Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Quadrature”

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.

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

At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Evaluation of the Abel inversion integral in O-mode plasma reflectometry using Chebyshev–Gauss quadrature

The Abel transform is often used to reconstruct plasma density profiles from O-Mode polarized reflectometry diagnostics. However, standard numerical trapezoidal evaluation of the Abel inversion integral can be computationally expensive for a large number of evaluation points, and an endpoint singularity exists on the upper-bound of the integral, which can result in an increased error. In this work, Chebyshev–Gauss quadrature is introduced as a new method to evaluate the Abel inversion integral for the problem of O-Mode plasma reflectometry. Here, the method does not require numerical evaluation of an integral singularity and is shown to have similar accuracy compared to existing methods while being computationally efficient.

47 OTHER INSTRUMENTATION↗
DOE OSTI2022

Monolithic Multigrid for a Reduced-Quadrature Discretization of Poroelasticity

Advanced finite-element discretizations and preconditioners for models of poroelasticity have attracted significant attention in recent years. The equations of poroelasticity offer significant challenges in both areas, due to the potentially strong coupling between unknowns in the system, saddle-point structure, and the need to account for wide ranges of parameter values, including limiting behavior such as incompressible elasticity. This paper was motivated by an attempt to develop monolithic multigrid preconditioners for the discretization developed in [C. Rodrigo et al., Comput. Methods App. Mech. Engrg, 341 (2018), pp. 467--484]; we show here why this is a difficult task and, as a result, we modify the discretization in [Rodrigo et al.] through the use of a reduced-quadrature approximation, yielding a more “solver-friendly” discretization. Local Fourier analysis is used to optimize parameters in the resulting monolithic multigrid method, allowing a fair comparison between the performance and costs of methods based on Vanka and Braess--Sarazin relaxation. Further, numerical results are presented to validate the local Fourier analysis predictions and demonstrate efficiency of the algorithms. Finally, a comparison to existing block-factorization preconditioners is also given.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Efficient quadrature rules for finite element discretizations of nonlocal equations

In this paper we design efficient quadrature rules for finite element discretizations of nonlocal diffusion problems with compactly supported kernel functions. Two of the main challenges in nonlocal modeling and simulations are the prohibitive computational cost and the nontrivial implementation of discretization schemes, especially in three-dimensional settings. In this work we circumvent both challenges by introducing a parametrized mollifying function that improves the regularity of the integrand, utilizing an adaptive integration technique, and exploiting parallelization. We first showthat the “mollified” solution converges to the exact one as the mollifying parameter vanishes, then we illustrate the consistency and accuracy of the proposed method on several two- and three-dimensional test cases. Furthermore, we demonstrate the good scaling properties of the parallel implementation of the adaptive algorithm and we compare the proposed method with recently developed techniques for efficient finite element assembly.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Ultra-broadband quadrature squeezing with thin-film lithium niobate nanophotonics

Squeezed light is a key quantum resource that enables quantum advantages for sensing, networking, and computing applications. The scalable generation and manipulation of squeezed light with integrated platforms are highly desired for the development of quantum technology with continuous variables. In this Letter, we demonstrate squeezed light generation with thin-film lithium niobate integrated photonics. Parametric down-conversion is realized with quasi-phase matching using ferroelectric domain engineering. With sub-wavelength mode confinement, efficient nonlinear processes can be observed with single-pass configuration. We measure 0.56 ± 0.09 dB quadrature squeezing (∼2.6 dB inferred on-chip). The single-pass configuration further enables the generation of squeezed light with large spectral bandwidth up to 7 THz. This work represents a significant step towards the on-chip implementation of continuous-variable quantum information processing.

Chen, Pao-Kang↗
DOE OSTI2023

Adaptive Angular Quadrature Scheme for a backwards-in-time Method of Characteristics Solution to the Radiative Transfer Equation [Slides]

Radiative transfer/radiation transport are important problems to solve in astrophysics and high energy density physics. Various methods exist to solve radiation transport, such as Monte Carlo (MC), Discrete Ordinates (S N ), Method of Characteristics (MOC), and the spherical harmonics (P N ) method. Method of Characteristics requires “launching” of rays in discrete directions. Unresolved details of angular mesh create ray effects and can miss sources in the domain. Ray effects can lead to unphysical “stepping” in solution and incorrect energy deposition. Adaptive quadrature schemes can be used to detect and mitigate these effects. The Method of Characteristics (MOC) is a common method for solving hyperbolic PDEs in radiation transport and supersonic flow problems. Generally in MOC for radiation transport, virtual particles are tracked from birth to the end of a timestep. This requires interpolation to go from final location to cell averaged or corner values of angular intensity. Backwards-in-Time (BIT) particle tracking avoids this by prescribing the final position of the virtual particle at the cell nodes/corners. Angular intensities are computed at time k + 1 by launching ray back to previous timestep(s), or t = 0. Scheme allows solution to be computed as the characteristic ray is traced backwards in time.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Hybrid Entanglement between Optical Discrete Polarizations and Continuous Quadrature Variables

By coherently combining advantages while largely avoiding limitations of two mainstream platforms, optical hybrid entanglement involving both discrete and continuous variables has recently garnered widespread attention and emerged as a promising idea for building heterogenous quantum networks. In contrast to previous results, here we propose a new scheme to remotely generate hybrid entanglement between discrete polarization and continuous quadrature optical qubits heralded by two-photon Bell-state measurement. As a novel nonclassical light resource, we further use it to discuss two examples of ways—entanglement swapping and quantum teleportation—in which quantum information processing and communications could make use of this hybrid technique.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

A multi-center quadrature scheme for the molecular continuum

We report a common way to evaluate electronic integrals for polyatomic molecules is to use Becke’s partitioning scheme (Becke and Chem, 1988) in conjunction with overlapping grids centered at each atomic site. The Becke scheme was designed for integrands that fall off rapidly at large distances, such as those approximating bound electronic states. When applied to states in the electronic continuum, however, Becke scheme exhibits slow convergence and it is highly redundant. Here, we present a modified version of Becke scheme that is applicable to functions of the electronic continuum, such as those involved in molecular photoionization and electron–molecule scattering, and which ensures convergence and efficiency comparable to those realized in the calculation of bound states. In this modified scheme, the atomic weights already present in Becke’s partition are smoothly switched off within a range of few bond lengths from their respective nuclei, and complemented by an asymptotically unitary weight. The atomic integrals are evaluated on small spherical grids, centered on each atom, with size commensurate to the support of the corresponding atomic weight. The residual integral of the interstitial and long-range region is evaluated with a central master grid. The accuracy of the method is demonstrated by evaluating integrals involving integrands containing Gaussian Type Orbitals and Yukawa potentials, on the atomic sites, as well as spherical Bessel functions centered on the master grid. These functions are representative of those encountered in realistic electron-scattering and photoionization calculations in polyatomic molecules.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗