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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 559 records · Page 31
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Coupled‐cluster singles, doubles and perturbative triples with density fitting approximation for massively parallel heterogeneous platforms

Abstract A high‐performance implementation of the coupled‐cluster singles, doubles, and perturbative triples [CCSD(T)] is developed in the Massively Parallel Quantum Chemistry program. Novel features include: (1) reduced memory requirements via a density‐fitting (DF) CCSD implementation utilizing distributed lazy evaluation for tensors with more than two unoccupied indices and (2) the ability to utilize efficiently many‐core nodes (Intel Xeon Phi) and heterogeneous nodes with multiple NVIDIA GPUs on each node. All data that are greater than quadratic in the system size are distributed among processes. Excellent strong scaling is observed on distributed‐memory computers equipped with conventional CPUs, Intel Xeon Phi processors, and heterogeneous nodes with multiple NVIDIA GPUs Canonical CCSD(T) energies can be evaluated for systems containing 200 electrons and 1000 basis functions in a few days using a small size commodity cluster, with even larger computations possible on leadership‐class computing resources.

Peng, Chong↗
DOE OSTI2025

Kinematic flow for cosmological loop integrands

Recently, an interesting pattern was found in the differential equations satisfied by the Feynman integrals describing tree-level correlators of conformally coupled scalars in a power-law FRW cosmology [1, 2]. It was proven that simple and universal graphical rules predict the equations for arbitrary graphs as a flow in kinematic space. In this note, we show that the same rules — with one small addition — also determine the differential equations for loop integrands. We explain that both the basis of master integrals and the singularities of the differential equations can be represented by tubings of marked graphs. An important novelty in the case of loops is that some basis functions can vanish, and we present a graphical rule to identify these vanishing functions. Taking this into account, we then demonstrate that the kinematic flow correctly predicts the differential equations for all loop integrands.

Cosmological models↗
DOE OSTI2018

High-order fully implicit solver for all-speed fluid dynamics: AUSM ride from nearly incompressible variable-density flows to shock dynamics

We introduce a novel Newton–Krylov (NK)-based fully implicit algorithm for solving fluid flows in a wide range of flow conditions—from variable density nearly incompressible to supersonic shock dynamics. The key enabling feature of our all-speed solver is the ability to efficiently solve conservation laws by choosing a set of independent variables that produce a well-conditioned Jacobian matrix for the linear iterations of the global nonlinear iterative solver. In particular, instead of choosing to discretize the conservative variables (density, momentum, total energy), which is traditionally used in Eulerian high-speed compressible fluid dynamics, we demonstrate superior performance by discretizing the primitive variables—pressure–velocity–temperature in the very low-Mach flow limits or density–velocity–temperature/entropy in the shock dynamics range. Moreover, our method allows us to avoid direct inversion of the mass matrix in discrete time derivatives, which is usually an additional source for stiffness, especially pronounced when going to very high-order schemes with non-orthogonal basis functions. Here, we show robust solutions obtained for discontinuous finite element discretization up to seventh-order accuracy. Another important aspect of the solution algorithm is the Advection Upstream Splitting Method (AUSM), adopted to compute numerical fluxes within our reconstructed discontinuous Galerkin (rDG) spatial discretization scheme. The use of the low-Mach modification of the hyperbolic flux operator is found to be necessary for enabling robust simulations of very stiff liquids and metals for Mach numbers below M=10 -5 , which is well known to be very computationally challenging for compressible solvers. We demonstrate that our fully implicit rDG-NK solver with the AUSM + -up flux treatment produces efficient and high-resolution numerical solutions at all speeds, ranging from vanishing Mach numbers to transonic and supersonic, without substantial modifications of the solution procedures. (At high speed, we add limiting and use a simpler preconditioning of the Krylov solver.) Numerical examples include nearly incompressible constant-property flow past a backward-facing step with heat transfer, low-Mach variable-property channel flow of water at supercritical state, phase change and melt pool dynamics for laser spot welding and selective laser melting in additive manufacturing, and Mach 3 flow in a wind tunnel with a step.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Enriched immersed finite element and isogeometric analysis: algorithms and data structures

Immersed finite element methods provide a convenient analysis framework for problems involving geometrically complex domains, such as those found in topology optimization and microstructures for engineered materials. However, their implementation remains a major challenge due to, among other things, the need to apply nontrivial stabilization schemes and generate custom quadrature rules. This article introduces the robust and computationally efficient algorithms and data structures comprising an immersed finite element preprocessing framework. The input to the preprocessor consists of a background mesh and one or more geometries defined on its domain. The output is structured into groups of elements with custom quadrature rules formatted such that common finite element assembly routines may be used without or with only minimal modifications. The key to the preprocessing framework is the construction of material topology information, concurrently with the generation of a quadrature rule, which is then used to perform enrichment and generate stabilization rules. While the algorithmic framework applies to a wide range of immersed finite element methods using different types of meshes, integration, and stabilization schemes, the preprocessor is presented within the context of the extended isogeometric analysis. This method utilizes a structured B-spline mesh, a generalized Heaviside enrichment strategy considering the material layout within individual basis functions’ supports, and face-oriented ghost stabilization. Using a set of examples, the effectiveness of the enrichment and stabilization strategies is demonstrated alongside the preprocessor’s robustness in geometric edge cases. Additionally, the performance and parallel scalability of the implementation are evaluated.

Computer implementation↗
DOE OSTI2018

Adaptive wavelet compression of large additive manufacturing experimental and simulation datasets

New manufacturing technologies such as additive manufacturing require research and development to minimize the uncertainties in the produced parts. The research involves experimental measurements and large simulations, which result in huge quantities of data to store and analyze. We address this challenge by alleviating the data storage requirements using lossy data compression. We select wavelet bases as the mathematical tool for compression. Unlike images, additive manufacturing data is often represented on irregular geometries and unstructured meshes. Thus, we use Alpert tree-wavelets as bases for our data compression method. We first analyze different basis functions for the wavelets and find the one that results in maximal compression and miminal error in the reconstructed data. We then devise a new adaptive thresholding method that is data-agnostic and allows a priori estimation of the reconstruction error. Finally, we propose metrics to quantify the global and local errors in the reconstructed data. One of the error metrics addresses the preservation of physical constraints in reconstructed data fields, such as divergence-free stress field in structural simulations. While our compression and decompression method is general, we apply it to both experimental and computational data obtained from measurements and thermal/structural modeling of the sintering of a hollow cylinder from metal powders using a Laser Engineered Net Shape process. The results show that monomials achieve optimal compression performance when used as wavelet bases. The new thresholding method results in compression ratios that are two to seven times larger than the ones obtained with commonly used thresholds. Overall, adaptive Alpert tree-wavelets can achieve compression ratios between one and three orders of magnitude depending on the features in the data that are required to preserve. Furthermore, these results show that Alpert tree-wavelet compression is a viable and promising technique to reduce the size of large data structures found in both experiments and simulations.

42 ENGINEERING↗
DOE OSTI2019

Toward practical approaches for ergodicity analysis

It is of importance to perform hydrological forecast using a finite hydrological time series. Most time series analysis approaches presume a data series to be ergodic without justifying this assumption. To our knowledge, there are no methods available for test of ergodicity to date. As such, this paper presents a practical approach to analyze the mean ergodic property of hydrological processes by means of augmented Dickey Fuller test, Mann-Kendall trend test, a radial basis function neural network, and the assessment methods derived from the definition of ergodicity. The mean ergodicity of precipitation processes at Newberry, MI, USA, is analyzed using the proposed approach. The results indicate that the precipitations of January, May, and July in Newberry are highly likely to have ergodic property, the precipitations of February, and October through December have tendency toward mean ergodicity, and the precipitations of all the other months are non-ergodic.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

Multiscale two-stage solver for Biot’s poroelasticity equations in subsurface media

In this paper, we propose a two-stage preconditioner for accelerating the iterative solution by a Krylov subspace method of Biot’s poroelasticity equations based on a displacement-pressure formulation. The spatial discretization combines a finite element method for mechanics and a finite volume approach for flow. The fully implicit backward Euler scheme is used for time integration. The result is a 2 × 2 block linear system for each timestep. The preconditioning operator is obtained by applying a two-stage scheme. The first stage is a global preconditioner that employs multiscale basis functions to construct coarse-scale coupled systems using a Galerkin projection. This global stage is effective at damping low-frequency error modes associated with long-range coupling of the unknowns. The second stage is a local block-triangular smoothing preconditioner, which is aimed at high-frequency error modes associated with short-range coupling of the variables. Lastly, various numerical experiments are used to demonstrate the robustness of the proposed solver.

58 GEOSCIENCES↗
DOE OSTI2018

Mathematical Simulation of Humidification of Earth on a Slope and Calculation of Its Safety Factor

This paper presents a mathematical model of the simultaneous processes of moisture, heat, and salt transfer in a porous medium, as well as a pattern of calculation of earth stability on a slope depending on the above factors and nonlinear dependences on them of the strength characteristics of the earth. The corresponding boundary-value problem has been solved by the method of radial basis functions. A comparison has been made between the results of numerical experiments showing the relationship between the change in the value of the safety factor and the position of the slip curve depending on the heat, salt, and moisture transfer.

42 ENGINEERING↗
DOE OSTI2024

A Particle-in-Cell Method for Plasmas with a Generalized Momentum Formulation, Part II: Enforcing the Lorenz Gauge Condition

In a previous paper Christlieb et al. (A particle-in-cell method for plasmas with a generalized momentum formulation, part I: Model formulation, 2024), we developed a new particle-in-cell (PIC) method for the relativistic Vlasov–Maxwell system in which the electromagnetic fields and the equations of motion for the particles were cast in terms of scalar and vector potentials through a Hamiltonian formulation. This new method evolved the potentials under the Lorenz gauge using integral equation methods. New methods to construct spatial derivatives of the potentials that converge at the same rates as the fields were also presented. The new particle method was compared against standard explicit discretizations, including the well-known FDTD-PIC method, for a range of applications involving sheaths and particle beams. Here, this paper extends this new class of methods by focusing on the enforcement the Lorenz gauge condition in both exact and approximate forms using co-located meshes. A time-consistency property of the proposed field solver for the vector potential form of Maxwell’s equations is established, which is shown to preserve the equivalence between the semi-discrete Lorenz gauge condition and the analogous semi-discrete continuity equation. Using this property, we present three methods to enforce a semi-discrete gauge condition. The first method introduces an update for the continuity equation that is consistent with the discretization of the Lorenz gauge condition. Both the finite difference and spectral implementations satisfy this discrete gauge condition to machine precision. The second approach we propose enforces a semi-discrete continuity equation using the boundary integral solution to the field equations. The potential benefit of this approach is that it eliminates spatial derivatives that appear on the particle data, namely the current density, which is often calculated by linear combinations of low-order spline basis functions. This method is ideally suited to boundary integral equation methods that invert multi-dimensional operators without dimensional splitting techniques and will be the subject of future work. The third approach introduces a gauge correcting method that makes direct use of the gauge condition to modify the scalar potential and uses local maps for both the charge and current densities. This results in a gauge error, as the maps do not enforce the continuity equation. The vector potential coming from the current density is taken to be exact, and using the Lorenz gauge, we compute a correction to the scalar potential that makes the two potentials satisfy the gauge condition. This method also enforces the gauge condition to machine precision. We demonstrate two of the proposed methods in the context of periodic domains. Problems defined on bounded domains, including those with complex geometric features remain an ongoing effort. However, this work shows that it is possible to design computationally efficient methods that can effectively enforce the Lorenz gauge condition in a non-staggered PIC formulation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

Application of Noise Cancelling and Damage Detection Algorithms in NDE of Concrete Bridge Decks Using Impact Signals

Delamination is a commonly observed distress in concrete bridge decks. Among all the delamination detection methods, acoustic methods have the advantages of being fast and inexpensive. In traditional acoustic inspection methods, the inspector drags a chain along or hammers on the bridge deck and detects delamination from the 'hollowness' of the sounds. The signals are often contaminated by ambient traffic noise and the detection of delamination is highly subjective. This paper describes the performance of an impact-bases acoustic NDE method where the traffic noise was filtered by employing a noise cancelling algorithm and where subjectivity was eliminated by introducing feature extraction and pattern recognition algorithms. Different algorithms were compared and the best one was selected in each category. The comparison showed that the modified independent component analysis (ICA) algorithm was most effective in cancelling the traffic noise and features consisting of mel-frequency cepstral coefficients (MFCCs) had the best performance in terms of repeatability and separabillty. The condition of the bridge deck was then detected by a radial basis function (RBF) neural network. The performance of the system was evaluated using both experimental and field data. The results show that the selected algorithms increase the noise robustness of acoustic methods and perform satisfactorily if the training data is representative.

42 ENGINEERING↗
DOE OSTI2017

Occupation Time of a Randomly Accelerated Particle on the Positive Half Axis: Results for the First Five Moments

In the random acceleration process a point particle is accelerated by Gaussian white noise with zero mean. Although several fundamental statistical properties of the motion have been analyzed in detail, the statistics of occupation times is still not well understood. We consider the occupation or residence time T{sub +} on the positive x axis of a particle which is randomly accelerated on the unbounded x axis for a time t. The first two moments of T{sub +} were recently derived by Ouandji Boutcheng et al. (J Stat Mech 053213:1–10, 2016). With an alternate approach utilizing basis functions which have proved useful in other studies of randomly accelerated motion, results for the first five moments are obtained in this paper.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

A new computational approach for the solutions of generalized pantograph-delay differential equations

In this study, a new computational approach is presented to solve the generalized pantograph-delay differential equations (PDDEs). The solutions obtained by our scheme represent by a linear combination of a special kind of basis functions, and can be deduced in a straightforward manner. Firstly, using the least squares approximation method and the Lagrange-multiplier method, the given PDDE is converted to a linear system of algebraic equations, and those unknown coefficients of the solution of the problem are determined by solving this linear system. Secondly, a PDDE related to the error function of the approximate solution is constructed based on the residual error function technique, and error estimation is presented for the suggested method. The convergence of the approximate solution is proved. Several numerical examples are given to demonstrate the accuracy and efficiency. Comparisons are made between the proposed method and other existing methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A line search algorithm for wind field adjustment with incomplete data and RBF approximation

The problem of concern in this work is the construction of free divergence fields given scattered horizontal components. As customary, the problem is formulated as a PDE constrained least squares problem. The novelty of our approach is to construct the so-called adjusted field, as the unique solution along an appropriately chosen descent direction. The latter is obtained by the adjoint equation technique. It is shown that the classical adjusted field of Sasaki’s is a particular case. On choosing descent directions, the underlying mass consistent model leads to the solution of an elliptic problem which is solved by means of a radial basis functions method. Finally, some numerical results for wind field adjustment are presented.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Fifth-kind orthonormal Chebyshev polynomial solutions for fractional differential equations

The principal aim of the current paper is to present and analyze two new spectral algorithms for solving some types of linear and nonlinear fractional-order differential equations. The proposed algorithms are obtained by utilizing a certain kind of shifted Chebyshev polynomials called the shifted fifth-kind Chebyshev polynomials as basis functions along with the application of a modified spectral tau method. The class of fifth-kind Chebyshev polynomials is a special class of a basic class of symmetric orthogonal polynomials which are constructed with the aid of the extended Sturm–Liouville theorem for symmetric functions. An investigation for the convergence and error analysis of the proposed Chebyshev expansion is performed. For this purpose, a new connection formulae between Chebyshev polynomials of the first and fifth kinds are derived. The obtained numerical results ascertain that our two proposed algorithms are applicable, efficient and accurate.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Continuity conditions for tensor product Q-Bézier surfaces of degree (m, n)

Based on a kind of Q-Bézier surfaces with shape parameters, the basic properties of the surfaces and the geometric significance of the shape parameters are analyzed. To resolve the problem of shape control and adjustment of composite surfaces, the continuity conditions for Q-Bézier surfaces of degree (m, n) are investigated. Taking advantage of the terminal properties of generalized Bernstein basis functions, we derive the conditions of G{sup 1} and G{sup 2} continuity between two adjacent Q-Bézier surfaces. In addition, the specific steps of smooth continuity between Q-Bézier surfaces and the shape adjustment function of shape parameters for composite surfaces are discussed. The modeling examples show that the proposed smooth continuity conditions are not only intuitive and easy to implement, but also greatly enhance the shape adjustability, which provide a useful method for constructing complex surfaces in engineering design.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Rational RBF-based partition of unity method for efficiently and accurately approximating 3D objects

We consider the problem of reconstructing 3D objects via meshfree interpolation methods. In this framework, we usually deal with large data sets and thus develop an efficient local scheme via the well-known partition of unity method. The main contribution in this paper consists in constructing the local interpolants for the implicit interpolation by means of rational radial basis functions. Numerical experiments, devoted to test the accuracy of the scheme, confirm that the proposed method is particularly performing when 3D objects, or more in general implicit functions defined by scattered points, need to be approximated.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Jacobi collocation scheme for variable-order fractional reaction-subdiffusion equation

We developed a numerical scheme to solve the variable-order fractional linear subdiffusion and nonlinear reaction-subdiffusion equations using the shifted Jacobi collocation method. Basically, a time-space collocation approximation for temporal and spatial discretizations is employed efficiently to tackle these equations. The convergence and stability analyses of the suggested basis functions are presented in-depth. The validity and efficiency of the proposed method are investigated and verified through numerical examples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Leveraging operator learning to accelerate convergence of the preconditioned conjugate gradient method

We propose a new deflation strategy to accelerate the convergence of the preconditioned conjugate gradient (PCG) method for solving parametric large-scale linear systems of equations. Unlike traditional deflation techniques that rely on eigenvector approximations or recycled Krylov subspaces, we generate the deflation subspaces using operator learning, specifically the Deep Operator Network (DeepONet). To this aim, we introduce two complementary approaches for assembling the deflation operators. The first approach approximates near-null space vectors of the discrete PDE operator using the basis functions learned by the DeepONet. The second approach directly leverages solutions predicted by the DeepONet. To further enhance convergence, we also propose several strategies for prescribing the sparsity pattern of the deflation operator. Here, a comprehensive set of numerical experiments encompassing steady-state, time-dependent, scalar, and vector-valued problems posed on both structured and unstructured geometries is presented and demonstrates the effectiveness of the proposed DeepONet-based deflated PCG method, as well as its generalization across a wide range of model parameters and problem resolutions.

Deflation↗