Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Spectral element method”

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 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
NASA NTRS2000

High Order Discontinuous Gelerkin Methods for Convection Dominated Problems with Application to Aeroacoustics

This project is about the investigation of the development of the discontinuous Galerkin finite element methods, for general geometry and triangulations, for solving convection dominated problems, with applications to aeroacoustics. On the analysis side, we have studied the efficient and stable discontinuous Galerkin framework for small second derivative terms, for example in Navier-Stokes equations, and also for related equations such as the Hamilton-Jacobi equations. This is a truly local discontinuous formulation where derivatives are considered as new variables. On the applied side, we have implemented and tested the efficiency of different approaches numerically. Related issues in high order ENO and WENO finite difference methods and spectral methods have also been investigated. Jointly with Hu, we have presented a discontinuous Galerkin finite element method for solving the nonlinear Hamilton-Jacobi equations. This method is based on the RungeKutta discontinuous Galerkin finite element method for solving conservation laws. The method has the flexibility of treating complicated geometry by using arbitrary triangulation, can achieve high order accuracy with a local, compact stencil, and are suited for efficient parallel implementation. One and two dimensional numerical examples are given to illustrate the capability of the method. Jointly with Hu, we have constructed third and fourth order WENO schemes on two dimensional unstructured meshes (triangles) in the finite volume formulation. The third order schemes are based on a combination of linear polynomials with nonlinear weights, and the fourth order schemes are based on combination of quadratic polynomials with nonlinear weights. We have addressed several difficult issues associated with high order WENO schemes on unstructured mesh, including the choice of linear and nonlinear weights, what to do with negative weights, etc. Numerical examples are shown to demonstrate the accuracies and robustness of the methods for shock calculations. Jointly with P. Montarnal, we have used a recently developed energy relaxation theory by Coquel and Perthame and high order weighted essentially non-oscillatory (WENO) schemes to simulate the Euler equations of real gas. The main idea is an energy decomposition under the form epsilon = epsilon(sub 1) + epsilon(sub 2), where epsilon(sub 1) is associated with a simpler pressure law (gamma)-law in this paper) and the nonlinear deviation epsilon(sub 2) is convected with the flow. A relaxation process is performed for each time step to ensure that the original pressure law is satisfied. The necessary characteristic decomposition for the high order WENO schemes is performed on the characteristic fields based on the epsilon(sub l) gamma-law. The algorithm only calls for the original pressure law once per grid point per time step, without the need to compute its derivatives or any Riemann solvers. Both one and two dimensional numerical examples are shown to illustrate the effectiveness of this approach.

Shu, Chi-Wang↗
DOE OSTI2023

Large-Scale Materials Modeling at Quantum Accuracy: Ab Initio Simulations of Quasicrystals and Interacting Extended Defects in Metallic Alloys

Ab initio electronic-structure has remained dichotomous between achievable accuracy and length-scale. Quantum many-body (QMB) methods realize quantum accuracy but fail to scale. Density functional theory (DFT) scales favorably but remains far from quantum accuracy. We present a framework that breaks this dichotomy by use of three interconnected modules: (i) invDFT: a methodological advance in inverse DFT linking QMB methods to DFT; (ii) MLXC: a machine-learned density functional trained with invDFT data, commensurate with quantum accuracy; (iii) DFT-FE-MLXC: an adaptive higher-order spectral finite-element (FE) based DFT implementation that integrates MLXC with efficient solver strategies and HPC innovations in FE-specific dense linear algebra, mixed-precision algorithms, and asynchronous compute-communication. Furthermore, we demonstrate a paradigm shift in DFT that not only provides an accuracy commensurate with QMB methods in ground-state energies, but also attains an unprecedented performance of 659.7 PFLOPS (43.1% peak FP64 performance) on 619,124 electrons using 8,000 GPU nodes of Frontier supercomputer.

density functional theory↗
DOE OSTI2022

BACCHUS Analysis of Weak Lines in APOGEE Spectra (BAWLAS)

Elements with weak and blended spectral features in stellar spectra are challenging to measure and require specialized analysis methods to precisely measure their chemical abundances. In this work, we have created a catalog of approximately 120,000 giants with high signal-to-noise Apache Point Observatory Galactic Evolution Experiment (APOGEE) Data Release 17 (DR17) spectra, for which we explore weak and blended species to measure Na, P, S, V, Cu, Ce, and Nd abundances and 12 C/ 13 C isotopic ratios. We employ an updated version of the Brussels Automatic Code for Characterizing High-accuracy Spectra (BACCHUS) code to derive these abundances using the stellar parameters measured by APOGEE's DR17 Stellar Parameters and Chemical Abundances Pipeline, quality flagging to identify suspect spectral lines, and a prescription for upper limits. Combined, these allow us to provide our BACCHUS Analysis of Weak Lines in APOGEE Spectra catalog of precise chemical abundances for these weak and blended species, which agrees well with the literature and improves upon APOGEE abundances for these elements, some of which are unable to be measured with APOGEE's current, grid-based approach without computationally expensive expansions. This new catalog can be used alongside APOGEE and provides measurements for many scientific applications ranging from nuclear physics to Galactic chemical evolution and Milky Way population studies. To illustrate this we show some examples of uses for this catalog, such as showing that we observe stars with enhanced s-process abundances or that we can use the 12 C/ 13 C ratios to explore extra mixing along the red giant branch.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1974

Feasibility study in the application of optical signal analysis to non-destructive testing of complex structures

Advantages of the large time bandwidth product of optical processing are presented. Experiments were performed to study the feasibility of the use of optical spectral analysis for detection of flaws in structural elements excited by random noise. Photographic and electronic methods of comparison of complex spectra were developed. Limitations were explored, and suggestions for further work are offered.

Baker, B.↗
NASA NTRS1987

Dual laser diode array emission coherently summed in an external cavity

The output power from two ten-element laser diodes arrays has been efficiently summed in an external cavity to obtain a coherent, continuous wave beam. In this technique, laser emission from each front surface antireflection coated diode array is stimulated by injection of emission from a second such array. This method was also applied to single-element diode lasers. The output beam characteristics such as spectral distribution, far-field and near-field beam patterns, and overall efficiency have been measured.

Hemmati, Hamid↗
NASA NTRS1993

Numerical simulation using vorticity-vector potential formulation

An accurate and efficient computational method is needed for three-dimensional incompressible viscous flows in engineering applications. On solving the turbulent shear flows directly or using the subgrid scale model, it is indispensable to resolve the small scale fluid motions as well as the large scale motions. From this point of view, the pseudo-spectral method is used so far as the computational method. However, the finite difference or the finite element methods are widely applied for computing the flow with practical importance since these methods are easily applied to the flows with complex geometric configurations. However, there exist several problems in applying the finite difference method to direct and large eddy simulations. Accuracy is one of most important problems. This point was already addressed by the present author on the direct simulations on the instability of the plane Poiseuille flow and also on the transition to turbulence. In order to obtain high efficiency, the multi-grid Poisson solver is combined with the higher-order, accurate finite difference method. The formulation method is also one of the most important problems in applying the finite difference method to the incompressible turbulent flows. The three-dimensional Navier-Stokes equations have been solved so far in the primitive variables formulation. One of the major difficulties of this method is the rigorous satisfaction of the equation of continuity. In general, the staggered grid is used for the satisfaction of the solenoidal condition for the velocity field at the wall boundary. However, the velocity field satisfies the equation of continuity automatically in the vorticity-vector potential formulation. From this point of view, the vorticity-vector potential method was extended to the generalized coordinate system. In the present article, we adopt the vorticity-vector potential formulation, the generalized coordinate system, and the 4th-order accurate difference method as the computational method. We present the computational method and apply the present method to computations of flows in a square cavity at large Reynolds number in order to investigate its effectiveness.

Tokunaga, Hiroshi↗
NASA NTRS1991

Determination of alloy content from plume spectral measurements

The mathematical derivation for a method to determine the identities and amounts of alloys present in a flame where numerous alloys may be present is described. This method is applicable if the total number of elemental species from all alloys that may be in the flame is greater than or equal to the total number of alloys. Arranging the atomic spectral line emission equations for the elemental species as a series of simultaneous equations enables solution for identity and amount of the alloy present in the flame. This technique is intended for identification and quantification of alloy content in the plume of a rocket engine. Spectroscopic measurements reveal the atomic species entrained in the plume. Identification of eroding alloys may lead to the identification of the eroding component.

Madzsar, George C.↗
NASA NTRS1991

Determination of alloy content from plume spectral measurements

The mathematical derivation for a method to determine the identities and amounts of alloys present in a flame where numerous alloys may be present is described. This method is applicable if the total number of elemental species from all alloys that may be in the flame is greater than or equal to the total number of alloys. Arranging the atomic spectral line emission equations for the elemental species as a series of simultaneous equations enables solution for identify and amount of the alloy present in the flame. This technique is intended for identification and quantification of alloy content in the plume of a rocket engine. Spectroscopic measurements reveal the atomic species entrained in the plume. Identification of eroding alloys may lead to the identification of the eroding component.

Madzsar, George C.↗
DOE OSTI2025

Machine Learning in the Context of Laser-Induced Breakdown Spectroscopy

The integration of machine learning (ML) with Laser-Induced Breakdown Spectroscopy (LIBS) has revolutionized the analytical capabilities of LIBS. The combi-nation of both methods enables more accurate and efficient data analysis. While LIBS itself is a powerful technique for elemental analysis, the vast amount of spectral data it generates can be hard to interpret. Machine learning addresses these challenges by leveraging algorithms that can learn from data, identify patterns, and make predictions without explicit programming for the interpretation of each specific task. In LIBS application, ML techniques are used to enhance various analytical processes. For example, ML algorithms can classify materials based on their spectral fingerprints, predict the concentration of elements in a sample, and identify underlying patterns within complex datasets. Here, this application improves the precision of LIBS analyses while significantly reducing the time required for data processing and interpretation. In this chapter, the fundamental concepts of ML will be discussed first. Following this, the process of data splitting and the importance of feature selection will be examined. Several machine learning methods will then be closely examined, exploring how each can benefit LIBS analysis and highlighting their respective advantages and shortcomings. This structured approach will provide a comprehensive understanding of the integration of ML in the context of LIBS analysis.

47 OTHER INSTRUMENTATION↗
NASA NTRS1995

Large-eddy simulation of flow past a circular cylinder

Some of the most challenging applications of large-eddy simulation are those in complex geometries where spectral methods are of limited use. For such applications more conventional methods such as finite difference or finite element have to be used. However, it has become clear in recent years that dissipative numerical schemes which are routinely used in viscous flow simulations are not good candidates for use in LES of turbulent flows. Except in cases where the flow is extremely well resolved, it has been found that upwind schemes tend to damp out a significant portion of the small scales that can be resolved on the grid. Furthermore, it has been found that even specially designed higher-order upwind schemes that have been used successfully in the direct numerical simulation of turbulent flows produce too much dissipation when used in conjunction with large-eddy simulation. The objective of the current study is to perform a LES of incompressible flow past a circular cylinder at a Reynolds number of 3900 using a solver which employs an energy-conservative second-order central difference scheme for spatial discretization and compare the results obtained with those of Beaudan & Moin (1994) and with the experiments in order to assess the performance of the central scheme for this relatively complex geometry.

Mittal, R.↗
NASA NTRS1983

Preconditioned Minimal Residual Methods for Chebyshev Spectral Caluclations

The problem of preconditioning the pseudospectral Chebyshev approximation of an elliptic operator is considered. The numerical sensitiveness to variations of the coefficients of the operator are investigated for two classes of preconditioning matrices: one arising from finite differences, the other from finite elements. The preconditioned system is solved by a conjugate gradient type method, and by a DuFort-Frankel method with dynamical parameters. The methods are compared on some test problems with the Richardson method and with the minimal residual Richardson method.

Canuto, C.↗
NASA NTRS1985

Preconditioned minimal residual methods for Chebyshev spectral calculations

The problem of preconditioning the pseudospectral Chebyshev approximation of an elliptic operator is considered. The numerical sensitiveness to variations of the coefficients of the operator are investigated for two classes of preconditioning matrices: one arising from finite differences, the other from finite elements. The preconditioned system is solved by a conjugate gradient type method, and by a Dufort-Frankel method with dynamical parameters. The methods are compared on some test problems with the Richardson method and with the minimal residual Richardson method.

Canuto, C.↗
NASA NTRS1973

An interpretation of a geologic map of Fannin County, Texas, prepared by ADP techniques from ERTS MSS data

Multispectral scanner data, collected by ERTS-1 from an area in northeast Texas underlain by structurally simple cretaceous sedimentary rocks, were analyzed using several automatic data processing techniques. Training areas for the computer analysis were selected in three ways using: (1) an unsupervised classifier, (2) the unsupervised classifier to further refine training areas, and (3) available ground information. The first two methods utilize the capability of the unsupervised classifier to the unsupervised classifier to group resolution elements with similar spectral properties. With the imagery produced by these procedures, several geologic features can be identified. The most easily recognizable features are streams and other water bodies. The approximate location of contacts between several rock units can be mapped.

Henderson, J. A., Jr.↗
NASA NTRS1986

Preconditioned conjugate residual methods for the solution of spectral equations

Conjugate residual methods for the solution of spectral equations are described. An inexact finite-difference operator is introduced as a preconditioner in the iterative procedures. Application of these techniques is limited to problems for which the symmetric part of the coefficient matrix is positive definite. Although the spectral equation is a very ill-conditioned and full matrix problem, the computational effort of the present iterative methods for solving such a system is comparable to that for the sparse matrix equations obtained from the application of either finite-difference or finite-element methods to the same problems. Numerical experiments are shown for a self-adjoint elliptic partial differential equation with Dirichlet boundary conditions, and comparison with other solution procedures for spectral equations is presented.

Wong, Y. S.↗
DOE OSTI2023

End-to-end GPU acceleration of low-order-refined preconditioning for high-order finite element discretizations

In this article, we present algorithms and implementations for the end-to-end GPU acceleration of matrix-free low-order-refined preconditioning of high-order finite element problems. The methods described here allow for the construction of effective preconditioners for high-order problems with optimal memory usage and computational complexity. The preconditioners are based on the construction of a spectrally equivalent low-order discretization on a refined mesh, which is then amenable to, for example, algebraic multigrid preconditioning. The constants of equivalence are independent of mesh size and polynomial degree. For vector finite element problems in H(curl) and H(div) (e.g., for electromagnetic or radiation diffusion problems), a specially constructed interpolation–histopolation basis is used to ensure fast convergence. Detailed performance studies are carried out to analyze the efficiency of the GPU algorithms. The kernel throughput of each of the main algorithmic components is measured, and the strong and weak parallel scalability of the methods is demonstrated. The different relative weighting and significance of the algorithmic components on GPUs and CPUs is discussed. Results on problems involving adaptively refined nonconforming meshes are shown, and the use of the preconditioners on a large-scale magnetic diffusion problem using all spaces of the finite element de Rham complex is illustrated.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1989

Finite element analysis in fluids; Proceedings of the Seventh International Conference on Finite Element Methods in Flow Problems, University of Alabama, Huntsville, Apr. 3-7, 1989

Recent advances in computational fluid dynamics are examined in reviews and reports, with an emphasis on finite-element methods. Sections are devoted to adaptive meshes, atmospheric dynamics, combustion, compressible flows, control-volume finite elements, crystal growth, domain decomposition, EM-field problems, FDM/FEM, and fluid-structure interactions. Consideration is given to free-boundary problems with heat transfer, free surface flow, geophysical flow problems, heat and mass transfer, high-speed flow, incompressible flow, inverse design methods, MHD problems, the mathematics of finite elements, and mesh generation. Also discussed are mixed finite elements, multigrid methods, non-Newtonian fluids, numerical dissipation, parallel vector processing, reservoir simulation, seepage, shallow-water problems, spectral methods, supercomputer architectures, three-dimensional problems, and turbulent flows.

Chung, T. J.↗
NASA NTRS2000

Comparison of Fatigue Life Estimation Using Equivalent Linearization and Time Domain Simulation Methods

The Monte Carlo simulation method in conjunction with the finite element large deflection modal formulation are used to estimate fatigue life of aircraft panels subjected to stationary Gaussian band-limited white-noise excitations. Ten loading cases varying from 106 dB to 160 dB OASPL with bandwidth 1024 Hz are considered. For each load case, response statistics are obtained from an ensemble of 10 response time histories. The finite element nonlinear modal procedure yields time histories, probability density functions (PDF), power spectral densities and higher statistical moments of the maximum deflection and stress/strain. The method of moments of PSD with Dirlik's approach is employed to estimate the panel fatigue life.

Mei, Chuh↗
DOE OSTI2022

Form factors and spectral densities from Lightcone Conformal Truncation

We use the method of Lightcone Conformal Truncation (LCT) to obtain form factors and spectral densities of local operators $\mathcal{O}$ in $\phi^4$ theory in two dimensions. We show how to use the Hamiltonian eigenstates from LCT to obtain form factors that are matrix elements of a local operator $\mathcal{O}$ between single-particle bra and ket states, and we develop methods that significantly reduce errors resulting from the finite truncation of the Hilbert space. We extrapolate these form factors as a function of momentum to the regime where, by crossing symmetry, they are form factors of $\mathcal{O}$ between the vacuum and a two-particle asymptotic scattering state. We also compute the momentum-space time-ordered two-point functions of local operators in LCT. These converge quickly at momenta away from branch cuts, allowing us to indirectly obtain the time-ordered correlator and the spectral density at the branch cuts. We focus on the case where the local operator $\mathcal{O}$ is the trace Θ of the stress tensor.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗