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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Numerical solutions of FitzHugh–Nagumo equation by exact finite-difference and NSFD schemes

In this paper, numerical solution of the FitzHugh–Nagumo (FN) equation is presented based on the nonstandard finite-difference (NSFD) scheme. At first, two exact finite-difference schemes for FN equation are obtained. Moreover, two NSFD schemes are presented for this equation. The positivity, boundedness, and local truncation error of the schemes are discussed. The numerical results obtained by the NSFD schemes are compared with the exact solution and some available methods, to verify the accuracy and efficiency of the NSFD schemes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Generalized trigonometric Fourier-series method with automatic time step control for non-linear point kinetics equations

The trigonometric Fourier-series method (TFS) is generalized to provide approximate solutions for non-linear point kinetics equations with feedback using varying step sizes. This method can provide a very stable solution against the size of the discrete time step allowing much larger step sizes to be used. Systems of the point kinetics equations are solved using Fourier-series expansion over a partition of the total time interval. The approximate solution requires determining the series coefficients over each time step in that partition. These coefficients are determined using the high-order derivatives of the solution vector at the beginning of the time step introducing a system of linear algebraic equations to be solved at each step. This system is similar to the Vandermonde system. Two successive orders of the partial sums are used to estimate the local truncation error. This error and some other constrains are used to produce the largest step size allowable at each step while keeping the error within a specific tolerance. The process of calculating suitable step sizes should be automatic and inexpensive. Convergence and stability of the proposed method are discussed and a new formula is introduced to maintain stability. The proposed method solves the general linear and non-linear kinetics problems. The method has been applied to five different types of reactivities including step/ramp insertions with temperature feedback. The method is seemed to be valid for larger time intervals than those used in the conventional numerical integration, and is thus useful in reducing computing time. Computational results are found to be consistent with the analysis, they demonstrate that the convergence of the iteration scheme can be accelerated and the resulting computing times can be greatly reduced while maintain computational accuracy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Accelerating Multivariate Functional Approximation Computation with Domain Decomposition Techniques⋆

Modeling large datasets through Multivariate Functional Approximations (MFA) provide an elegant way to handle many visualization and scientific analysis workflows. The process necessitates scalable data partitioning methods to compute MFA representations efficiently without compromising the accuracy or continuity of the reconstructed solution. We propose a domain -decomposed method for computing the MFA with B -spline bases, which reduces the total work per task and uses a restricted Additive Schwarz (RAS) method to converge the control point data degrees -of -freedom along subdomain boundaries. We provide an in-depth analysis of the parallel approach with domain decomposition solvers, aiming to minimize local subdomain error residuals and recover high -order continuity at subdomain interfaces with appropriate choices of knot overlaps. The communication cost, determined by the overlap regions in the RAS implementation, is optimized to recover the numerical error profile of the single subdomain case. Our proposed method stands in contrast to previous methods, which typically only recover either C 0 or at best C 1 continuity for arbitrary B -spline degree expansions, or those that require post -processing to blend discontinuities in the reconstructed data. We demonstrate the effectiveness of our approach using analytical and real -world datasets in 1D, 2D, and 3D through both strong and weak scaling studies. The performance results indicate that the overall cost of computing the approximation is directly proportional to the underlying nearest -neighbor communication implementation, and is only weakly dependent on the overlap region size that determines the size of the messages. This finding underscores the efficiency and scalability of our proposed method, making it a promising solution for handling large datasets in scientific workflows.

additive Schwarz solvers↗
DOE OSTI2025

Resolving discrepancies in bang-time predictions for indirect-drive ICF experiments on the NIF: Insights from the Build-A-Hohlraum campaign

This study investigated discrepancies between measured and simulated x-ray drive in Indirect-Drive Inertial Confinement Fusion (ID-ICF) hohlraums at the National Ignition Facility. Despite advances in radiation-hydrodynamic simulations, a consistent “drive deficit” remains. Experimentally measured ID-ICF capsule bang-times are systematically 400–700 ps later than simulations predict. The Build-A-Hohlraum (BAH) campaign explored potential causes for this discrepancy by systematically varying hohlraum features, including laser entrance hole (LEH) windows, capsules, and gas fills. Overall, the agreement between simulated and experimental x-ray drive was found to be largely unaffected by these changes. The data allow us to exclude some hypotheses put forward to potentially explain the discrepancy. Errors in the local thermodynamic equilibrium (LTE) atomic modeling, errors in the modeling of LEH closure, and errors due to a lack of plasma species mix physics in simulations are shown to be inconsistent with our measurements. Instead, the data support the hypothesis that errors in NLTE emission modeling are a significant contributor to the discrepancy. X-ray emission in the 2–4 keV range is found to be approximately 30% lower than in simulations. This is accompanied by higher than predicted electron temperatures in the gold bubble region, pointing to errors in non-LTE modeling. Introducing an opacity multiplier of 0.87 on energy groups above 1.8 keV improves agreement with experimental data, reducing the bang-time discrepancy from 300 to 100 ps. These results underscore the need for refined NLTE opacity models to enhance the predictive power of hohlraum simulations.

Band emission↗
DOE OSTI2025

Deterministic High-Fidelity Neutronics Simulation of Pebble Bed Reactors Using Pebble Tracking Transport

The pebble tracking transport (PTT) algorithm offers a high-fidelity deterministic approach for neutron transport for pebble bed reactors (PBRs). This approach requires the mesh for the active-core region to consist exclusively of tetrahedral elements, where each node in the pebble-packing region represents a pebble centroid. This paper investigates the application of PTT for full-scale PBRs, considering both the isothermal and the temperature-dependent core conditions. Macroscopic cross sections are generated using Serpent 2 full-core eigenvalue simulations where pebbles are grouped into disjoint subsets using machine learning. To minimize the need for individual cross-section sets for each pebble in the core, K-means clustering is used to group pebbles by temperature and neutronic environment parameters. Here, we compare the multiplication factor and power rate distributions between PTT simulations using the Griffin reactor physics software and reference solutions from Serpent 2. Our analysis shows that a full-core, high-fidelity PTT calculation produces accurate results with minimal local (pebblewise) errors. Additionally, timing results indicate that PTT simulations converge rapidly on modern supercomputing platforms.

Griffin↗
DOE OSTI2020

Accurate and complete genomes from metagenomes

Genomes are an integral component of the biological information about an organism; thus, the more complete the genome, the more informative it is. Historically, bacterial and archaeal genomes were reconstructed from pure (monoclonal) cultures, and the first reported sequences were manually curated to completion. However, the bottleneck imposed by the requirement for isolates precluded genomic insights for the vast majority of microbial life. Shotgun sequencing of microbial communities, referred to initially as community genomics and subsequently as genome-resolved metagenomics, can circumvent this limitation by obtaining metagenome-assembled genomes (MAGs); but gaps, local assembly errors, chimeras, and contamination by fragments from other genomes limit the value of these genomes. Here, we discuss genome curation to improve and, in some cases, achieve complete (circularized, no gaps) MAGs (CMAGs). To date, few CMAGs have been generated, although notably some are from very complex systems such as soil and sediment. Through analysis of about 7000 published complete bacterial isolate genomes, we verify the value of cumulative GC skew in combination with other metrics to establish bacterial genome sequence accuracy. The analysis of cumulative GC skew identified potential misassemblies in some reference genomes of isolated bacteria and the repeat sequences that likely gave rise to them. We discuss methods that could be implemented in bioinformatic approaches for curation to ensure that metabolic and evolutionary analyses can be based on very high-quality genomes.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2019

Investigation of assumptions and approximations in the virtual fields method for a viscoplastic material model

The Virtual Fields Method (VFM) is an inverse technique used for parameter estimation and calibration of constitutive models. Many assumptions and approximations—such as plane stress, incompressible plasticity, and spatial and temporal derivative calculations—are required to use VFM with full-field deformation data, for example, from Digital Image Correlation (DIC). Here, this work presents a comprehensive discussion of the effects of these assumptions and approximations on parameters identified by VFM for a viscoplastic material model for 304L stainless steel. We generated synthetic data from a Finite-Element Analysis (FEA) in order to have a reference solution with a known material model and known model parameters, and we investigated four cases in which successively more assumptions and approximations were included in the data. We found that VFM is tolerant to small deviations from the plane stress condition in a small region of the sample, and that the incompressible plasticity assumption can be used to estimate thickness changes with little error. A local polynomial fit to the displacement data was successfully employed to compute the spatial displacement gradients. The choice of temporal derivative approximation (i.e., backwards difference versus central difference) was found to have a significant influence on the computed rate of deformation and on the VFM results for the rate-dependent model used in this work. Finally, the noise introduced into the displacement data from a stereo-DIC simulator was found to have negligible influence on the VFM results. Evaluating the effects of assumptions and approximations using synthetic data is a critical first step for verifying and validating VFM for specific applications. Finally, the results of this work provide the foundation for confidently using VFM for experimental data.

304L stainless steel↗
DOE OSTI2023

Adaptive Time Step Control for Multirate Infinitesimal Methods

Multirate methods have been used for decades to temporally evolve initial-value problems in which different components evolve on distinct time scales, and thus use of different step sizes for these components can result in increased computational efficiency. Generally, such methods select these different step sizes based on experimentation or stability considerations. For problems that evolve on a single time scale, adaptivity approaches that strive to control local temporal error are widely used to achieve numerical results of a desired accuracy with minimal computational effort, while alleviating the need for manual experimentation with different time step sizes. However, there is a notable gap in the publication record on the development of adaptive time step controllers for multirate methods. In this paper, we extend the single-rate controller work of Gustafsson [ACM Trans. Math. Software, 20 (1994), pp. 496-517] to the multirate method setting. Specifically, we develop controllers based on polynomial approximations to the principal error functions for both the "fast" and "slow" time scales within multirate infinitesimal (MRI) methods. We additionally investigate a variety of approaches for estimating the errors arising from each time scale within MRI methods. We then numerically evaluate the proposed multirate controllers and error estimation strategies on a range of multirate test problems, comparing their performance against an estimated optimal performance. Through this work, we combine the most performant of these approaches to arrive at a set of multirate adaptive time step controllers that robustly achieve desired solution accuracy with minimal computational effort.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

CFL Optimized Forward–Backward Runge–Kutta Schemes for the Shallow-Water Equations

Abstract We present the formulation and optimization of a Runge–Kutta-type time-stepping scheme for solving the shallow-water equations, aimed at substantially increasing the effective allowable time step over that of comparable methods. This scheme, called FB-RK(3,2), uses weighted forward–backward averaging of thickness data to advance the momentum equation. The weights for this averaging are chosen with an optimization process that employs a von Neumann–type analysis, ensuring that the weights maximize the admittable Courant number. Through a simplified local truncation error analysis and numerical experiments, we show that the method is at least second-order in time for any choice of weights and exhibits low dispersion and dissipation errors for well-resolved waves. Further, we show that an optimized FB-RK(3,2) can take time steps up to 2.8 times as large as a popular three-stage, third-order strong stability-preserving Runge–Kutta method in a quasi-linear test case. In fully nonlinear shallow-water test cases relevant to oceanic and atmospheric flows, FB-RK(3,2) outperforms SSPRK3 in admittable time step by factors roughly between 1.6 and 2.2, making the scheme approximately twice as computationally efficient with little to no effect on solution quality. Significance Statement The purpose of this work is to develop and optimize time-stepping schemes for models relevant to oceanic and atmospheric flows. Specifically, for the shallow-water equations we optimize for schemes that can take time steps as large as possible while retaining solution quality. We find that our optimized schemes can take time steps between 1.6 and 2.2 times larger than schemes that cost the same number of floating point operations, translating directly to a corresponding speedup. Our ultimate goal is to use these schemes in climate-scale simulations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Random adaptive tool path for zonal optics fabrication

Deterministic optics fabrication using sub-aperture tools has been vital for manufacturing precision optical surfaces. The fabrication process requires the tool influence function and the tool path to calculate the dwell time that guides the tool to bring surface quality within tight design tolerances. Widely used spiral and raster paths may leave excess waviness from the tool path, and the unavoidable constant removal layer is added to obtain positive dwell time. This waviness can be removed by either using smaller tools sequentially or randomizing the tool path. However, the existing tool-path solutions can hardly adapt to different surface aperture shapes and localized surface errors. Process efficiency and accuracy are also not well considered in tool-path planning. We propose an innovative zonal Random Adaptive Path (RAP) to solve these problems in this study. Firstly, RAP can be flexibly adapted to different surface aperture shapes by introducing part boundary. Secondly, an average threshold strategy is used in the RAP planning to improve efficiency, enabling the surface errors to be selectively corrected. Finally, the threshold is performed in several passes within one processing cycle, each with its RAP, until the desired residual is achieved. The performance of the proposed RAP is studied by comparing it with the conventional tool paths. The results demonstrated that RAP takes the least processing time and achieves the best surface quality, which verifies the effectiveness of RAP in deterministic optics fabrication.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Relativistic Hydrodynamics with Wavelets

Methods to solve the relativistic hydrodynamic equations are important in a large number of astrophysical simulations, which may be very dynamic and involve multiscale features. This requires computational methods that are highly adaptive and capable of automatically resolving numerous localized features and instabilities that emerge across the computational domain and over many temporal scales. While this has been historically accomplished with adaptive-mesh-refinement-based methods, alternatives using wavelet bases and the wavelet transformation have recently achieved significant success in adaptive representation for advanced engineering applications. The current work presents a new method, extending the wavelet adaptive multiresolution representation method, for the integration of the relativistic hydrodynamic equations using iterated interpolating wavelets and introduces a highly adaptive implementation for multidimensional simulation. We note the wavelet coefficients provide a direct measure of the local approximation error for the solution and place collocation points that naturally adapt to the fluid flow while providing good conservation of fluid quantities. The resulting implementation, OAHU , is applied to a series of demanding 1D and 2D problems that explore high Lorentz factor outflows and the formation of several instabilities, including the Kelvin–Helmholtz instability and the Rayleigh–Taylor instability.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Spin-state gaps and self-interaction-corrected density functional approximations: Octahedral Fe(II) complexes as case study

Accurate prediction of a spin-state energy difference is crucial for understanding the spin crossover phenomena and is very challenging for density functional approximations, especially for local and semi-local approximations due to delocalization errors. Here, we investigate the effect of the self-interaction error removal from the local spin density approximation (LSDA) and Perdew–Burke–Ernzerhof generalized gradient approximation on the spin-state gaps of Fe(II) complexes with various ligands using recently developed locally scaled self-interaction correction (LSIC) by Zope et al. [J. Chem. Phys. 151, 214108 (2019)]. The LSIC method is exact for one-electron density, recovers the uniform electron gas limit of the underlying functional, and approaches the well-known Perdew–Zunger self-interaction correction (PZSIC) as a particular case when the scaling factor is set to unity. Our results, when compared with reference diffusion Monte Carlo results, show that the PZSIC method significantly overestimates spin-state gaps favoring low spin states for all ligands and does not improve upon density functional approximations. The perturbative LSIC-LSDA using PZSIC densities significantly improves the gaps with a mean absolute error of 0.51 eV but slightly overcorrects for the stronger CO ligands. Finally, the quasi-self-consistent LSIC-LSDA, such as coupled-cluster single double and perturbative triple [CCSD(T)], gives a correct sign of spin-state gaps for all ligands with a mean absolute error of 0.56 eV, comparable to that of CCSD(T) (0.49 eV).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Adaptive mesh refinement for steady flows in Nek5000

Adaptive mesh refinement is performed in the framework of the spectral element method augmented by approaches to error estimation and control. The h-refinement technique is used for adapting the mesh, where selected grid elements are split by a quadtree (2D) or octree (3D) structure. Continuity between parent-child elements is enforced by high-order interpolation of the solution across the common faces. Parallel mesh partitioning and grid management respectively, are taken care of by the external libraries ParMETIS and p4est. Two methods are considered for estimating and controlling the error of the solution. The first error estimate is local and based on the spectral properties of the solution on each element. This method gives a local measure of the L-2-norm of the solution over the entire computational domain. The second error estimate uses the dual-weighted residuals method - it is based on and takes into account both the local properties of the solution and the global dependence of the error in the solution via an adjoint problem. The objective of this second approach is to optimize the computation of a given functional of physical interest. The simulations are performed by using the code Nek5000 and three steady-state test cases are studied: a two-dimensional lid-driven cavity at Re = 7, 500, a two-dimensional flow past a cylinder at Re = 40, and a three-dimensional lid-driven cavity at Re = 2,000 with a moving lid tilted by an angle of 30 degrees. Finally, the efficiency of both error estimators is compared in terms of refinement patterns and accuracy on the functional of interest. In the case of the adjoint error estimators, the trend on the error of the functional is shown to be correctly represented up to a multiplicative constant.

42 ENGINEERING↗
DOE OSTI2019

Modeling mechanical behavior of an additively manufactured metal structure with local texture variations: a study on model form error

Here, the repetitive rapid solidification that occurs in metal additive manufacturing (AM) processes creates microstructures distinctly different from wrought materials. Local variability in AM microstructures (either by design or unintentional) raises questions as to how AM structures should be modeled at the part-scale to minimize modeling error. The key goal of this work is to demonstrate a posteriori error estimation applied to an AM part. It is assumed that the actual microstructure is unknown and an approximate, spatially uniform material model is used. Error bounds are calculated for many reference models based on AM microstructures with elongated grain morphology and localized or global fiber textures during a post-processing step. The current findings promote confidence that a posteriori model form error estimation could be used effectively in mechanical performance simulations of AM parts to quickly obtain quantitative error metrics between an approximate model result and many microstructure-based reference models. The a posteriori error estimation introduces significant time savings compared to computing the full reference model solutions. Tight bounds on model form error are obtained when texture variations in the reference models occur on large length scales. For materials with property variation at small length scales, multi-scale error estimation techniques are needed to properly account for the many interfaces present between areas with different properties.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Distributed output-feedback model predictive control for multi-agent consensus

We introduce a distributed output-feedback model predictive control approach for achieving consensus among multiple agents. Each agent computes a distributed control action based on an output-feedback measurement of a local neighborhood tracking error and communicates information only to its neighbors, according to a communication network modeled as a directed graph. Each agent computes its distributed control action by solving a local min–max optimization problem that simultaneously computes a local state estimate and control input under worst-case assumptions on unmeasured input disturbances and measurement noise. Under easily verified controllability and observability assumptions, this distributed output-feedback model predictive control approach provides an upper bound on the group consensus error, thereby ensuring practical consensus in the presence of unmeasured disturbances and noise. A numerical example with four agents connected in a directed graph is demonstrated to illustrate the results.

42 ENGINEERING↗
DOE OSTI2023

Q-BEEP: Quantum Bayesian Error Mitigation Employing Poisson Modeling over the Hamming Spectrum

Quantum computing technology has grown rapidly in recent years, with new technologies being explored, error rates being reduced, and quantum processor’s qubit capacity growing. However, near-term quantum algorithms are still unable to be induced without compounding consequential levels of noise, leading to non-trivial erroneous results. Quantum Error Correction (in-situ error mitigation) and Quantum Error Mitigation (post-induction error mitigation) are promising fields of research within the quantum algorithm scene, aiming to alleviate quantum errors, increasing the overall fidelity and hence the overall quality of circuit induction. Earlier this year, a pioneering work, namely HAMMER, published in ASPLOS-22 demonstrated the existence of a latent structure regarding post-circuit induction errors when mapping to the Hamming spectrum. However, they intuitively assumed that errors occur in local clusters, and that at higher average Hamming distances this structure falls away. In this work, we show that such a correlation structure is not only local but extends certain non-local clustering patterns which can be precisely described by a Poisson distribution model taking the input circuit, the device run time status (i.e., calibration statistics) and qubit topology into consideration. Using this quantum error characterizing model, we developed an iterative algorithm over the generated Bayesian network state-graph for post-induction error mitigation. Thanks to more precise modeling of the error distribution latent structure and the new iterative method, our Q-Beep approach provides state of the art performance and can boost circuit execution fidelity by up to 234.6% on Bernstein-Vazirani circuits and on average 71.0% on QAOA solution quality, using 16 practical IBMQ quantum processors. For other benchmarks such as those in QASMBench, the fidelity improvement is up to 17.8%. Q-Beep is a light-weight post-processing technique that can be performed offline and remotely, making it a useful tool for quantum vendors to integrate and provide more reliable circuit induction results.

Stein, Samuel A.↗