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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 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

A fourth-order phase-field fracture model: Formulation and numerical solution using a continuous/discontinuous Galerkin method

Modeling crack initiation and propagation in brittle materials is of great importance to be able to predict sudden loss of load-carrying capacity and prevent catastrophic failure under severe dynamic loading conditions. Second-order phase-field fracture models have gained wide adoption given their ability to capture the formation of complex fracture patterns, e.g. via crack merging and branching, and their suitability for implementation within the context of the conventional finite element method. Higher-order phase-field models have also been proposed to increase the regularity of the exact solution and thus increase the spatial convergence rate of its numerical approximation. However, they require special numerical techniques to enforce the necessary continuity of the phase field solution. In this paper, we derive a fourth-order phase-field model of fracture in two independent ways; namely, from Hamilton’s principle and from a higher-order micromechanics-based approach. The latter approach is novel, and provides a physical interpretation of the higher-order terms in the model. In addition, we propose a continuous/discontinuous Galerkin (C/DG) method for use in computing the approximate phase-field solution. This method employs Lagrange polynomial shape functions to guarantee -continuity of the solution at inter-element boundaries, and enforces the required regularity with the aid of additional variational and interior penalty terms in the weak form. Finally, the phase-field equation is coupled with the momentum balance equation to model dynamic fracture problems in hyper-elastic materials. Two benchmark problems are presented to compare the numerical behavior of the C/DG method with mixed finite element methods.

42 ENGINEERING↗
NASA NTRS1975

Comparison of techniques for approximating ocean bottom topography in a wave-refraction computer model

A study of the effects of using different methods for approximating bottom topography in a wave-refraction computer model was conducted. Approximation techniques involving quadratic least squares, cubic least squares, and constrained bicubic polynomial interpolation were compared for computed wave patterns and parameters in the region of Saco Bay, Maine. Although substantial local differences can be attributed to use of the different approximation techniques, results indicated that overall computed wave patterns and parameter distributions were quite similar.

Poole, L. R.↗
DOE OSTI2020

Approximate inverse-based block preconditioners in poroelasticity

We focus on the fully implicit solution of the linear systems arising from a three-field mixed finite element approximation of Biot’s poroleasticity equations. The objective is to develop algebraic block preconditioners for the efficient solution of such systems by Krylov subspace methods. In this work, we investigate the use of approximate inverse-based techniques to decouple the native system of equations and obtain explicit sparse approximations of the Schur complements related to the physics-based partitioning of the unknowns by field type. Here, the proposed methods are tested in various numerical experiments including real-world applications dealing with petroleum and geotechnical engineering.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

The stabilized mixed finite element scheme of elasticity problem

In this paper, we consider a new mixed finite element scheme of the elasticity problem in two and three dimensions, and the new scheme can impose Neumann boundary condition directly. A new stabilized method is proposed for this scheme, in which the equal order linear element pair is employed to approximate the stress and displacement, and an abstract operator is used to characterize the lack of the inf-sup condition. The new stabilized method is locking free. Numerical results show the excellent stability and accuracy of the new method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Analytical Modeling of Triple-Metal Hetero-Dielectric DG SON TFET

In this paper, a 2-D analytical model of triple-metal hetero-dielectric DG TFET is presented by combining the concepts of triple material gate engineering and hetero-dielectric engineering. Three metals with different work functions are used as both front- and back gate electrodes to modulate the barrier at source/channel and channel/drain interface. In addition to this, front gate dielectric consists of high-K HfO{sub 2} at source end and low-K SiO{sub 2} at drain side, whereas back gate dielectric is replaced by air to further improve the ON current of the device. Surface potential and electric field of the proposed device are formulated solving 2-D Poisson’s equation and Young’s approximation. Based on this electric field expression, tunneling current is obtained by using Kane’s model. Several device parameters are varied to examine the behavior of the proposed device. The analytical model is validated with TCAD simulation results for proving the accuracy of our proposed model.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

On a stochastic approach to a code performance estimation

The main goal of an efficient profiling of software is to minimize the runtime overhead under certain constraints and requirements. The traces built by a profiler during the work, affect the performance of the system itself. One of important aspect of an overhead arises from the randomness of variability in the context in which the application is embedded, e.g., due to possible cache misses, etc. Such uncertainty needs to be taken into account in the design phase. In order to overcome these difficulties we propose to investigate this issue through the analysis of the probability distribution of the difference between profiler’s times for the same code. The approximating model is based on the finite normal mixtures within the framework of the method of moving separation of mixtures. We demonstrate some results for the MATLAB profiler using plotting of 3D surfaces by the function surf. The idea can be used for an estimating of a program efficiency.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Superconvergence results of Legendre spectral projection methods for Volterra integral equations of second kind

In this paper, Legendre spectral projection methods are applied for the Volterra integral equations of second kind with a smooth kernel. We prove that the approximate solutions of the Legendre Galerkin and Legendre collocation methods converge to the exact solution with the order O(n{sup −r}) in L{sup 2}-norm and order O(n{sup −r+(1/2)}) in infinity norm, and the iterated Legendre Galerkin solution converges with the order O(n{sup −2r}) in both L{sup 2}-norm and infinity norm, whereas the iterated Legendre collocation solution converges with the order O(n{sup −r}) in both L{sup 2}-norm and infinity norm, n being the highest degree of Legendre polynomials employed in the approximation and r being the smoothness of the kernels. We have also considered multi-Galerkin method and its iterated version, and prove that the iterated multi-Galerkin solution converges with the order O(n{sup −3r}) in both infinity and L{sup 2} norm. Numerical examples are given to illustrate the theoretical results.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Applying Legendre wavelet method with Tikhonov regularization for one-dimensional time-fractional diffusion equations

In this paper, a new method based on two-dimensional Legendre wavelet basis is proposed to solve time-fractional diffusion equations. This technique is used to convert the problem into a system of linear algebraic equations via expanding the required approximation based on the Legendre wavelet basis. The effectiveness of the proposed method is examined by comparing the numerical results with other methods. When the desired system is large, it is ill-conditioned; in this case, Tikhonov regularization method, with discrepancy principle for finding the regularization parameter, is applied to stabilize the solution.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

An Efficient Time-Domain Model to Simulate Parametric Resonances in a Floating Body Free to Move in Six Degrees of Freedom: Preprint

We present a computationally efficient time-domain model capable of simulating parametric resonances in a floating body in waves. The model assumes all wave forces to be linear, but the inertia and restoring forces acting on the body are expanded to second order in body motions. The simulation speed on a standard computer is approximately 40 times faster than real time. The model is applied to a soft-moored floating axisymmetric body which absorbs energy through heave, but is otherwise free to move in six degrees of freedom. Under certain conditions, we show that the body responds parametrically with large amplitudes not only in surge and pitch, but also in sway, roll, and yaw, provided it is given some small initial displacement in one of these out-of-plane modes. The predictions are confirmed by simulations using state-of-the-art nonlinear Froude-Krylov and computational fluid dynamics models.

parametric resonance↗
DOE OSTI2018

On differential singular perturbation problems: a simple variational approach

An alternative approach for the analysis and the numerical approximation of singular perturbation problems, using a variational framework, is presented. It is based on the natural idea of minimizing the residual of the differential equation measured in the L{sup 2} norm. By this strategy, the approximation is based in the solution of a set of linear problems giving the descent step directions of the problem. This is the main advantage of our approach, since we can use stable and convergent methods for linear problems (without assuming the knowledge of good initial guesses used in the approximation of the associated non-linear systems necessary in Newton-type methods). Remember that for this type of problems, we should use implicit methods. We prove that our procedure can never get stuck in local minima, and the error decreases until getting to the original solution independent of the perturbation parameter. Finally, we include some numerical examples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Stabilization of model-based networked control systems

A class of networked control systems called Model-Based Networked Control Systems (MB-NCSs) is considered. Stabilization of MB-NCSs is studied using feedback controls and simulation of stabilization for different feedbacks is made with the purpose to reduce the network trafic. The feedback control input is applied in a compensated model of the plant that approximates the plant dynamics and stabilizes the plant even under slow network conditions. Conditions for global exponential stabilizability and for the choosing of a feedback control input for a given constant time between the information moments of the network are derived. An optimal control problem to obtain an optimal feedback control is also presented.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Communication: Rotational excitation of HCl by H: Rigid rotor vs. reactive approaches

We report fully quantum time-independent calculations of cross sections for the collisional excitation of HCl by H, an astrophysically relevant process. Our calculations are based on the Bian-Werner ClH{sub 2} potential energy surface and include the possibility of HCl destruction through reactive collisions. The strongest collision-induced rotational HCl transitions are those with Δj = 1, and the magnitude of the HCl-H inelastic cross sections is of the same order of magnitude as the HCl-H{sub 2} ones. Results of exact calculations, i.e., including the reactive channels, are compared to pure inelastic calculations based on the rigid rotor approximation. A very good agreement is found between the two approaches over the whole energy range 10–3000 cm{sup −1}. At the highest collisional energies, where the reaction takes place, the rigid rotor approach slightly overestimates the cross sections, as expected. Hence, the rigid rotor approach is found to be reliable at interstellar temperatures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

MOC Efficiency Improvements Using a Jacobi Inscatter Approximation

In recent weeks, attention has been given to resolving the convergence issues encountered with TCP 0 by trying a Jacobi (J) inscatter approach when group sweeping, where the inscatter source is constructed using the previous iteration flux. This is in contrast to a Gauss-Seidel (GS) approach, which has been the default to-date, where the scattering source uses the most up-to-date flux values. The former is consistent with CASMO, which has no issues with TCP 0 convergence. Testing this out on a variety of problems has demonstrated that the Jacobi approach does indeed provide substantially more stability, though can take more outer iterations to converge. While this is not surprising, there are improvements that can be made to the MOC sweeper to capitalize on the Jacobi approximation and provide substantial speedup. For example, the loop over groups, which has traditionally been the outermost loop in MPACT, can be moved to the interior, avoiding duplicate modular ray trace and coarse ray trace setup (mapping coarse mesh surface indexes), which needs to be performed repeatedly when group is outermost.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2015

Reduced density-matrix functional theory: Correlation and spectroscopy

In this work, we explore the performance of approximations to electron correlation in reduced density-matrix functional theory (RDMFT) and of approximations to the observables calculated within this theory. Our analysis focuses on the calculation of total energies, occupation numbers, removal/addition energies, and spectral functions. We use the exactly solvable Hubbard dimer at 1/4 and 1/2 fillings as test systems. This allows us to analyze the underlying physics and to elucidate the origin of the observed trends. For comparison, we also report the results of the GW approximation, where the self-energy functional is approximated, but no further hypothesis is made concerning the approximations of the observables. In particular, we focus on the atomic limit, where the two sites of the dimer are pulled apart and electrons localize on either site with equal probability, unless a small perturbation is present: this is the regime of strong electron correlation. In this limit, using the Hubbard dimer at 1/2 filling with or without a spin-symmetry-broken ground state allows us to explore how degeneracies and spin-symmetry breaking are treated in RDMFT. We find that, within the used approximations, neither in RDMFT nor in GW, the signature of strong correlation is present, when looking at the removal/addition energies and spectral function from the spin-singlet ground state, whereas both give the exact result for the spin-symmetry broken case. Moreover, we show how the spectroscopic properties change from one spin structure to the other.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Lensing substructure quantification in RXJ1131-1231: a 2 keV lower bound on dark matter thermal relic mass

We study the substructure content of the strong gravitational lens RXJ1131-1231 through a forward modelling approach that relies on generating an extensive suite of realistic simulations. We use a semi-analytic merger tree prescription that allows us to stochastically generate substructure populations whose properties depend on the dark matter particle mass. These synthetic halos are then used as lenses to produce realistic mock images that have the same features, e.g. luminous arcs, quasar positions, instrumental noise and PSF, as the data. We then analyse the data and the simulations in the same way with summary statistics that are sensitive to the signal being targeted and are able to constrain models of dark matter statistically using Approximate Bayesian Computing (ABC) techniques. (In this work, we focus on the thermal relic mass estimate and fix the semi-analytic descriptions of the substructure evolution based on recent literature.) We are able, based on the HST data for RXJ1131-1231, to rule out a warm dark matter thermal relic mass below 2 keV at the 2σ confidence level.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Fully discrete schemes for monotone optimal control problems

In this article, we study an infinite horizon optimal control problem with monotone controls. We analyze the associated Hamilton–Jacobi–Bellman (HJB) variational inequality which characterizes the value function and consider the totally discretized problem using Lagrange elements to approximate the state space Ω. The convergence orders of these approximations are proved, which are in general (h+(k/(√h))){sup γ} where γ is the Hölder constant of the value function u, h and k are the time and space discretization parameters, respectively. A special election of the relations between h and k allows to obtain a convergence of order k{sup (2/3)γ}, which is valid without semiconcavity hypotheses over the problem’s data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Response analysis of a class of quasi-linear systems with fractional derivative excited by Poisson white noise

The Poisson white noise, as a typical non-Gaussian excitation, has attracted much attention recently. However, little work was referred to the study of stochastic systems with fractional derivative under Poisson white noise excitation. This paper investigates the stationary response of a class of quasi-linear systems with fractional derivative excited by Poisson white noise. The equivalent stochastic system of the original stochastic system is obtained. Then, approximate stationary solutions are obtained with the help of the perturbation method. Finally, two typical examples are discussed in detail to demonstrate the effectiveness of the proposed method. The analysis also shows that the fractional order and the fractional coefficient significantly affect the responses of the stochastic systems with fractional derivative.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗