SEARCH · Engineering Papers

Results for “Bernstein polynomials”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

7 records

All sources NASA NTRS DOE OSTI

DOE OSTI2026

Polynomial range estimation as a troubled-cell indicator for high-order methods

Two troubled-cell indicators based on polynomial range estimation methods are used to flag cells that may violate positivity constraints. One method uses interval extension, and the second uses the range enclosure property of the Bernstein polynomial basis. Furthermore, both methods reduce compute time for the positivity preserver by limiting its application to a subset of cells. The Bernstein polynomial method remains effective as the problem dimensionality increases. Interval extension applied to the internal energy equation permits the use of the troubled-cell indicators for rational functions, though performance suffers compared to directly applying the indicators to polynomial functions.

42 ENGINEERING↗

DOE OSTI2025

A method for bounding high-order finite element functions: Applications to mesh validity and bounds-preserving limiters

We introduce a novel method for bounding high-order multi-dimensional polynomials in finite element approximations. The method involves precomputing optimal piecewise-linear bounding boxes for polynomial basis functions, which can then be used to locally bound any combination of these basis functions. This approach can be applied to any element/basis type at any approximation order, can provide local (i.e., subcell) extremum bounds to a desired level of accuracy, and can be evaluated efficiently on-the-fly in simulations. Furthermore, we show that this approach generally yields more accurate bounds in comparison to traditional methods based on convex hull properties (e.g., Bernstein polynomials). Furthermore, the efficacy of this technique is shown in applications such as mesh validity checks and optimization for high-order curved meshes, where positivity of the element Jacobian determinant can be ensured throughout the entire element, and continuously bounds-preserving limiters for hyperbolic systems, which can enforce maximum principle bounds across the entire solution polynomial.

Bounding box↗

DOE OSTI2020

Continuous-time look-ahead flexible ramp scheduling in real-time operation

This paper develops a novel continuous-time look-ahead optimization model for co-optimizing balancing energy and flexible ramp products in real-time power systems operation. In addition, a continuous-time day-ahead operation model is developed to commit and schedule an adequate subset of generating units for providing balancing energy and ramping requirements in real-time operation. The up and down flexible ramp products are defined as continuous-time decision trajectories that continuously supply the real-time up and down ramping requirements of the system. The deliverability of flexible ramp products is secured through reserving the respective power requirements in generation capacity constraints of generating units. A function space solution method is proposed to reduce the dimensionality of day-ahead and real-time models through projecting them into finite-dimensional function spaces spanned by Bernstein polynomials, where the real-time operation decisions are modeled with a higher accuracy level than day-ahead decisions. Simulations are conducted on the IEEE-RTS system using CAISO load data, and the numerical results showcase the effectiveness of the proposed model in supplying the energy and flexible ramp requirements and avoiding ramping scarcity in the system, while reducing the operation costs.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2020

Data-driven learning of nonlocal models: from high-fidelity simulations to constitutive laws

We show that machine learning can improve the accuracy of simulations of stress waves in one-dimensional composite materials. We propose a data-driven technique to learn nonlocal constitutive laws for stress wave propagation models. The method is an optimization-based technique in which the nonlocal kernel function is approximated via Bernstein polynomials. The kernel, including both its functional form and parameters, is derived so that when used in a nonlocal solver, it generates solutions that closely match high-fidelity data. The optimal kernel therefore acts as a homogenized nonlocal continuum model that accurately reproduces wave motion in a smaller-scale, more detailed model that can include multiple materials. We apply this technique to wave propagation within a heterogeneous bar with a periodic microstructure. Several one-dimensional numerical tests illustrate the accuracy of our algorithm. The optimal kernel is demonstrated to reproduce high-fidelity data for a composite material in applications that are substantially different from the problems used as training data.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Matrix-free subcell residual distribution for Bernstein finite elements: Monolithic limiting

This paper is focused on the aspects of limiting in residual distribution (RD) schemes for high-order finite element approximations to advection problems. Both continuous and discontinuous Galerkin methods are considered in this work. Discrete maximum principles are enforced using algebraic manipulations of element contributions to the global nonlinear system. The required modifications can be carried out without calculating the element matrices and assembling their global counterparts. The components of element vectors associated with the standard Galerkin discretization are manipulated directly using localized subcell weights to achieve optimal accuracy. Low-order nonlinear RD schemes of this kind were originally developed to calculate local extremum diminishing predictors for flux-corrected transport (FCT) algorithms. In the present paper, we incorporate limiters directly into the residual distribution procedure, which makes it applicable to stationary problems and leads to well-posed nonlinear discrete problems. To circumvent the second-order accuracy barrier, the correction factors of monolithic limiting approaches and FCT schemes are adjusted using smoothness sensors based on second derivatives. Finally, the convergence behavior of presented methods is illustrated by numerical studies for two-dimensional test problems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

The complexity of NISQ

Abstract The recent proliferation of NISQ devices has made it imperative to understand their power. In this work, we define and study the complexity class , which encapsulates problems that can be efficiently solved by a classical computer with access to noisy quantum circuits. We establish super-polynomial separations in the complexity among classical computation, , and fault-tolerant quantum computation to solve some problems based on modifications of Simon’s problems. We then consider the power of for three well-studied problems. For unstructured search, we prove that cannot achieve a Grover-like quadratic speedup over classical computers. For the Bernstein-Vazirani problem, we show that only needs a number of queries logarithmic in what is required for classical computers. Finally, for a quantum state learning problem, we prove that is exponentially weaker than classical computers with access to noiseless constant-depth quantum circuits.

42 ENGINEERING↗

DOE OSTI2024

Determination of short- and long-distance contributions in B 0 → K * 0 μ + μ − decays

An amplitude analysis of the B 0 → K * 0 μ + μ − decay is presented. The analysis is based on data collected by the LHCb experiment from proton-proton collisions at s = 7 , 8 and 13 TeV, corresponding to an integrated luminosity of 4.7 fb − 1 . For the first time, Wilson coefficients and nonlocal hadronic contributions are accessed directly from the unbinned data, where the latter are parametrized as a function of q 2 with a polynomial expansion. Wilson coefficients and nonlocal hadronic parameters are determined under two alternative hypotheses: the first relies on experimental information alone, while the second one includes information from theoretical predictions for the nonlocal contributions. Both models obtain similar results for the parameters of interest. The overall level of compatibility with the Standard Model is evaluated to be between 1.8 and 1.9 standard deviations when looking at the C 9 Wilson coefficient alone, and between 1.3 and 1.4 standard deviations when considering the full set of C 9 , C 10 , C 9 ′ and C 10 ′ Wilson coefficients. The ranges reflect the theoretical assumptions made in the analysis. © 2024 CERN, for the LHCb Collaboration 2024 CERN

Aaij, R. (ORCID:0000000305331952)↗