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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 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
NASA NTRS1997

A High-Order Direct Solver for Helmholtz Equations with Neumann Boundary Conditions

In this study, a compact finite-difference discretization is first developed for Helmholtz equations on rectangular domains. Special treatments are then introduced for Neumann and Neumann-Dirichlet boundary conditions to achieve accuracy and separability. Finally, a Fast Fourier Transform (FFT) based technique is used to yield a fast direct solver. Analytical and experimental results show this newly proposed solver is comparable to the conventional second-order elliptic solver when accuracy is not a primary concern, and is significantly faster than that of the conventional solver if a highly accurate solution is required. In addition, this newly proposed fourth order Helmholtz solver is parallel in nature. It is readily available for parallel and distributed computers. The compact scheme introduced in this study is likely extendible for sixth-order accurate algorithms and for more general elliptic equations.

Sun, Xian-He↗
NASA NTRS2003

Validation of a High-Order Prefactored Compact Code on Nonlinear Flows with Complex Geometries

A finite-difference time domain solution of the airfoil gust problem is obtained using a high-accuracy nonlinear computational aeroacoustics code. For computational efficiency, the equations are cast in chain-rule curvilinear form, and a structured multiblock solver is used in parallel. In order to fully investigate the performance of this solver, a test matrix of eight problems are computed (two airfoil geometries, two gust frequencies, and two gust configurations). These results are compared to solutions obtained by the GUST3D frequency-domain solver both on the airfoil surface and in the far field. Grid density and domain size studies are included.

Hixon, R.↗
DOE OSTI2020

Multiscale modeling high-order methods and data-driven modeling

Projection-based reduced-order models (ROMs) comprise a promising set of data-driven approaches for accelerating the simulation of high-fidelity numerical simulations. Standard projection-based ROM approaches, however, suffer from several drawbacks when applied to the complex nonlinear dynamical systems commonly encountered in science and engineering. These limitations include a lack of stability, accuracy, and sharp a posteriori error estimators. This work addresses these limitations by leveraging multiscale modeling, least-squares principles, and machine learning to develop novel reduced-order modeling approaches, along with data-driven a posteriori error estimators, for dynamical systems. Theoretical and numerical results demonstrate that the two ROM approaches developed in this work - namely the windowed least-squares method and the Adjoint Petrov - Galerkin method - yield substantial improvements over state-of-the-art approaches. Additionally, numerical results demonstrate the capability of the a posteriori error models developed in this work.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Optical high-order harmonic generation as a structural characterization tool

Structural characterization is essential to material engineering, but few tools can detect structural properties in the time domain. High harmonic generation (HHG) emerges as a new frontier that touches the heart of condensed-matter physics from the symmetry to quantum geometrical nature of electrons, but its capability in structural characterization has not been materialized. Here, we establish a crucial connection between the symmetry of a material and the helicity of light. We employ monolayer MoS 2 as an example. In this work, we show that a linearly polarized laser pulse used in experiments is not ideal for structural characterization because it only generates in-plane anisotropy. It is the circularly polarized laser field that is capable of producing four distinctive HHG signals from the four phases of MoS 2 . This finally links the laser helicity to the crystal structure. The results are generic and are not affected by the Berry curvature, the interband or intraband contribution. Our study unleashes the power of HHG as a structural characterization tool for technologically important materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Fourier Analyses of High-Order Continuous and Discontinuous Galerkin Methods

In this paper, we present a Fourier analysis of wave propagation problems subject to a class of continuous and discontinuous discretizations using high-degree Lagrange polynomials. This allows us to obtain explicit analytical formulas for the dispersion relation and group velocity and, for the first time to our knowledge, characterize analytically the emergence of gaps in the dispersion relation at specific wavenumbers, when they exist, and compute their specific locations. Wave packets with energy at these wavenumbers will fail to propagate correctly, leading to significant numerical dispersion. We also show that the Fourier analysis generates mathematical artifacts, and we explain how to remove them through a branch selection procedure conducted by analysis of eigenvectors and associated reconstructed solutions. The higher frequency eigenmodes, named erratic in this study, are also investigated analytically and numerically.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

High-throughput computational framework for high-order anharmonic thermal transport in cubic and tetragonal crystals

Accurate first-principles prediction of lattice thermal conductivity (κL) remains challenging in identifying materials with extreme thermal behavior. While the harmonic approximation with three-phonon scattering (HA + 3ph) is now routine, reliable κL prediction often requires higher-order anharmonic effects, including self-consistent phonon renormalization, three- and four-phonon scattering, and off-diagonal heat flux (SCPH + 3, 4ph + OD). We present a state-of-the-art high-throughput workflow that unifies these effects and apply it to 773 cubic and tetragonal crystals spanning diverse chemistries and structures. From 562 dynamically stable compounds, we assess the hierarchical impacts of higher-order anharmonicity. For around 60% of materials, HA + 3ph predictions closely match those from SCPH + 3, 4ph + OD. SCPH generally increases κ L , by over 8 times in extreme cases, whereas four-phonon scattering universally suppresses κ L , sometimes to 15% of the HA + 3ph value. Off-diagonal contributions are negligible in high-κ L systems but can rival diagonal terms in highly anharmonic low-κ L compounds. We highlight four case studies, Rb 2 TlAlH 6 , Cu 3 VSe 4 , CuBr, and KTlCl 4 , that exhibit distinct extreme behaviors. This work delivers not only a robust workflow for high-fidelity κL dataset but also a quantitative framework to determine when higher-order effects are essential. The hierarchy of κ L results, from the HA + 3ph to SCPH + 3, 4ph + OD level, offers a scalable, interpretable route to discovering next-generation extreme thermal materials.

36 MATERIALS SCIENCE↗
NASA NTRS1993

Some aspects of high-order numerical solutions of the linear convection equation with forced boundary conditions

A six-stage low-storage Runge-Kutta time-marching method is presented and shown to be an efficient method for use with high-accuracy spatial difference operators for wave propagation problems. The accuracy of the method for inhomogeneous ordinary differential equations is demonstrated through numerical solutions of the linear convection equation with forced boundary conditions. Numerical experiments are presented simulating a sine wave and a Gaussian pulse propagating into and through the domain. For practical levels of mesh refinement corresponding to roughly ten points per wavelength, the six-stage Runge-Kutta method is more accurate than the popular fourth-order Runge-Kutta method. Further numerical experiments are presented which show that the numerical boundary scheme at an inflow boundary can be a significant source of error when high-accuracy spatial discretizations are used.

Zingg, D. W.↗
DOE OSTI2021

Removal of correlated background in a high-order harmonic transient absorption spectra with principal component regression

We demonstrate a 40x mean noise power reduction (NPR) in core-to-valence extreme ultraviolet (XUV) femtosecond transient absorption spectroscopy with a high harmonic generation (HHG) light source. An adaptive iteratively reweighted principal component regression (airPCR) is used to analyze and suppress spectrally correlated HHG intensity fluctuations. The technique requires significantly less user input and leads to a higher mean NPR than a previously introduced edge-pixel PCR method that relies on the manual identification of signal-free spectral regions. Both techniques are applied in a time-resolved XUV absorption study of the 2 snp 1 P o ( n ≥ 2) autoionizing Rydberg states of helium, demonstrating sub-10 −3 optical density sensitivity.

Faccialà, Davide (ORCID:0000000250720394)↗
DOE OSTI2021

Parallel Algorithms for Efficient Computation of High-Order Line Graphs of Hypergraphs

This paper considers structures of systems beyond dyadic (pairwise) interactions and investigates mathematical modeling of multi-way interactions and connections as hypergraphs, where captured relationships among system entities are set-valued. To date, in most situations, entities in a hypergraph are considered connected as long as there is at least one common ``neighbor''. However, minimal commonality sometimes discards the ``strength'' of connections and interactions among groups. To this end, considering the ``width'' of a connection, referred to as the \emph{$s$-overlap} of neighbors, provides more meaningful insights into how closely the communities or entities interact with each other. In addition, $s$-overlap computation is the fundamental kernel to construct the line graph of a hypergraph, a low-order approximation of the hypergraph which can carry significant information about the original hypergraph. Subsequent stages of a data analytics pipeline then can apply highly-tuned graph algorithms on the line graph to reveal important features. Given a hypergraph, computing the $s$-overlaps by exhaustively considering all pairwise entities can be computationally prohibitive. To tackle this challenge, we develop efficient algorithms to compute $s$-overlaps and the corresponding line graph of a hypergraph. We propose several heuristics to avoid execution of redundant work and improve performance of the $s$-overlap computation. Our parallel algorithm, combined with these heuristics, is orders of magnitude (more than $10\times$) faster than the naive algorithm in all cases and the SpGEMM algorithm with filtration in most cases (especially with large $s$ value).

hypergraph algorithms, graph algorithms, parallel ↗
DOE OSTI2024

High‐Order Nonlinear Frequency Conversion in Transparent Conducting Oxide Thin Films

The study of conductive oxides has gained momentum within the photonics community due to their unique linear and nonlinear optical properties. Despite recent experiments reporting on high harmonic generation from thin films, the optical/electronic behavior of these compounds at the nanoscale is still not fully understood due to the lack of a suitable theoretical model. In the present work, aluminum zinc oxide is excited near its epsilon-near-zero crossing point using incident femtosecond pulses having peak power densities in the 1 TW cm −2 range. A relatively efficient frequency up-conversion including even and odd harmonics up to the seventh order is observed. A hydrodynamic-Maxwell theoretical approach is adopted, capable of simultaneously taking into account linear and nonlinear dispersions, nonlocal effects, surface, magnetic, and bulk nonlinearities in a spectral region that spans over two and a half octaves from the UV to the NIR region. The study enables a deeper understanding of the fundamental material parameters regulating optical nonlinearities, providing important insights to engineer this class of materials for applications in sensing, ultra-fast physics, and spectroscopy.

material modeling↗
DOE OSTI2020

Angle-resolved nonresonant two-photon single ionization of argon using 9.3-eV photons produced via high-order harmonic generation

Here we present an experimental study on the photoionization dynamics of nonresonant one-color two-photon single valence ionization of neutral argon atoms. Using 9.3-eV photons produced via high harmonic generation and a three-dimensional momentum imaging spectrometer, we detect the photoelectrons and ions produced from nonresonant two-photon ionization in coincidence. Photoionization from the $3p$ orbital produces a photoelectron scattering wave function with $p$- and $f$-partial-wave components, which interfere and result in a photoelectron angular distribution with peak amplitude perpendicular to the vacuum ultraviolet polarization. The comparison between the present results and the two previous sets of theoretical calculations [Phys. Rev. A 44, 324 (1991), and J. Phys. B: At. Mol. Phys. 16, 2737 (1983)] indicates that electron-electron correlation contributes appreciably to the two-photon ionization dynamics.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

High-Order Fractal Quantum Oscillations in Graphene/BN Superlattices in the Extreme Doping Limit

Recent studies of van der Waals (vdW) heterostructures and superlattices have shown intriguing quantum phenomena, but these have been largely explored only in the moderate carrier density regime. Here, we report the probe of high-temperature fractal Brown-Zak (BZ) quantum oscillations through magnetotransport in the extreme doping regimes by applying a newly developed electron beam doping technique. Further, this technique gives access to both ultrahigh electron and hole densities beyond the dielectric breakdown limit in graphene/BN superlattices, enabling the observation of nonmonotonic carrier-density dependence of fractal BZ states and up to fourth-order fractal BZ features despite strong electron-hole asymmetry. Theoretical tight-binding simulations qualitatively reproduce all observed fractal BZ features and attribute the nonmonotonic dependence to the weakening of superlattice effects at high carrier densities.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Accelerating high-order continuum kinetic plasma simulations using multiple GPUs

Kinetic plasma simulations solve the Vlasov-Poisson or Vlasov-Maxwell equations to evolve scalar-variable distribution functions in position-velocity phase space and vector-variable electromagnetic fields in configuration space. The immense computational cost of evolving high-dimensional variables, and their large number of degrees of freedom, often limits the utility of continuum kinetic simulations and presents a challenge when it comes to accurately simulating real-world physical phenomena. To address this challenge, we present techniques that accelerate and minimize the computational work required for a scalable Vlasov-Poisson solver. We show theoretical hardware compute and communication bounds for solving a fourth-order finite-volume Vlasov-Poisson system. These bounds are then used to inform and evaluate the design of performance portable algorithms for a multiple graphics processing unit (GPU) accelerated version of the Vlasov-Poisson solver VCK-CPU [1]. We demonstrate that the multi-GPU Vlasov solver implementation, VCK-GPU, simultaneously minimizes required inter-process data transfer while also being bounded by the machine network performance limits. This results in an overall strong scaling speedup per timestep of up to 40x in three-dimensional phase space (one position, two velocity coordinates) and 54x in four dimensional phase space (two position, two velocity coordinates) and a 341x increase in simulation throughput of the GPU accelerated code over the existing CPU code. The GPU code is also able to weak scale up to 256 compute nodes and 1024 GPUs. In conclusion, we demonstrate that the improved compute performance enables exploring configurations which were previously computationally infeasible, including resolving fine-scale distribution function filamentation and multi-species dynamics with realistic electron-proton mass ratios.

Continuum kinetics↗
NASA NTRS2008

High-Order Energy Stable WENO Schemes

A new third-order Energy Stable Weighted Essentially NonOscillatory (ESWENO) finite difference scheme for scalar and vector linear hyperbolic equations with piecewise continuous initial conditions is developed. The new scheme is proven to be stable in the energy norm for both continuous and discontinuous solutions. In contrast to the existing high-resolution shock-capturing schemes, no assumption that the reconstruction should be total variation bounded (TVB) is explicitly required to prove stability of the new scheme. A rigorous truncation error analysis is presented showing that the accuracy of the 3rd-order ESWENO scheme is drastically improved if the tuning parameters of the weight functions satisfy certain criteria. Numerical results show that the new ESWENO scheme is stable and significantly outperforms the conventional third-order WENO finite difference scheme of Jiang and Shu in terms of accuracy, while providing essentially nonoscillatory solutions near strong discontinuities.

Yamaleev, Nail K.↗
NASA NTRS2014

On the Computation of High Order Rys Quadrature Weights and Nodes

Since its introduction in 1976, the Rys Quadrature method has proven a very attractive method for evaluating electron repulsion integrals for calculations using Gaussian type orbitals. Since then, there have been considerable refinements of the method, but at it's core, Gaussian weights and nodes are used to exactly evaluate using a numerical approach to the transform integral. One of the powers of the Rys Quadrature method is the relative ease in evaluating integrals involving functions of high angular momentum. In this work we report on the complete resolution of these numerical difficulties, and we have easily computed accurate quadrature weights and nodes up to order 101. All calculations were carried out using 128-bit precision.

Computation↗
NASA NTRS2012

High Order Finite Difference Methods with Subcell Resolution for 2D Detonation Waves

In simulating hyperbolic conservation laws in conjunction with an inhomogeneous stiff source term, if the solution is discontinuous, spurious numerical results may be produced due to different time scales of the transport part and the source term. This numerical issue often arises in combustion and high speed chemical reacting flows.

Wang, W.↗
NASA NTRS2013

Performance of Improved High-Order Filter Schemes for Turbulent Flows with Shocks

The performance of the filter scheme with improved dissipation control κ has been demonstrated for different flow types. The scheme with local κ is shown to obtain more accurate results than its counterparts with global or constant κ. At the same time no additional tuning is needed to achieve high accuracy of the method when using the local κ technique. However, further improvement of the method might be needed for even more complex and/or extreme flows.

Flows↗
NASA NTRS2002

Designing Adaptive Low Dissipative High Order Schemes

Proper control of the numerical dissipation/filter to accurately resolve all relevant multiscales of complex flow problems while still maintaining nonlinear stability and efficiency for long-time numerical integrations poses a great challenge to the design of numerical methods. The required type and amount of numerical dissipation/filter are not only physical problem dependent, but also vary from one flow region to another. This is particularly true for unsteady high-speed shock/shear/boundary-layer/turbulence/acoustics interactions and/or combustion problems since the dynamics of the nonlinear effect of these flows are not well-understood. Even with extensive grid refinement, it is of paramount importance to have proper control on the type and amount of numerical dissipation/filter in regions where it is needed.

Yee, H. C.↗