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DOE OSTI2022

The Schwarz alternating method for transient solid dynamics

Abstract In our earlier work, we formulated the Schwarz alternating method as a means for concurrent multiscale coupling in finite deformation solid mechanics for quasi‐static problems. Herein, we advance this method for the study of transient dynamic multiscale solid mechanics problems where information is exchanged back and forth between small and large scales. The extension to dynamics relies on the notion of a global time stepper. Within each global time step, the subdomains are coupled by the standard Schwarz iterative process. Remarkably, each subdomain can use its own time step or even its own time integrator to advance its solution in time, provided that they synchronize at each global time step. We study the performance of the Schwarz method on several examples designed for this purpose. Our numerical experiments demonstrate that the method is capable of coupling regions with different mesh resolutions, different element types, and different time integration schemes (e.g., implicit and explicit), all without introducing any artifacts that afflict other coupling methods for transient dynamics. Finally, we apply the dynamic Schwarz alternating method to the simulation of a bolted joint subjected to dynamic loading, as a demonstration of the performance of the method in a realistic scenario.

Mota, Alejandro↗

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↗

DOE OSTI2020

Estimation of stress and stress-induced permeability change in a geological nuclear waste repository in a thermo-hydrologically coupled simulation

Geologic disposal is a promising solution for a safe permanent isolation of accumulated high-level nuclear waste from nuclear powerplants. The behavior of host rock is highly coupled thermally, hydromechanically, and chemically. Numerical simulations of such coupled phenomena for the extremely long term (>100,000 years) and large length scale (>1 km) of geologic disposal remain to be computationally challenging. In this study, a methodology has been developed to approximate stress and stress-induced permeability change in host rock using only thermo-hydrological (TH) variables. A coupled thermo-hydromechanical (THM) simulation is carried out using TOUGH-FLAC simulator to model THM behaviors of a generic nuclear waste repository, in order to evaluate the performance of the developed methodology, which is implemented in a coupled TH simulation. Results show that stress and permeability change estimated by the developed methodology in the TH-coupled simulation match those calculated in the THM-coupled simulation over the simulated timeframe of over 10,000 years. Details about errors in stress and permeability estimates accrued by the developed methodology are discussed here. The developed methodology will help incorporate stress-induced permeability change into existing TH simulators for the long-term radionuclide transport in geologic disposal.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2023

Exponential Runge-Kutta Parareal for non-diffusive equations

Parareal is a well-known parallel-in-time algorithm that combines a coarse and fine propagator within a parallel iteration. It allows for large-scale parallelism that leads to significantly reduced computational time compared to serial time-stepping methods. However, like many parallel-in-time methods it can fail to converge when applied to non-diffusive equations such as hyperbolic systems or dispersive nonlinear wave equations. Here, this paper explores the use of exponential integrators within the Parareal iteration. Exponential integrators are particularly interesting candidates for Parareal because of their ability to resolve fast-moving waves, even at the large stepsizes used by coarse propagators. This work begins with an introduction to exponential Parareal integrators followed by several motivating numerical experiments involving the nonlinear Schrödinger equation. These experiments are then analyzed using linear analysis that approximates the stability and convergence properties of the exponential Parareal iteration on nonlinear problems. The paper concludes with two additional numerical experiments involving the dispersive Kadomtsev-Petviashvili equation and the hyperbolic Vlasov-Poisson equation. These experiments demonstrate that exponential Parareal methods offer improved time-to-solution compared to serial exponential integrators when solving certain non-diffusive equations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Dimensional Interpolation for Random Walk

In this work, we employ a simple and accurate dimensional interpolation formula for the shapes of random walks at D = 3 and D = 2 based on the analytically known solutions at both limits D = ∞ and D = 1. The results obtained for the radius of gyration of an arbitrary shaped object have about 2% error compared with accurate numerical results at D = 3 and D = 2. We also calculated the asphericity for a three-dimensional random walk using the dimensional interpolation formula. The results agree very well with the numerically simulated results. The method is general and can be used to estimate other properties of random walks.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Thermal transport exceeding bulk heat conduction due to nonthermal micro/nanoscale phonon populations

While classical size effects usually lead to a reduced effective thermal conductivity, we report here that nonthermal phonon populations produced by a micro/nanoscale heat source can lead to enhanced heat conduction, exceeding the prediction from Fourier's law. We study nondiffusive thermal transport by phonons at small distances within the framework of the Boltzmann transport equation (BTE) and demonstrate that the transport is significantly affected by the distribution of phonons emitted by the source. We discuss analytical solutions of the steady-state BTE for a source with a sinusoidal spatial profile, as well as for a three-dimensional Gaussian “hot spot,” and provide numerical results for single crystal silicon at room temperature. If a micro/nanoscale heat source produces a thermal phonon distribution, it gets hotter than that predicted by the heat diffusion equation; however, if the source predominantly produces low-frequency acoustic phonons with long mean free paths, it may get significantly cooler than that predicted by the heat equation, yielding an enhanced heat transport beyond bulk heat conduction.

42 ENGINEERING↗

DOE OSTI2021

Protein-assisted scalable mechanochemical exfoliation of few-layer biocompatible graphene nanosheets

A facile method to produce few-layer graphene (FLG) nanosheets is developed using protein-assisted mechanical exfoliation. The predominant shear forces that are generated in a planetary ball mill facilitate the exfoliation of graphene layers from graphite flakes. The process employs a commonly known protein, bovine serum albumin (BSA), which not only acts as an effective exfoliation agent but also provides stability by preventing restacking of the graphene layers. The latter is demonstrated by the excellent long-term dispersibility of exfoliated graphene in an aqueous BSA solution, which exemplifies a common biological medium. The development of such potentially scalable and toxin-free methods is critical for producing cost-effective biocompatible graphene, enabling numerous possible biomedical and biological applications. A methodical study was performed to identify the effect of time and varying concentrations of BSA towards graphene exfoliation. The fabricated product has been characterized using Raman spectroscopy, powder X-ray diffraction, transmission electron microscopy and scanning electron microscopy. The BSA-FLG dispersion was then placed in media containing Astrocyte cells to check for cytotoxicity. It was found that lower concentrations of BSA-FLG dispersion had only minute cytotoxic effects on the Astrocyte cells.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

General relativistic hydrodynamic simulations of binary strange star mergers

We perform fully general-relativistic simulations of binary strange star mergers considering two different approaches for thermal effects. The first uses a cold equation of state (EOS) derived from a modified version of the MIT bag model which is then supplemented by a Γ-law correction. The second approach employs a microphysical description of the finite-temperature effects. We describe results obtained with the two treatments, highlighting the influence of thermal effects. We find that the postmerger dynamics differs significantly in the two cases, leading to quantitative differences in the postmerger gravitational-wave spectrum and ejecta mass. The peak frequency of the postmerger gravitational-wave emission is consistent with the established quasi-universal relations for binary neutron star mergers and as a result, our simulations cannot distinguish between mergers of neutron stars and those of strange stars. Our models with realistic treatment of finite-temperature effects produce a significant amount of ejecta ≳0.02 M ⊙ . Here, the resulting flux of strangelets near the Earth, computed assuming that all neutron star mergers are in fact strange-stars mergers and that the binary considered here is representative, is in tension with experimental upper limits. As such, our results tentatively disfavor a scenario in which strange-quark matter is the lowest energy state of matter.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Optimal Control of Biomass Feedstock Processing System Under Uncertainty in Biomass Quality

Planning of biorefinery operations is complicated by the stochastic nature of physical and chemical characteristics of biomass feedstock, such as, moisture level and carbohydrate content. Biomass characteristics affect the performance of the equipment which feed the reactor and the efficiency of the conversion process in a biorefinery. We propose a stochastic optimization model to identify a blend of feedstocks, inventory levels, and operating conditions of equipment to ensure a continuous flowing of biomass to the reactor while meeting the requirements of the biochemical conversion process. We propose a sample average approximation (SAA) of the model, and develop an efficient algorithm to solve the SAA model. A feedstock preprocessing process consists of two-stage grinding and pelleting is used to develop a case study. Extensive numerical analysis are conducted which lead to a number of observations. Our main observation is that sequencing bales based on moisture level and carbohydrate content leads to robust solutions that improve processing time and processing rate of the reactor. We provide a number of managerial insights that facilitate the implementation of the model proposed. Note to Practitioners—This paper is motivated by the challenges faced in the bioenergy industry. The focus of this paper is on plants which use the biochemical conversion process to generate liquid fuels. It has been observed that variations in biomass characteristics, such as moisture content, cause variations in feeding of the system which lead to under-utilization of equipment. A requirement of biochemical conversion process is to maintain the carbohydrate content of biomass processed by the reactor, larger than a threshold. We propose a model that identifies the inventory levels and operating conditions of equipment to ensure a continuous flowing of biomass to the reactor. The goal is to improve equipment utilization while satisfying the requirements of the conversion process. The model is tested using real-life data. We found out that by sequencing bales based on moisture level and carbohydrate content, a plant can reduce variability in the system leading to improved system reliability, higher processing rates of the reactor, and higher throughput.

09 BIOMASS FUELS↗

DOE OSTI2021

Multi-Period Active Distribution Network Planning Using Multi-Stage Stochastic Programming and Nested Decomposition by SDDIP

This paper presents a multi-period active distribution network planning (ADNP) with distributed generation (DG). The objective of the proposed ADNP is to minimize the total planning cost, subject to both investment and operation constraints. The paper proposes a multi-stage stochastic optimization model to address DG uncertainties over several periods, in which the decisions are made sequentially by only using the present-stage information. A nested decomposition method is proposed which applies the stochastic dual dynamic integer programming (SDDIP) method to address computational intractabilities of the proposed ADNP approach. The presented numerical results and discussions on a 33-bus distribution system and a large-scale 906-bus system verify the effectiveness of the proposed ADNP method and its solution method.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2025

Simulating many-engine spacecraft: Exceeding 1 quadrillion degrees of freedom via information geometric regularization

We present an optimized implementation of the recently proposed information geometric regularization (IGR) for unprecedented scale simulation of compressible fluid flows applied to multi-engine spacecraft boosters. We improve upon state-of-the-art computational fluid dynamics (CFD) techniques in terms of computational cost, memory footprint, and energy-to-solution metrics. Unified memory on coupled CPU–GPU or APU platforms increases problem size with negligible overhead. Mixed half/single-precision storage and computation are used on well-conditioned numerics. We simulate flow at 200 trillion grid points and 1 quadrillion degrees of freedom, exceeding the current record by a factor of 20. A factor of 4 wall-time speedup is achieved over optimized baselines. Ideal weak scaling is observed on OLCF Frontier, LLNL El Capitan, and CSCS Alps using the full systems. Strong scaling is near ideal at extreme conditions, including 80% efficiency on CSCS Alps with an 8 node baseline and stretching to the full system.

Wilfong, Benjamin [Georgia Institute of Technology↗

DOE OSTI2022

A Quantized State Integrator With Second Order Errors Over Monotonic Segments

We introduce a novel quantized state integration method that is analogous to the explicit, second order Runge-Kutta technique. A feature of this method is that, for a single differential equation over an interval where the solution is monotonic, it exhibits an error proportional to the square of the integration quantum. We offer a theoretical proof of this behavior and demonstrate it with a numerical example. At the same time, an extension of the method to a system with input causes the errors to become proportional to the integration quantum. The latter observation fits established theory; the former appears to be a new result that might offer new insights into the construction of quantized state integration methods.

Mahawattege, Rasika↗

DOE OSTI2020

Tycho: Realistically Simulating Exoplanets within Stellar Clusters. I. Improving the Monte Carlo Approach

To fully understand the diverse population of exoplanets, we must study their early lives within open clusters, the birthplace of most stars with masses >0.5M {sub ⊙} (including those currently in the field). Indeed, when we observe planets within clustered environments, we notice highly eccentric and odd systems that suggest the importance of dynamical pathways created by interactions with additional bodies (as in the case of HD 285507b). However, it has proven difficult to investigate these effects, as many current numerical solvers for the multi-scale N-body problem are simplified and limited in scope. To remedy this, we aim to create a physically complete computational solution to explore the role of stellar close encounters and interplanetary interactions in producing the observed exoplanet populations for both open cluster stars and field stars. We present a new code, Tycho, which employs a variety of different computational techniques, including multiple N-body integration methods, close encounter handling, modified Monte Carlo scattering experiments, and a variety of empirically informed initial conditions. We discuss the methodology in detail, and its implementation within the AMUSE software framework. Approximately 1% of our systems are promptly disrupted by star-star encounters contributing to the rogue planets occurrence rate. Additionally, we find that close encounters which that perturb long-period planets lead to 38.3% of solar-system-like planetary systems becoming long-term unstable.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Techno-economic feasibility of borehole thermal energy storage system connected to geothermal heat pumps for seasonal heating load of two buildings in Fairbanks, Alaska

Borehole thermal energy storage (BTES) is an effective solution for managing imbalanced heating and cooling loads in cold regions. This study evaluated the long-term feasibility of a BTES system in the Fairbanks area, Alaska, through building energy modeling, resource characterization, and numerical modeling. The system was designed to store waste heat from a nearby coal power plant during summer and provide thermal energy during winter to geothermal heat pumps supplying heating loads in two buildings. Heating load profiles were modeled for the buildings using EnergyPlus, and the results indicated the annual heating load was 5.6 times greater than the cooling load. 40 borehole heat exchangers were pre-designed approximately 100 m away from the two buildings in terms of land availability and regulatorily optimized depth. The 20-year performance of the designed BTES system under two operational scenarios—one with a 5-year preheating period and one without—was numerically modeled using subsurface temperature and properties characterized through the literature review and thermal response tests. Both scenarios demonstrated that the BTES has the capacity to fully cover the heating loads in the two buildings throughout the 20-year lifetime. Production temperatures at central wells were 33 % higher on average than at outer wells in both scenarios. The 5-year preheating period increased subsurface and extraction temperatures, and correspondingly annual average and total thermal energy production was higher for 8 years than in the scenario without the preheating period. These results highlight the long-term reliability and sustainability of the BTES system in meeting heating demands over its lifetime, with the preheating period offering potential performance improvements. Implementing the BTES system in cold regions with high heating demand, such as Fairbanks, Alaska, could provide a long-term, sustainable energy solution for managing imbalanced heating and cooling loads.

15 GEOTHERMAL ENERGY↗

DOE OSTI2022

Significant improvement of conversion efficiency by passivation of low-angle grain boundaries in flexible low-cost single-crystal-like GaAs thin-film solar cells directly deposited on metal tape

We develop an easily implementable yet effective process to achieve high power conversion efficiency in newly-developed flexible single-crystal-like GaAs thin-film photovoltaic solar cells on cheap metal tape. We study various techniques on the fabricated devices to passivate the defect states associated with dangling bonds at low-angle grain boundaries (LA-GBs) existing in the single-crystal-like GaAs material. We report that sulfur by trioctylphosphine sulfide (TOP:S) solution treatment can partially but effectively passivate the defect states at the LA-GBs to increase all the solar cell performance parameters of open-circuit voltage VOC (33.2%), short-circuit current JSC (19.5%), and fill factor FF (25.8%), resulting in the improvement of the power conversion efficiency more than double. The material and device characterizations and numerical modeling are performed to propose a mechanism, also suggesting that the power conversion efficiency higher than 20%, which is an important target milestone in emerging solar cell technologies, can be achieved. This work presents the first effective passivation of the bulk defects in GaAs at the device level and can also offer a solution for other photonic and electronic devices using non-single-crystalline GaAs films for flexible electronics.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Pyomo.GDP: an ecosystem for logic based modeling and optimization development

We present three core principles for engineering-oriented integrated modeling and optimization tool sets—intuitive modeling contexts, systematic computer-aided reformulations, and flexible solution strategies—and describe how new developments in Pyomo.GDP for Generalized Disjunctive Programming (GDP) advance this vision. We describe a new logical expression system implementation for Pyomo.GDP allowing for a more intuitive description of logical propositions. The logical expression system supports automated reformulation of these logical constraints to linear constraints. We also describe two new logic-based global optimization solver implementations built on Pyomo.GDP that exploit logical structure to avoid “zero-flow” numerical difficulties that arise in nonlinear network design problems when nodes or streams disappear. These new solvers also demonstrate the capability to link to external libraries for expanded functionality within an integrated implementation. We present these new solvers in the context of a flexible array of solution paths available to GDP models. Finally, we present results on a new library of GDP models demonstrating the value of multiple solution approaches.

42 ENGINEERING↗

DOE OSTI2023

Generalized analytical and numerical modeling of optical second harmonic generation in anisotropic crystals and complex heterostructures using #SHAARP package

Optical second harmonic generation (SHG) is a nonlinear optical effect widely used for nonlinear optical microscopy and laser frequency conversion. The closed-form analytical solution of the nonlinear optical responses is essential for evaluating the optical responses of new materials whose optical properties are unknown a priori. Many approximations have therefore been employed in the existing analytical approaches, such as slowly varying approximation, weak reflection of the nonlinear polarization, transparent medium, high crystallographic symmetry, Kleinman symmetry, easy crystal orientation along a high-symmetry direction, phase matching conditions and negligible interference among nonlinear waves, which may lead to large errors in the reported material properties. To avoid these approximations, here we have developed an open-source package named Second Harmonic Analysis of Anisotropic Rotational Polarimetry (#SHAARP) for single interface (si) and in multilayers (ml) for homogeneous crystals. The reliability and accuracy are established by experimentally benchmarking with both the SHG polarimetry and Maker fringes predicted from the package using standard materials. SHAARP.si and SHAARP.ml are available through GitHub https://github.com/Rui-Zu/SHAARP and https://github.com/bzw133/SHAARP.ml, respectively.

complex systems↗

DOE OSTI2024

Bayesian optimization algorithms for accelerator physics

Accelerator physics relies on numerical algorithms to solve optimization problems in online accelerator control and tasks such as experimental design and model calibration in simulations. The effectiveness of optimization algorithms in discovering ideal solutions for complex challenges with limited resources often determines the problem complexity these methods can address. The accelerator physics community has recognized the advantages of Bayesian optimization algorithms, which leverage statistical surrogate models of objective functions to effectively address complex optimization challenges, especially in the presence of noise during accelerator operation and in resource-intensive physics simulations. In this review article, we offer a conceptual overview of applying Bayesian optimization techniques toward solving optimization problems in accelerator physics. We begin by providing a straightforward explanation of the essential components that make up Bayesian optimization techniques. We then give an overview of current and previous work applying and modifying these techniques to solve accelerator physics challenges. Finally, we explore practical implementation strategies for Bayesian optimization algorithms to maximize their performance, enabling users to effectively address complex optimization challenges in real-time beam control and accelerator design. Published by the American Physical Society 2024

43 PARTICLE ACCELERATORS↗