of the equations is presented for the one-dimensional version, from which a more general model is proposed. Particular cases are studied using analytical approximations and numerical simulations. Results indicate that the approach proposed produces results that are coherent with mainstream models in evolutionary dynamics, suggesting that the reaction–diffusion model could be an alternative tool in the analysis of evolutionary dynamics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Trigonometric polynomial approximation, K-functionals and generalized moduli of smoothness

Best approximation and approximation by families of linear polynomial operators (FLPO) in the spaces L{sub p}, 0<p⩽+∞, are investigated for periodic functions of an arbitrary number of variables in terms of the generalized modulus of smoothness generated by a periodic generator which, near the origin, is assumed to be close in a certain sense to some homogeneous function of positive order. Direct and inverse theorems (Jackson- and Bernstein-type estimates) are proved; conditions on the generators are obtained under which the approximation error by an FLPO is equivalent to an appropriate modulus of smoothness. These problems are solved by going over from the modulus to an equivalent K-functional. The general results obtained are applied to classical objects in the theory of approximation and smoothness. In particular, they are applied to the methods of approximation generated by Fejér, Riesz and Bochner-Riesz kernels, and also to the moduli of smoothness and K-functionals corresponding to the conventional, Weyl and Riesz derivatives and to the Laplace operator. Bibliography: 24 titles. (paper)

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2000

2D Quantum Mechanical Study of Nanoscale MOSFETs

With the onset of quantum confinement in the inversion layer in nanoscale MOSFETs, behavior of the resonant level inevitably determines all device characteristics. While most classical device simulators take quantization into account in some simplified manner, the important details of electrostatics are missing. Our work addresses this shortcoming and provides: (a) a framework to quantitatively explore device physics issues such as the source-drain and gate leakage currents, DIBL, and threshold voltage shift due to quantization, and b) a means of benchmarking quantum corrections to semiclassical models (such as density-gradient and quantum-corrected MEDICI). We have developed physical approximations and computer code capable of realistically simulating 2-D nanoscale transistors, using the non-equilibrium Green's function (NEGF) method. This is the most accurate full quantum model yet applied to 2-D device simulation. Open boundary conditions and oxide tunneling are treated on an equal footing. Electrons in the ellipsoids of the conduction band are treated within the anisotropic effective mass approximation. We present the results of our simulations of MIT 25, 50 and 90 nm "well-tempered" MOSFETs and compare them to those of classical and quantum corrected models. The important feature of quantum model is smaller slope of Id-Vg curve and consequently higher threshold voltage. Surprisingly, the self-consistent potential profile shows lower injection barrier in the channel in quantum case. These results are qualitatively consistent with ID Schroedinger-Poisson calculations. The effect of gate length on gate-oxide leakage and subthreshold current has been studied. The shorter gate length device has an order of magnitude smaller current at zero gate bias than the longer gate length device without a significant trade-off in on-current. This should be a device design consideration.

Svizhenko, Alexei↗
NASA NTRS2001

2-D Modeling of Nanoscale MOSFETs: Non-Equilibrium Green's Function Approach

We have developed physical approximations and computer code capable of realistically simulating 2-D nanoscale transistors, using the non-equilibrium Green's function (NEGF) method. This is the most accurate full quantum model yet applied to 2-D device simulation. Open boundary conditions and oxide tunneling are treated on an equal footing. Electrons in the ellipsoids of the conduction band are treated within the anisotropic effective mass approximation. Electron-electron interaction is treated within Hartree approximation by solving NEGF and Poisson equations self-consistently. For the calculations presented here, parallelization is performed by distributing the solution of NEGF equations to various processors, energy wise. We present simulation of the "benchmark" MIT 25nm and 90nm MOSFETs and compare our results to those from the drift-diffusion simulator and the quantum-corrected results available. In the 25nm MOSFET, the channel length is less than ten times the electron wavelength, and the electron scattering time is comparable to its transit time. Our main results are: (1) Simulated drain subthreshold current characteristics are shown, where the potential profiles are calculated self-consistently by the corresponding simulation methods. The current predicted by our quantum simulation has smaller subthreshold slope of the Vg dependence which results in higher threshold voltage. (2) When gate oxide thickness is less than 2 nm, gate oxide leakage is a primary factor which determines off-current of a MOSFET (3) Using our 2-D NEGF simulator, we found several ways to drastically decrease oxide leakage current without compromising drive current. (4) Quantum mechanically calculated electron density is much smaller than the background doping density in the poly silicon gate region near oxide interface. This creates an additional effective gate voltage. Different ways to. include this effect approximately will be discussed.

Svizhenko, Alexei↗
DOE OSTI2018

Approximation of Two-Dimensional Viscoelastic Flows of General Form

We consider the initial-boundary value problem for approximations of the system of integro-differential equations generalizing the equations of motion for viscoelastic fluids. We prove the existence and convergence theorems and give some examples of non-Newtonian fluids described by the model under consideration.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Interaction of Harmonic Longitudinal Shear Waves with V-Shaped Inclusions

We solve the problem of determination of the stressed state in the vicinity of a tunnel rigid inclusion whose cross section consists of two segments originating out from the same point. The inclusion is placed in an infinite elastic medium with propagating plane harmonic longitudinal shear waves. The problem is reduced to the solution of a system of two singular integral equations with fixed singularities. For the approximate solution of this system, we apply a numerical method that takes into account the true asymptotics of the unknown functions and is based on the use of special quadrature formulas for the evaluation of singular integrals.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2001

2D Quantum Transport Modeling in Nanoscale MOSFETs

With the onset of quantum confinement in the inversion layer in nanoscale MOSFETs, behavior of the resonant level inevitably determines all device characteristics. While most classical device simulators take quantization into account in some simplified manner, the important details of electrostatics are missing. Our work addresses this shortcoming and provides: (a) a framework to quantitatively explore device physics issues such as the source-drain and gate leakage currents, DIBL, and threshold voltage shift due to quantization, and b) a means of benchmarking quantum corrections to semiclassical models (such as density- gradient and quantum-corrected MEDICI). We have developed physical approximations and computer code capable of realistically simulating 2-D nanoscale transistors, using the non-equilibrium Green's function (NEGF) method. This is the most accurate full quantum model yet applied to 2-D device simulation. Open boundary conditions, oxide tunneling and phase-breaking scattering are treated on equal footing. Electrons in the ellipsoids of the conduction band are treated within the anisotropic effective mass approximation. Quantum simulations are focused on MIT 25, 50 and 90 nm "well- tempered" MOSFETs and compared to classical and quantum corrected models. The important feature of quantum model is smaller slope of Id-Vg curve and consequently higher threshold voltage. These results are quantitatively consistent with I D Schroedinger-Poisson calculations. The effect of gate length on gate-oxide leakage and sub-threshold current has been studied. The shorter gate length device has an order of magnitude smaller current at zero gate bias than the longer gate length device without a significant trade-off in on-current. This should be a device design consideration.

Svizhenko, Alexei↗
DOE OSTI2018

Construction and Investigation of the Third-Order Approximation to the Solution of the Heat-Conduction Equation for Thin Shallow Shells by Using Legendre Polynomials in the Case of Stationary Heat Exchange

By using the N th order approximation of temperature function and its first derivative by Legendre polynomials, we construct the solution of problem of heat conduction for a thin-walled shallow isotropic shell and deduce the system of resolving equations for the N th approximation. For the first and third approximations, we solve this problem for the case of concentrated heat sources. In the third approximation, we also construct the plots of the dependences of temperature on the distance to the heat source and on the curvature of the shell under the conditions of symmetric or asymmetric stationary heat exchange.

42 ENGINEERING↗
DOE OSTI2015

Thermodynamics and luminosities of rainbow black holes

Doubly special relativity (DSR) is an effective model for encoding quantum gravity in flat spacetime. As result of the nonlinearity of the Lorentz transformation, the energy-momentum dispersion relation is modified. One simple way to import DSR to curved spacetime is ''Gravity's rainbow'', where the spacetime background felt by a test particle would depend on its energy. Focusing on the ''Amelino-Camelia dispersion relation'' which is E{sup 2} = m{sup 2}+p{sup 2}[1−η(E/m{sub p}){sup n}] with n > 0, we investigate the thermodynamical properties of a Schwarzschild black hole and a static uncharged black string for all possible values of η and n in the framework of rainbow gravity. It shows that there are non-vanishing minimum masses for these two black holes in the cases with η < 0 and n ≥ 2. Considering effects of rainbow gravity on both the Hawking temperature and radius of the event horizon, we use the geometric optics approximation to compute luminosities of a 2D black hole, a Schwarzschild one and a static uncharged black string. It is found that the luminosities can be significantly suppressed or boosted depending on the values of η and n.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2014

3D Space Radiation Transport in a Shielded ICRU Tissue Sphere

A computationally efficient 3DHZETRN code capable of simulating High Charge (Z) and Energy (HZE) and light ions (including neutrons) under space-like boundary conditions with enhanced neutron and light ion propagation was recently developed for a simple homogeneous shield object. Monte Carlo benchmarks were used to verify the methodology in slab and spherical geometry, and the 3D corrections were shown to provide significant improvement over the straight-ahead approximation in some cases. In the present report, the new algorithms with well-defined convergence criteria are extended to inhomogeneous media within a shielded tissue slab and a shielded tissue sphere and tested against Monte Carlo simulation to verify the solution methods. The 3D corrections are again found to more accurately describe the neutron and light ion fluence spectra as compared to the straight-ahead approximation. These computationally efficient methods provide a basis for software capable of space shield analysis and optimization.

Wilson, John W.↗
DOE OSTI2022

Ensemble approximate control variate estimators: Applications to multi-fidelity importance sampling.

The recent growth in multifidelity uncertainty quantification has given rise to a large set of variance reduction techniques that leverage information from model ensembles to provide variance reduction for estimates of the statistics of a high-fidelity model. In this paper we provide two contributions: (1) we utilize an ensemble estimator to account for uncertainties in the optimal weights of approximate control variate (ACV) approaches and derive lower bounds on the number of samples required to guarantee variance reduction; and (2) we extend an existing multifidelity importance sampling (MFIS) scheme to leverage control variates. Our approach directly addresses a limitation of many multifidelity sampling strategies that require the usage of pilot samples to estimate covariances. As such we make significant progress towards both increasing the practicality of approximate control variates—for instance, by accounting for the effect of pilot samples—and using multifidelity approaches more effectively for estimating low-probability events. The numerical results indicate our hybrid MFIS-ACV estimator achieves up to 50% improvement in variance reduction over the existing state-of-the-art MFIS estimator, which had already shown an outstanding convergence rate compared to the Monte Carlo method, on several problems of computational mechanics.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1977

Computation of viscous transonic flow about a lifting airfoil

The Reynolds averaged Navier-Stokes equations are solved numerically for the viscous transonic flow about a stationary NACA 64A010 airfoil in free air. This paper presents descriptions of the numerical method, turbulence models employed, and boundary conditions appropriate to simulation of free-air flight. Computed results are presented for the airfoil at a free-stream Mach number of 0.8, angles of attack of 0 and 2 deg, and a Reynolds number based on a chord of 4 x 10 to the 6th. For the lifting case, unsteady periodic motion was calculated along the aft portion of the airfoil and in its wake. Recent experimental results obtained by Johnson indicate periodicity aft of the shock closely approximates the computed frequency, but the amplitude of the disturbances was significantly less than the calculated amplitude.

Walitt, L.↗
DOE OSTI2016

An Algebraic Multilevel Preconditioner with Low-Rank Corrections for Sparse Symmetric Matrices

In this work, we describe a multilevel preconditioning technique for solving sparse symmetric linear systems of equations. This “Multilevel Schur Low-Rank” (MSLR) preconditioner first builds a tree structure $\mathcal{T}$ based on a hierarchical decomposition of the matrix and then computes an approximate inverse of the original matrix level by level. Unlike classical direct solvers, the construction of the MSLR preconditioner follows a top-down traversal of $\mathcal{T}$ and exploits a low-rank property that is satisfied by the difference between the inverses of the local Schur complements and specific blocks of the original matrix. A few steps of the generalized Lanczos tridiagonalization procedure are applied to capture most of this difference. Numerical results are reported to illustrate the efficiency and robustness of the MSLR preconditioner with both two- and three-dimensional discretized PDE problems and with publicly available test problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Computational and analytical comparison of flux discretizations for the semiconductor device equations beyond Boltzmann statistics

We compare three thermodynamically consistent numerical fluxes known in the literature, appearing in a Voronoï finite volume discretization of the van Roosbroeck system with general charge carrier statistics. Our discussion includes an extension of the Scharfetter–Gummel scheme to non-Boltzmann (e.g. Fermi–Dirac) statistics. It is based on the analytical solution of a two-point boundary value problem obtained by projecting the continuous differential equation onto the interval between neighboring collocation points. Hence, it serves as a reference flux. The exact solution of the boundary value problem can be approximated by computationally cheaper fluxes which modify certain physical quantities. One alternative scheme averages the nonlinear diffusion (caused by the non-Boltzmann nature of the problem), another one modifies the effective density of states. To study the differences between these three schemes, we analyze the Taylor expansions, derive an error estimate, visualize the flux error and show how the schemes perform for a carefully designed p-i-n benchmark simulation. We present strong evidence that the flux discretization based on averaging the nonlinear diffusion has an edge over the scheme based on modifying the effective density of states.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Coupled Experiment and Theory to Explore the Limits of Material Strength at High Strain Rates

Critical components such as detonators in Sandia's stockpile are heterogeneous materials that rely on accurate constitutive models for each material used in the component. However, experiments to study materials at high pressure are challenging and time consumptive, therefore we turn to modeling tools to refine and predict outcomes beforehand. Efficient models balance absolute physical accuracy against approximate but computationally lightweight constitutive inputs. By using a relatively small number of high fidelity simulations and experiments we have be able to broaden the predictive power of the shock response in metals and polymers. We have tailored the analysis of these simulations to determine a size dependent material strength, which can be used as constitutive model inputs for continuum hydrodynamics codes. For the shocked Cu, MD simulations show a yield strength from RMI jet growth of approximately 450MPa that depends on the details of the free surface geometry. This value is close to the yield strength of 500MPa parameterized for an elastic-perfectly-plastic strength model from experiments at the Dynamic Compression Sector at Argonne National Lab. The same analysis applied to MD simulations of PMMA jetting resulted in no clear determination of yield strength, implying a more complex RMI process in polymeric materials. Atomistic simulations of both materials are shown to be valuable training metrics and show the need for explicit strain rate dependent strength for future improvements in strength models used in continuum codes.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Approximation of functions and their conjugates in variable Lebesgue spaces

One-sided Steklov means are used to introduce moduli of continuity of natural order in variable L{sub 2π}{sup p(⋅)}-spaces. A direct theorem of Jackson- Stechkin type and an inverse theorem of Salem-Stechkin type are given. Similar results are obtained for the conjugate functions. Bibliography: 24 titles. (paper)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A new modified BFGS method for unconstrained optimization problems

Using chain rule, we propose a modified secant equation to get a more accurate approximation of the second curvature of the objective function. Then, based on this modified secant equation we present a new BFGS method for solving unconstrained optimization problems. The proposed method makes use of both gradient and function values, and utilizes information from two most recent steps, while the usual secant relation uses only the latest step information. Under appropriate conditions, we show that the proposed method is globally convergent without convexity assumption on the objective function. Comparative numerical results show computational efficiency of the proposed method in the sense of the Dolan–Moré performance profiles.

97 MATHEMATICS AND COMPUTING↗