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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

HyKKT: a hybrid direct-iterative method for solving KKT linear systems

Here, we propose a solution strategy for the large indefinite linear systems arising in interior methods for nonlinear optimization. The method is suitable for implementation on hardware accelerators such as graphical processing units (GPUs). The current gold standard for sparse indefinite systems is the LBLT factorization where L is a lower triangular matrix and B is 1×1 or 2×2 block diagonal. However, this requires pivoting, which substantially increases communication cost and degrades performance on GPUs. Our approach solves a large indefinite system by solving multiple smaller positive definite systems, using an iterative solver on the Schur complement and an inner direct solve (via Cholesky factorization) within each iteration. Cholesky is stable without pivoting, thereby reducing communication and allowing reuse of the symbolic factorization. We demonstrate the practicality of our approach on large optimal power flow problems and show that it can efficiently utilize GPUs and outperform LBL T factorization of the full system.

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 OSTI2024

DG-IMEX method for a two-moment model for radiation transport in the $\mathscr{O}$($v$/$c$) limit

Here, we consider neutral particle systems described by moments of a phase-space density and propose a realizability-preserving numerical method to evolve a spectral two-moment model for particles interacting with a background fluid moving with nonrelativistic velocities. The system of nonlinear moment equations, with special relativistic corrections to $\mathscr{O}$($v$/$c$), expresses a balance between phase-space advection and collisions and includes velocity-dependent terms that account for spatial advection, Doppler shift, and angular aberration. The model is conservative for the correct $\mathscr{O}$($v$/$c$) Eulerian-frame number density and is consistent, to $\mathscr{O}$($v$/$c$), with Eulerian-frame energy and momentum conservation. This model is closely related to the one promoted by Lowrie et al. and similar to models currently used to study transport phenomena in large-scale simulations of astrophysical environments. The proposed numerical method is designed to preserve moment realizability, which guarantees that the moments correspond to a nonnegative phase-space density. The realizability-preserving scheme consists of the following key components: (i) a strong stability-preserving implicit-explicit (IMEX) time-integration method; (ii) a discontinuous Galerkin (DG) phase-space discretization with carefully constructed numerical uxes; (iii) a realizability-preserving implicit collision update; and(iv) a realizability-enforcing limiter. In time integration, nonlinearity of the moment model necessitates solution of nonlinear equations, which we formulate as fixed-point problems and solve with tailored iterative solvers that preserve moment realizability with guaranteed global convergence. We also analyze the simultaneous Eulerian-frame number and energy conservation properties of the semi-discrete DG scheme and propose a "spectral redistribution" scheme that promotes Eulerian-frame energy conservation. Through numerical experiments, we demonstrate the accuracy and robustness of this DG-IMEX method and investigate its Eulerian-frame energy conservation properties.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Enhancing EV Motor Design Through Knowledge-Based AI and Hierarchical Fuzzy Logic Model

This work presents a novel approach to optimizing electric vehicle motor design through the integration of Knowledge-Based Artificial Intelligence (KB-AI) and Hierarchical Fuzzy Logic. Traditional motor design processes are time-intensive, relying heavily on iterative simulations and domain-specific expertise. These processes are further complicated by the nonlinear relationships between key design parameters. The proposed framework addresses these challenges by systematically encoding expert knowledge from scientific literature into a fuzzy logic system, allowing for the efficient handling of complex design variables. The hierarchical fuzzy logic model reduces computational complexity by decomposing the nonlinear relationships into manageable rule sets while maintaining design accuracy. The proposed methodology was applied to the design of a 100 kW motor, yielding optimal values for key parameters. This resulted in a compact motor design with a volume of 2.2 liters, showcasing the framework’s ability to deliver high-performance, application-specific motor configurations.

Kumar, Praveen [ORNL] (ORCID:0000000291877857)↗
DOE OSTI2025

Assessing Edge Localized Mode (ELM) Mitigation by Pellet Triggering in Smallest-Possible Affordable Robust Compact (SPARC) Low-Collisionality Discharges

Simulations of pellet edge-localized mode (ELM) triggering with the M3D-C1 code confirmed experimentally observed pellet mass thresholds in low-collisionality DIII-D discharges and predicted extremely large thresholds in ITER [A. Wingen et al, Nucl. Fusion 64, 066015(2024)]. The linear (static) and nonlinear (dynamic) workflows developed in this previous work are now applied to the SPARC tokamak. Multiple synthetic equilibria for the high-performance H-mode scenario are tested for MHD stability without pellets using the linear workflow and ELITE simulations; a stable one is identified. Pellets of various mass are injected along an inboard, near-midplane trajectory in the M3D-C1 simulation. No pellet mass threshold for ELM triggering can be found for realistic pellet masses, concluding that fueling from this injection location would not trigger ELMs. A poloidal scan of possible injection locations shows very high thresholds on the high-field side and reasonable thresholds on the low-field-side (LFS). Based on results of this work the location for a LFS injection was finalized in the SPARC design. For this LFS injection the pellet mass threshold is determined using the linear workflow, aligning well with the poloidal scan.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

The W4 method: A new multi-dimensional root-finding scheme for nonlinear systems of equations

We propose a new class of method for solving nonlinear systems of equations, which, among other things, has four nice features: (i) it is inspired by the mathematical property of damped oscillators, (ii) it can be regarded as a simple extension to the Newton-Raphson (NR) method, (iii) it has the same local convergence as the NR method does, (iv) it has a significantly wider convergence region or the global convergence than that of the NR method. In this article, we present the evidence of these properties, applying our new method to some examples and comparing it with the NR method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

IMEX Runge-Kutta Parareal for Non-diffusive Equations

Parareal is a widely studied parallel-in-time method that can achieve meaningful speedup on certain problems. However, it is well known that the method typically performs poorly on non-diffusive equations. This paper analyzes linear stability and convergence for IMEX Runge-Kutta Parareal methods on non-diffusive equations. By combining standard linear stability analysis with a simple convergence analysis, we find that certain Parareal configurations can achieve parallel speedup on non-diffusive equations. These stable configurations all posses low iteration counts, large block sizes, and a large number of processors. Numerical examples using the nonlinear Schrodinger equation demonstrate the analytical conclusions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A note on higher-order and nonlinear limiting approaches for continuously bounds-preserving discontinuous Galerkin methods

In Dzanic (2024), a limiting approach for high-order discontinuous Galerkin schemes was introduced which allowed for imposing constraints on the solution continuously (i.e., everywhere within the element). While exact for linear constraint functionals, this approach only imposed a sufficient (but not the minimum necessary) amount of limiting for nonlinear constraint functionals. This short note shows how this limiting approach can be extended to allow exactness for general nonlinear quasiconcave constraint functionals through a nonlinear limiting procedure, reducing unnecessary numerical dissipation. Finally, some examples are shown for nonlinear pressure and entropy constraints in the compressible gas dynamics equations, where both analytic and iterative approaches are used.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Recent advances in computational mathematics and applications

We are honored to bring you this special issue dedicated to recent advances in computational mathematics and applications in science and engineering. The papers in this special issue were presented in ”Conference on Computational Mathematics and Applications (CCMA)” held at the University of Nevada Las Vegas (UNLV) during October 25–27, 2019. The conference has attracted about 90 attendees from six countries. The 15 papers in the special issue comprise a diverse collection of theoretical numerical analysis as well as applications in various subjects. Topics cover optimal control of PDEs, discontinuous Galerkin methods, fluid flow in porous media, turbulence flow, static and moving interface problems, complex fluids composed by the mixture of Newtonian fluid and nematic (liquid crystal) flows, modeling of ocean–atmosphere system, image segmentation algorithm, uncertainty quantification problems for turbulence model and Maxwell’s equations, iterative solver for systems resulting from mixed methods, and novel methods for solving systems of nonlinear equations. As the Guest Editors we would like to thank Dr. Leland Jameson at NSF (National Science Foundation) for kindly supporting our conference proposal which made this conference possible. We would also like to thank Darren Sugrue from Elsevier who provided partial support for our conference, and Thennarasu Gunasekaran and his production team from Elsevier who produced this nice special issue. We are grateful to many people (Dr. Zhijian Wu, Lori Ornelas, Elsa Juarez, and many Ph.D. students) at the Department of Mathematical Sciences of UNLV who provided tremendous support for the conference. Finally, we very much appreciate all authors who contributed their precious results to this special issue.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Resistive wall tearing mode disruptions

Abstract This paper deals with resistive wall tearing mode (RWTM) disruptions. RWTMs are closely related to resistive wall modes. RWTMs are tearing modes whose linear and nonlinear behavior is strongly dependent on the resistive wall outside the plasma. The consequence for ITER, is that the thermal quench timescale could be much longer than previously conjectured. Active feedback stabilization is another possible way to mitigate or prevent RWTM disruptions. Simulations of RWTM disruptions are reviewed for DIII-D and MST. MST has a longer resistive wall time than ITER, and disruptions are not observed experimentally when MST is operated as a standard tokamak. Simulations indicate that the RWTM disruption time scale is longer than the experimental shot time. Edge cooling causes contraction of the current profile, which can destabilize RWTMs. The equilibria studied here have the q = 2 rational surface close to the edge of the plasma, and low current density between the q = 2 surface and the wall. A sequence of low edge current model equilibria has major disruptions only for a resistive, not ideal, wall, and edge q ⩽ 3.4 . This is consistent with regimes of tokamak disruptivity, suggesting that tokamak disruptions caused by edge cooling at low edge q could be RWTMs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Enhancing Photosynthesis Simulation Performance in ESMs with Machine Learning-Assisted Solvers

When simulating vegetation dynamics, photosynthesis accounts for a large fraction of the computational cost in most Earth System Models (ESMs). This is largely since photosynthesis is represented as a system of nonlinear equations, and the solution requires the use of an initial guess followed by many iterations of the numerical solver to obtain a solution. We use machine learning (ML) to replicate the response surface of the model’s numerical solver to improve the choice of initial guess, therefore requiring fewer iterations to obtain a final solution. We implemented this test on the leaf-level calculations as well as at the canopy scale, and for both we observed fewer iterations of the photosynthesis solver when a ML-based initial guess was implemented. The model tested here is the Energy Exascale Earth System Model - Land Model (ELM). The ML-based algorithms used here are trained on simulations from the model itself and used only to improve the initial guess for the solver; therefore, the model maintains its own set of physics to obtain the final solution. This work shows novel ways to utilize ML-based methods to improve the performance of numerical solvers in ESMs.

Massoud, Elias [ORNL] (ORCID:0000000217725361)↗
DOE OSTI2025

Energetic particle physics: Chapter 7 of the special issue: on the path to tokamak burning plasma operation

We review the physics of energetic particles (EPs) in magnetically confined burning fusion plasmas with focus on advances since the last update of the ITER Physics Basis (Fasoli et al 2007 Nucl. Fusion 47 S264). Topics include basic EP physics, EP generation, diagnostics of EPs and instabilities, the interaction of EPs and thermal plasma instabilities, EP-driven instabilities, energetic particle modes (EPMs), and turbulence, linear and nonlinear stability and simulation of EP-driven instabilities and EPMs, 3D effects, scenario optimization strategies based on EP phase-space control, EPs in reduced field scenarios in ITER before DT, and the physics of runaway electrons. We describe the simulation and modeling of EPs in fusion plasmas, including instability drive and damping as well as EP transport, with a range of approaches from first-principles to reduced models, including gyrokinetic simulations, kinetic-MHD models, gyrofluid models, reduced models, and semi-analytical approaches.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

A Physics-Driven Deep-Learning Network for Solving Nonlinear Inverse Problems

Geosteering inversion, which can be viewed as a nonlinear inverse problem, is an important technique used by directional drilling. Traditional methods that rely on iterative procedures and regularization are sensitive to the selection of initial values and can be slow due to convergence issues. In industrial applications, a lookup table is used to produce fast predictions. However, performance is not guaranteed by this approach due to the limitation of the hardware. In this paper, we propose a novel physics-driven deep-learning framework for providing a fast, accurate surrogate to solve the inverse problem. Particularly, leveraged by the forward physical model and 1D convolutional neural network (1D-CNN), the proposed method provides more reliable solutions to the inverse problem with improved performance. In addition, a new physics-driven loss function is introduced to accommodate both the model misfit and the data misfit. In conclusion, our experiments demonstrate the effectiveness of our method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

thornado-transport: Anderson- and GPU-accelerated nonlinear solvers for neutrino-matter coupling

Algorithms for neutrino-matter coupling in core-collapse supernovae (CCSNe) are investigated in the context of a spectral two-moment model, which is discretized in space with the discontinuous Galerkin method, integrated in time with implicit-explicit (IMEX) methods, and implemented in the toolkit for high-order neutrino-radiation hydrodynamics (thornado). The model considers electron neutrinos and antineutrinos and tabulated opacities from Bruenn (1985), which includes neutrino-electron scattering and pair processes. The nonlinear system arising from implicit time discretization of the equations governing neutrino-matter coupling is iterated to convergence using Anderson-accelerated fixed-point methods, which avoid formation of Jacobians and inversion of dense linear systems. Numerical experiments show that, for a given tolerance, a nested iteration scheme which aims to reduce opacity evaluations can lower the computational cost. Our initial port to GPUs, using both OpenMP and OpenACC, shows an overall speedup of up to ~ 100× when compared to results using a single CPU core. These results indicate that the algorithms implemented in thornado are well-suited to GPU acceleration.

Laiu, Paul↗
DOE OSTI2024

A simulation study of the ability to detect power distribution perturbations in the texas A&M TRIGA reactor with self-powered neutron detectors

Given the variety of ways that nuclear reactor core power may be perturbed, reactor operators and developers are keen on understanding the accuracy and convergence time during which perturbations in reactor power distribution may be synthesized (i.e., inferred) from an array of in-core radiation detectors. A simulation study was conducted as described herein using a highly detailed model of the Texas A&M Training, Research, Isotopes, General Atomics Reactor, in which an array of self-powered neutron detectors (SPNDs) was considered for input to the power synthesis methodology. The core power synthesis is conducted using a point-based iterative method with an iterative loop built in to ensure working equation consistency. The forward problem of SPND response to simulated perturbations in reactor power was solved for Gaussian peak-type perturbations in the reactor power distribution. These perturbations varied in variance, amplitude, and core location to assess their impact on synthesis error and to determine the number of iterations required for convergence. A relation between the unique resolvability limit and perturbation width was identified such that the maximum synthesis error increased rapidly when the peak width went beneath this limit (a width approximating half the reactor’s fuel pin-to-pin pitch); this resolvability limit is specific to the SPND configuration and fuel segmentation considered herein. The synthesis error increased linearly with perturbation peak amplitude, whereas the convergence time increased nonlinearly. Perturbations located closer to the center of the core were synthesized more accurately, albeit with a higher number of required iterations. These findings provide a qualitative and quantitative understanding of the accuracy and speed at which different types of spatial power perturbations can be resolved in light-water reactors.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2020

Iterative Learning Control for Video-rate Atomic Force Microscopy

We present a control scheme for video-rate atomic force microscopy with rosette pattern. The controller structure involves a feedback internal-model-based controller and a feedforward iterative learning controller. The iterative learning controller is designed to improve tracking performance of the feedback-controlled scanner by rejecting the repetitive disturbances arising from the system nonlinearities. We investigate the performance of two inversion techniques for constructing the learning filter. We conduct tracking experiments using a two-degree-of-freedom microelectromechanical system (MEMS) nanopositioner at frame rates ranging from 5 to 20 frames per second. Furthermore, the results reveal that the algorithm converges rapidly and the iterative learning controller significantly reduces both the transient and steady-state tracking errors. We acquire and report a series of high-resolution time-lapsed video-rate AFM images with the rosette pattern.

42 ENGINEERING↗
DOE OSTI2026

Impact of n > 1 neoclassical tearing modes on fast ions, plasma rotation, and the onset of disruptive tearing modes in DIII-D ITER baseline scenario

We present integrated TRANSP-kick analyses quantitatively characterizing how n > 1 magnetic islands redistribute fast ions (FIs) and modify momentum balance in low-torque DIII-D H-mode scenarios operated with the ITER normalized parameter set and shape (ITER baseline scenario, or IBS). In this plasma scenario, disruptive neoclassical tearing modes (NTMs) are most commonly seeded by nonlinear 3-wave coupling when the differential rotation between the q = 1 and q = 2 surfaces ($δf_{1, 2}$) approaches zero. Analysis of a DIII-D IBS database of shots unstable to the 2/1 NTM demonstrates that the flattening rotation profile is correlated with n > 1 NTM amplitude growth, with a strong drop in $δf_{1, 2}$ occurring when the radial magnetic perturbation amplitude at the rational surface ($δB$ r s ) is estimated to be about 20 G. The interpretive TRANSP-kick simulations show that the experimentally observed reduction in core rotation is due to the fast-ion kicks. Nonlinearity in momentum losses versus NTM amplitude is found to be correlated with overlap of FI island chains, occurring when $δB$ r s is about 35 G, in rough agreement with the experimental results. This agreement suggests the primary mechanism for the conductive momentum loss in the core is due to chaotic FI orbits and FI losses developing from overlapping resonant FI island chains.

ITER baseline scenario↗
DOE OSTI2023

A fast Fourier transform-based solver for elastic micropolar composites

This work presents a spectral micromechanical formulation for obtaining the full-field and homogenized response of elastic micropolar composites. The algorithm relies on a coupled set of convolution integral equations for the micropolar strains, where periodic Green’s operators associated with a linear homogeneous reference medium are convolved with functions of the Cauchy and couple stress fields that encode the material’s heterogeneity, as well as any potential material nonlinearity. Such convolution integral equations take an algebraic form in the reciprocal Fourier space that can be solved iteratively. In this vein, the fast Fourier transform (FFT) algorithm is leveraged to accelerate the numerical solution, resulting in a mesh-free formulation in which the periodic unit cell representing the heterogeneous material can be discretized by a regular grid of pixels in two dimensions (or voxels in three dimensions). For verification, the numerical solutions obtained with the micropolar FFT solver are compared with analytical solutions for a matrix with a dilute circular inclusion subjected to plane strain loading. The developed computational framework is then used to study length-scale effects and effective (micropolar) moduli of composites with various topological configurations.

97 MATHEMATICS AND COMPUTING↗