Search NASA⌕ Search

SEARCH · Search NASA

Results for “numerical algorithm computing”

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 1,423 records · Page 79
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

A Fast Butterfly-Compressed Hadamard–Babich Integrator for High-Frequency Helmholtz Equations in Inhomogeneous Media with Arbitrary Sources

Here we present a butterfly-compressed representation of the Hadamard-Babich (HB) ansatz for the Green's function of the high-frequency Helmholtz equation in smooth inhomogeneous media. For a computational domain discretized with Nv discretization cells, the proposed algorithm first solves and tabulates the phase and HB coefficients via eikonal and transport equations with observation points and point sources located at the Chebyshev nodes using a set of much coarser computation grids, and then butterfly compresses the resulting HB interactions from all Nv cell centers to each other. The overall CPU time and memory requirement scale as O(Nv log2 Nv) for any bounded two-dimensional (2D) domains with arbitrary excitation sources. A direct extension of this scheme to bounded 3D domains yields an O(Nv4/3) CPU complexity, which can be further reduced to quasi-linear complexities with proposed remedies. The scheme can also efficiently handle scattering problems involving inclusions in inhomogeneous media. Although the current construction of our HB integrator does not accommodate caustics, the resulting HB integrator itself can be applied to certain sources, such as concave-shaped sources, to produce caustic effects. Compared to finite-difference frequency domain methods, the proposed HB integrator is free of numerical dispersion and requires fewer discretization points per wavelength. As a result, it can solve wave propagation problems well beyond the capability of existing solvers. Remarkably, the proposed scheme can accurately model wave propagation in 2D domains with 640 wavelengths per direction and in 3D domains with 54 wavelengths per direction on a state-of-the-art supercomputer at Lawrence Berkeley National Laboratory.

Hadamard--Babich ansatz↗
DOE OSTI2018

Assessment of uncertainty in the numerical simulation of solar irradiance over inclined PV panels: New algorithms using measurements and modeling tools

Development of accurate transposition models to simulate plane-of-array (POA) irradiance from horizontal measurements or simulations is a complex process mainly because of the anisotropic distribution of diffuse solar radiation in the atmosphere. The limited availability of reliable POA measurements at large temporal and spatial scales leads to difficulties in the comprehensive evaluation of transposition models. This paper proposes new algorithms to assess the uncertainty of transposition models using both surface-based observations and modeling tools. We reviewed the analytical derivation of POA irradiance and the approximation of isotropic diffuse radiation that simplifies the computation. Two transposition models are evaluated against the computation by the rigorous analytical solution. We proposed a new algorithm to evaluate transposition models using the clear-sky measurements at the National Renewable Energy Laboratory's (NREL's) Solar Radiation Research Laboratory (SRRL) and a radiative transfer model that integrates diffuse radiances of various sky-viewing angles. We found that the radiative transfer model and a transposition model based on empirical regressions are superior to the isotropic models when compared to measurements. We further compared the radiative transfer model to the transposition models under an extensive range of idealized conditions. Our results suggest that the empirical transposition model has slightly higher cloudy-sky POA irradiance than the radiative transfer model, but performs better than the isotropic models under clear-sky conditions. Significantly smaller POA irradiances computed by the transposition models are observed when the photovoltaics (PV) panel deviates from the azimuthal direction of the sun. The new algorithms developed in the current study have opened the door to a more comprehensive evaluation of transposition models for various atmospheric conditions and solar and PV orientations.

14 SOLAR ENERGY↗
DOE OSTI2022

Multistage mixed precision iterative refinement

Abstract Low precision arithmetic, in particular half precision (16‐bit) floating point arithmetic, is now available in commercial hardware. Using lower precision can offer significant savings in computation and communication costs with proportional savings in energy. Motivated by this, there has been a renewed interest in mixed precision iterative refinement schemes for solving linear systems , and new variants of GMRES‐based iterative refinement have been developed. Each particular variant with a given combination of precisions leads to different condition number‐based constraints for convergence of the backward and forward errors, and each has different performance costs. The constraints for convergence given in the literature are, as an artifact of the analyses, often overly strict in practice, and thus could lead a user to select a more expensive variant when a less expensive one would have sufficed. In this work, we develop a multistage mixed precision iterative refinement solver which aims to combine existing mixed precision approaches to balance performance and accuracy and improve usability. For a user‐specified initial combination of precisions, the algorithm begins with the least expensive approach and convergence is monitored via inexpensive computations with quantities produced during the iteration. If slow convergence or divergence is detected using particular stopping criteria, the algorithm switches to use a more expensive, but more reliable variant. A novel aspect of our approach is that, unlike existing implementations, our algorithm first attempts to use “stronger” GMRES‐based solvers for the solution update before resorting to increasing the precision(s). In some scenarios, this can avoid the need to refactorize the matrix in higher precision. We perform extensive numerical experiments on a variety of random dense problems and problems from real applications which confirm the benefits of the multistage approach.

Oktay, Eda↗
DOE OSTI2024

Steady-state properties of multi-orbital systems using quantum Monte Carlo

A precise dynamical characterization of quantum impurity models with multiple interacting orbitals is challenging. In quantum Monte Carlo methods, this is embodied by sign problems. A dynamical sign problem makes it exponentially difficult to simulate long times. A multi-orbital sign problem generally results in a prohibitive computational cost for systems with multiple impurity degrees of freedom even in static equilibrium calculations. Here, we present a numerically exact inchworm method that simultaneously alleviates both sign problems, enabling simulation of multi-orbital systems directly in the equilibrium or nonequilibrium steady-state. The method combines ideas from the recently developed steady-state inchworm Monte Carlo framework [Erpenbeck et al., Phys. Rev. Lett. 130, 186301 (2023)] with other ideas from the equilibrium multi-orbital inchworm algorithm [Eidelstein et al., Phys. Rev. Lett. 124, 206405 (2020)]. We verify our method by comparison with analytical limits and numerical results from previous methods.

Chemistry↗
DOE OSTI2024

Riemannian Optimization Applied to AC Optimal Power Flow: Preprint

The nonlinear, nonconvex AC optimal power flow problem is of growing importance as the nature of the power grid evolves. This problem can be difficult to solve for interior point methods. However, the advent of optimization algorithms over smooth Riemannian manifolds presents an alternative approach. The nonlinear, nonconvex constraints in the AC power flow problem form an embedded submanifold of Euclidean space. In this paper, the authors explore the performance of Riemannian optimization algorithms for the ACOPF problem where the optimization is performed directly on the AC power flow manifold. They demonstrate that these are viable computational alternatives to interior point methods. This is done by using Julia and the packages PowerModels.jl and Manopt.jl.

manifold optimization↗
DOE OSTI2019

Quantitative Parameter Estimation, Model Selection, and Variable Selection in Battery Science

Numerical physics-based models are useful in understanding battery performance and devel- oping optimal battery design architectures. Data science developments have enabled software algorithms to perform data analysis and decision making that traditionally could only be per- formed by technical experts. Traditional workflows of model development - manual parameter estimation through visual comparison of simulations to experimental observations, and model discrimination through expert intuition - are time-consuming, and difficult to justify. This paper compares the conclusions derived from computationally scalable algorithms to conclu- sions developed by expert researchers. This paper illustrates how data science techniques, such as cross-validation and lasso regression, can be used to augment physics-based simulations to perform data analysis such as parameter estimation, model selection, variable selection, and model-guided design of experiment. The validation of these algorithms is that they produce results similar to those of the expert modeler. The algorithms outlined are well-established and the approaches are general, so can be applied to a variety of battery chemistries and architectures. The conclusions reached using these approaches are in agreement with expert analysis (literature results), were reached with minimal human intervention, and provide quantitative justification. By minimizing the amount of expert time, and providing rigorous quantitative justifications, these methods may accelerate battery development.

25 ENERGY STORAGE↗
DOE OSTI2011

Verification of the Coupled Fluid/Solid Transfer in a CASL Grid-to-Rod-Fretting Simulation: A Technical Brief on the Analysis of Convergence Behavior and Demonstration of Software Tools for Verification

For a CASL grid-to-rod fretting problem, Sandia's Percept software was used in conjunction with the Sierra Mechanics suite to analyze the convergence behavior of the data transfer from a fluid simulation to a solid mechanics simulation. An analytic function, with properties relatively close to numerically computed fluid approximations, was chosen to represent the pressure solution in the fluid domain. The analytic pressure was interpolated on a sequence of grids on the fluid domain, and transferred onto a separate sequence of grids in the solid domain. The error in the resulting pressure in the solid domain was measured with respect to the analytic pressure. The error in pressure approached zero as both the fluid and solids meshes were refined. The convergence of the transfer algorithm was limited by whether the source grid resolution was the same or finer than the target grid resolution. In addition, using a feature coverage analysis, we found gaps in the solid mechanics code verification test suite directly relevant to the prototype CASL GTRF simulations.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2015

An improved numerical method to compute neutron/gamma deexcitation cascades starting from a high spin state

Numerous nuclear processes involve the deexcitation of a compound nucleus through the emission of several neutrons, gamma-rays and/or conversion electrons. The characteristics of such a deexcitation are commonly derived from a total statistical framework often called “Hauser–Feshbach” method. In this work, we highlight a numerical limitation of this kind of method in the case of the deexcitation of a high spin initial state. To circumvent this issue, an improved technique called the Fluctuating Structure Properties (FSP) method is presented. Two FSP algorithms are derived and benchmarked on the calculation of the total radiative width for a thermal neutron capture on 238 U. We compare the standard method with these FSP algorithms for the prediction of particle multiplicities in the deexcitation of a high spin level of 143 Ba. The gamma multiplicity turns out to be very sensitive to the numerical method. The bias between the two techniques can reach 1.5 γγ/cascade. Lastly, the uncertainty of these calculations coming from the lack of knowledge on nuclear structure is estimated via the FSP method.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2017

The accurate particle tracer code

The Accurate Particle Tracer (APT) code is designed for systematic large-scale applications of geometric algorithms for particle dynamical simulations. Based on a large variety of advanced geometric algorithms, APT possesses long-term numerical accuracy and stability, which are critical for solving multi-scale and nonlinear problems. To provide a flexible and convenient I/O interface, the libraries of Lua and Hdf5 are used. Following a three-step procedure, users can efficiently extend the libraries of electromagnetic configurations, external non-electromagnetic forces, particle pushers, and initialization approaches by use of the extendible module. APT has been used in simulations of key physical problems, such as runaway electrons in tokamaks and energetic particles in Van Allen belt. As an important realization, the APT-SW version has been successfully distributed on the world’s fastest computer, the Sunway TaihuLight supercomputer, by supporting master–slave architecture of Sunway many-core processors. Here, based on large-scale simulations of a runaway beam under parameters of the ITER tokamak, it is revealed that the magnetic ripple field can disperse the pitch-angle distribution significantly and improve the confinement of energetic runaway beam on the same time.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Description of the ARM Large-Scale Forcing Data from the Constrained Variational Analysis (VARANAL) Version 2

This technical report represents an update of the previous technical report written by Zhang et al. (2001a) (available at http://www.arm.gov/publications/tech_reports/arm-tr-005.pdf), which described the U.S. Department of Energy Atmospheric Radiation Measurement (ARM) user facility constrained variational analysis (VARANAL) that is used to develop the large-scale forcing data for driving single-column models (SCMs), cloud-resolving models (CRMs), and large-eddy simulation models (LES). The VARANAL algorithm was originally developed by Zhang and Lin (1997) and Zhang et al. (2001b) at Stony Brook University and was migrated to the Lawrence Livermore National Laboratory (LLNL) as the ARM operational objective analysis system in May 1999. Since then, the algorithm has been evolved with time along with the availability of new observations and techniques to meet various modeling needs. Major updates include: (1) The method used to develop multi-year continuous forcing data (Xie et al. 2004), (2) The incorporation of eddy correlation flux measurement system (ECOR) turbulent fluxes into the analysis (Tang et al. 2019), and (3) Improvements to the workflow (e.g., implementing part of the code into the ARM Data Integrator [ADI]) to increase efficiency. The ARM large-scale forcing data have been widely used for SCM/CRM/LES to understand and improve physical processes in models. Zhang et al. (2016) has provided a comprehensive review of the SCM concept, early efforts to derive forcing data for SCM studies, efforts of the ARM constrained variational analysis, and previous SCM studies using ARM cases. This technical report focuses on the constrained variational analysis algorithm and the introduction of the ARM VARANAL products.

58 GEOSCIENCES↗
DOE OSTI2013

Verification of the three-dimensional tetrahedral grid S{sub N} code THOR

In this work current capabilities implemented in the novel, arbitrary-order, tetrahedral-grid short characteristics S{sub N} radiation transport code THOR are verified based on four benchmark problems: (1) A one-group Method of Manufactured Solution (MMS) problem on a cuboidal domain, (2) an infinite medium eigenvalue problem with up-scattering, (3) a homogeneous torus and (4) a bare cube eigenvalue problem with anisotropic scattering up to order three. The first benchmark problem exercises the various spatial discretization options available in THOR: The short characteristics method in conjunction with polynomial expansions of the source and face fluxes either using the complete or Lagrange family of arbitrary orders. Using the numerical solution's order of convergence test in the framework of a mesh refinement study, correct implementation of a selection of spatial expansion orders is demonstrated for two meshes with tetrahedral aspect ratios close to unity and 50. The second benchmark problem exercises the implementation of angular fluxes on reflective boundary faces that are implicit within a mesh sweep, and up-scattering. The third benchmark problem comprises cyclic dependencies within the mesh sweep thus exercising the algorithm devised for 'breaking' the cyclic dependencies. Finally, the fourth benchmark problem, a simple bare cube, is used to test correct implementation of the anisotropic scattering capability. For all test problems THOR obtains solutions that converge to the reference/exact solution with the expected rate thereby contributing to our confidence in the correctness of its tested features in the present implementation. (authors)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A hybrid calibration approach to Hertz-type contact parameters for discrete element models

This study aims at providing a hybrid calibration framework to estimate Hertz-type contact parameters (particle-scale shear modulus and Poisson ratio) for both two-dimensional and three-dimensional discrete element modelling (DEM). On the basis of statistically isotropic granular packings, a set of analytical formulae between macroscopic material parameters (Young modulus and Poisson ratio) and particle-scale Hertz-type contact parameters for granular systems are derived under small-strain isotropic stress conditions. However, the derived analytical solutions are only estimated values for general models. By viewing each DEM modelling as an implicit mathematical function taking the particle-level parameters as independent variables and employing the derived analytical solutions as the initial input parameters, an automatic iterative scheme is proposed to obtain the calibrated parameters with higher accuracies. Considering highly nonlinear features and discontinuities of the macro-micro relationship in Hertz-based discrete element models, the adaptive moment estimation algorithm is adopted in this study because of its capacity of dealing with noise gradients of cost functions. Here, the proposed method is validated with several numerical cases including randomly distributed monodisperse and polydisperse packings. Noticeable improvements in terms of calibration efficiency and accuracy have been made.

Constitutive law↗
DOE OSTI2015

An ILP based Algorithm for Optimal Customer Selection for Demand Response in SmartGrids

Demand Response (DR) events are initiated by utilities during peak demand periods to curtail consumption. They ensure system reliability and minimize the utility’s expenditure. Selection of the right customers and strategies is critical for a DR event. An effective DR scheduling algorithm minimizes the curtailment error which is the absolute difference between the achieved curtailment value and the target. State-of-the-art heuristics exist for customer selection, however their curtailment errors are unbounded and can be as high as 70%. In this work, we develop an Integer Linear Programming (ILP) formulation for optimally selecting customers and curtailment strategies that minimize the curtailment error during DR events in SmartGrids. We perform experiments on real world data obtained from the University of Southern California’s SmartGrid and show that our algorithm achieves near exact curtailment values with errors in the range of 10 -7 to 10 -5 , which are within the range of numerical errors. We compare our results against the state-of-the-art heuristic being deployed in practice in the USC SmartGrid. We show that for the same set of available customer strategy pairs our algorithm performs 103 to 107 times better in terms of the curtailment errors incurred.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Accuracy and convergence properties of the fixed-stress iterative solution of two-way coupled poromechanics

Here, the paper deals with the numerical solution of Biot's equations of coupled consolidation obtained by a mixed formulation combining continuous Galerkin finite–element and multipoint flux approximation finite–volume methods. The solution algorithm relies on the recently developed fixed–stress solution scheme, in which first the flow problem and then the mechanical one are addressed iteratively. We show that the algorithm can be interpreted as a particular block triangular preconditioning strategy applied within a Richardson iteration. The key component to the success of the preconditioner is the sparse approximation to the Schur complement based on a pressure space mass matrix scaled by a weighting factor that depends element–wise on the inverse of a suitable bulk modulus. The accuracy of the method is assessed, making use of well–known analytical solutions from the literature. Numerical results demonstrate robustness and low computational cost of the fixed–stress scheme in accurately capturing the two–way coupling between deformation and pressure.

58 GEOSCIENCES↗
DOE OSTI2022

Investigation of plasmon relaxation mechanisms using nonadiabatic molecular dynamics

Hot carriers generated from the decay of plasmon excitation can be harvested to drive a wide range of physical or chemical processes. However, their generation efficiency is limited by the concomitant phonon-induced relaxation processes by which the energy in excited carriers is transformed into heat. However, simulations of dynamics of nanoscale clusters are challenging due to the computational complexity involved. Here, in this paper, we adopt our newly developed Trajectory Surface Hopping (TSH) nonadiabatic molecular dynamics algorithm to simulate plasmon relaxation in Au 20 clusters, taking the atomistic details into account. The electronic properties are treated within the Linear Response Time-Dependent Tight-binding Density Functional Theory (LR-TDDFTB) framework. The relaxation of plasmon due to coupling to phonon modes in Au 20 beyond the Born–Oppenheimer approximation is described by the TSH algorithm. The numerically efficient LR-TDDFTB method allows us to address a dense manifold of excited states to ensure the inclusion of plasmon excitation. Starting from the photoexcited plasmon states in Au 20 cluster, we find that the time constant for relaxation from plasmon excited states to the lowest excited states is about 2.7 ps, mainly resulting from a stepwise decay process caused by low-frequency phonons of the Au 20 cluster. Furthermore, our simulations show that the lifetime of the phonon-induced plasmon dephasing process is ~10.4 fs and that such a swift process can be attributed to the strong nonadiabatic effect in small clusters. Our simulations demonstrate a detailed description of the dynamic processes in nanoclusters, including plasmon excitation, hot carrier generation from plasmon excitation dephasing, and the subsequent phonon-induced relaxation process.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Efficient CP Rounding Using Alternating Least Squares with QR Decomposition

The CANDECOMP/PARAFAC (CP) decomposition is widely used for analyzing multidimensional data, and the alternating least squares (CP-ALS) algorithm is a common method for its computation. CP rounding is the problem of computing a lower-rank CP decomposition of an input already in a higher-rank CP format. While the normal equations (NE) approach in CP-ALS is efficient for the CP rounding problem and frequently used, it becomes unstable in the presence of ill-conditioned subproblems. This paper presents a new QR-based CP-ALS method for CP rounding that preserves both numerical stability and computational efficiency. Here, our experiments show that the proposed method offers significant speedup over a previous QR-based approach and the Tensor Toolbox's NE-based implementation, particularly for higher-order tensors. Furthermore, our approach demonstrates a marked reduction in error for ill-conditioned problems, with error reductions several orders of magnitude smaller compared to the NE-based method, while achieving faster convergence and more accurate solutions. By using a more numerically stable approach, we can solve more problems in reduced working precision, which enables further reduction in time to solution.

CANDECOMP/PARAFAC↗
DOE OSTI2022

Report of the Snowmass 2021 Topical Group on Lattice Gauge Theory

Lattice gauge theory continues to be a powerful theoretical and computational approach to simulating strongly interacting quantum field theories, whose applications permeate almost all disciplines of modern-day research in High-Energy Physics. Whether it is to enable precision quark- and lepton-flavor physics, to uncover signals of new physics in nucleons and nuclei, to elucidate hadron structure and spectrum, to serve as a numerical laboratory to reach beyond the Standard Model, or to invent and improve state-of-the-art computational paradigms, the lattice-gauge-theory program is in a prime position to impact the course of developments and enhance discovery potential of a vibrant experimental program in High-Energy Physics over the coming decade. This projection is based on abundant successful results that have emerged using lattice gauge theory over the years: on continued improvement in theoretical frameworks and algorithmic suits; on the forthcoming transition into the exascale era of high-performance computing; and on a skillful, dedicated, and organized community of lattice gauge theorists in the U.S. and worldwide. The prospects of this effort in pushing the frontiers of research in High-Energy Physics have recently been studied within the U.S. decadal Particle Physics Planning Exercise (Snowmass 2021), and the conclusions are summarized in this Topical Report.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2013

A variational multi-symplectic particle-in-cell algorithm with smoothing functions for the Vlasov-Maxwell system

Smoothing functions are commonly used to reduce numerical noise arising from coarse sampling of particles in particle-in-cell (PIC) plasma simulations. When applying smoothing functions to symplectic algorithms, the conservation of symplectic structure should be guaranteed to preserve good conservation properties. In this paper, we show how to construct a variational multi-symplectic PIC algorithm with smoothing functions for the Vlasov-Maxwell system. The conservation of the multi-symplectic structure and the reduction of numerical noise make this algorithm specifically suitable for simulating long-term dynamics of plasmas, such as those in the steady-state operation or long-pulse discharge of a super-conducting tokamak. The algorithm has been implemented in a 6D large scale PIC code. Numerical examples are given to demonstrate the good conservation properties of the multi-symplectic algorithm and the reduction of the noise due to the application of smoothing function.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗