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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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DOE OSTI2024

Convergence of Weak-SINDy Surrogate Models

In this paper, we give an in-depth error analysis for surrogate models generated by a variant of the Sparse Identification of Nonlinear Dynamics (SINDy) method. We start with an overview of a variety of nonlinear system identification techniques, namely SINDy, weak-SINDy, and the occupation kernel method. Under the assumption that the dynamics are a finite linear combination of a set of basis functions, these methods establish a linear system to recover coefficients. We illuminate the structural similarities between these techniques and establish a projection property for the weak-SINDy technique. Following the overview, we analyze the error of surrogate models generated by a simplified version of weak-SINDy. In particular, under the assumption of boundedness of a composition operator given by the solution, we show that (i) the surrogate dynamics converges towards the true dynamics and (ii) the solution of the surrogate model is reasonably close to the true solution. Finally, as an application, we discuss the use of a combination of weak-SINDy surrogate modeling and proper orthogonal decomposition (POD) to build a surrogate model for partial differential equations (PDEs).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Robustness of vortex-bound Majorana zero modes against correlated disorder

Here, we investigate the effect of correlated disorder on Majorana zero modes (MZMs) bound to magnetic vortices in two-dimensional topological superconductors. By starting from a lattice model of interacting fermions with a p x ±ip y superconducting ground state in the disorder-free limit, we use perturbation theory to describe the enhancement of the Majorana localization length at weak disorder and a self-consistent numerical solution to understand the breakdown of the MZMs at strong disorder. We find that correlated disorder has a much stronger effect on the MZMs than uncorrelated disorder and that it is most detrimental if the disorder correlation length ℓ is on the same order as the superconducting coherence length ξ. In contrast, MZMs can survive stronger disorder for ℓ $\ll$ξ as random variations cancel each other within the length scale of ξ, while an MZM may survive up to very strong disorder for ℓ$\gg$ξ if it is located in a favorable domain of the given disorder realization.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

The oscillatory anisotropy in the spatially flat cosmological models

Highlights: • Relations among asymptotic anisotropy and matter content. • A new scheme for obtaining physically motivated exact solutions. • The process of isotropization/anisotropization in cosmology. • The conversion among the anisotropy and the energy density into one another. In this manuscript, we investigate the oscillatory behaviour of the anisotropy in the diagonal Bianchi-I spacetimes. Our starting point is a simplification of Einstein’s equations using only observable or physical variables. As a consequence, we are able to: (a) Prove general results concerning the existence of oscillations of the anisotropy in the primordial and the late-time universe. For instance, in the expanding scenario, we show that a past weakly mixmaster behaviour (oscillations as we approach the Kasner solutions) might appear even with no violation of the usual energy conditions, while in the future, the pulsation (oscillations around isotropic solutions) seems to be most favoured; (b) Determine a large scheme for deriving classes of physically motivated exact solutions, and we give some (including the general barotropic perfect fluid and the magnetic one); (c) Understand the physical conditions for the occurrence of the isotropization or anisotropization during the cosmological evolution; (d) Understand how anisotropy and energy density are converted one into another. In particular, we call attention to the presence of a residue in the energy density in a late-time isotropic universe coming from its past anisotropic behaviour.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Exploring the Landscape of Distributed Graph Clustering on Leadership Supercomputers

The rapid growth of large-scale datasets in fields like biology and social networks has driven the need for advanced graph analytics techniques. Community detection, a fundamental task in graph analytics, identifies closely connected groups of nodes within a network, providing valuable insights across various disciplines. This study focuses on two classic community detection methods, the Louvain algorithm and Markov Clustering (MCL), and evaluates the performance of two prominent distributed community detection algorithms: HiPDPL-GPU, our prior implementation, and HipMCL. We conduct experiments on GPU-accelerated heterogeneous HPC systems, Summit and Frontier, to assess their performance under varying conditions. Our objective is to identify the strengths and weaknesses of these algorithms in terms of scalability, and quality of solutions. We evaluate these algorithms on a diverse set of 70+ networks spanning 13 domains, with sizes ranging up to 4.2 billion edges. Our results demonstrate that HiPDPL-GPU consistently outperforms HipMCL, especially for large-scale networks. HiPDPL-GPU achieves significantly faster runtimes (47x to 1439x), higher modularity scores, and improved scalability. These findings highlight HiPDPL-GPU as a promising solution for efficient and effective large-scale graph analytics in diverse application domains, and provide insights into the feasibility of using MCL-based approaches for certain application domains.

Community detection, graph algorithms↗
DOE OSTI2022

Nonadiabatic dissociation of molecular Bose-Einstein condensates: Competition between chemical reactions

Here, we provide a framework to solve generic models describing the dissociation of multiple molecular Bose Einstein condensates in a nonadiabatic regime. The competition between individual chemical reactions can lead to non-trivial dependence on critical components such as path interference and symmetries, thus, affecting the final distribution of atomic population. We find an analytical solution for an illustrative example model involving four atomic modes. When the system parameters satisfy CPT symmetry, where C is charge conjugation, P is parity, and T is time-reversal symmetry, our solution predicts a population imbalance between atomic modes that is exponentially sensitive to system parameters. However, a weakly broken symmetry alters the population in each atomic mode and can reverse the population imbalance. Our solution also demonstrates a strong quantum correlation between atomic modes that leads to the spontaneous production of atoms in a multi-mode squeezed state. Moreover, in our framework, a time-dependent non-Hermitian quantum mechanics naturally manifests which can alternatively be realized experimentally in photonic systems.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2020

Epsilon Metal: A Waste Form for Noble Metals from Used Nuclear Fuel

Epsilon metal (e-metal) is the metallic phase that forms as inclusions at the grain boundaries in the UO2 fuel during reactor operation. This metal is composed of Pd, Mo, Rh, Ru, and Tc. These metallic inclusions are insoluble in strong acid and remnants of these metallic inclusions have been found in the UO2 matrix that remains from the natural reactors in Gabon that were active 1.8 billion years ago, therefore e-metal should be an excellent waste form for the immobilization of the long-lived isotopes 107Pd (6.5 ? 106 a) and 99Tc (2.13 ? 105 a), with 99Tc being the isotope of interest for repository performance. Therefore, the chemical durability of this potential waste form is assessed in this study. Typically, corrosion rates for metallic materials are measured electrochemically because they are quick, inexpensive, and can reveal the mechanism by which a metal corrodes, at least initially. However, in a repository the waste form would be subjected to slowly flowing water without an applied electrical potential over long time periods. Therefore, the corrosion rates of e-metal specimens were measured with both electrochemical tests and the single-pass flow-through test (SPFT). Potentiodynamic and potentiostatic polarization results suggest that a thin passive film exists on the alloy surface, which seems to be responsible for its high corrosion resistance. Additionally, X-Ray photoelectron spectroscopic results suggest that Pd oxides are significantly enriched in the passive film Results from the SPFT show that the dissolution rates were weakly dependent on pH. Only Mo and Re were found in solution and were used for the calculation of the dissolution rates. In general, the electrochemically determined corrosion rates agree reasonably well with the initial dissolution rate measured with the SPFT test, but they are about one or two orders of magnitude higher than the steady state rates. The causes for this discrepancy are discussed.

epsilon-metal, nuclear waste form, corrosion, sing↗
DOE OSTI2022

A unified framework of stabilized finite element method for solving the Boltzmann transport equation

This paper presents a unified framework of stabilized finite element method for solving the Boltzmann transport equation. Unlike the traditional Petrov-Galerkin finite element method which modifies the test function to construct the stabilization term, we derive the stabilization methods from the standard Galerkin weak form with Sub-grid scale model. The basic idea of this method is to decompose the unknowns into its numerical solution and residual, with an approximation for the residual and embeds it in the Galerkin weak form to yield a stabilized variational formula. Different approximations of the residual lead to different stabilization methods, all the frequently used stabilized methods, including the Streamline Upwinding Petrov-Galerkin (SUPG) method, Galerkin/Least-Square (GLS) method, and Algebraic Sub-Grid Scale (ASGS) method can be obtained from this framework. The similarities and differences of the different approximations are compared in this paper. The numerical results show that the behaviors of the different methods area similar with the same stabilization parameter, and all these stabilized techniques can obtain a correct and stable solution. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Coupled Thermo-Hydrological-Mechanical-Chemical Behavior of Anisotropic Granite for Geologic Disposal of High-Level Radioactive Waste: A Core-Scale Laboratory Investigation

The coupled thermo-hydrological-mechanical-chemical (THMC) behavior of rock within an Excavation Damaged Zone (EDZ) is critical for the safety and long-term performance of a geological repository for high-level radioactive wastes. While many laboratory experiments have been conducted to investigate EDZ rocks, the flow and deformation characteristics resulting from anisotropic rock textures and microcrack distribution under triaxial loading and elevated temperatures remain poorly understood. Particularly, cracks at various scales serve as fast paths for fluid flow and solute transport and present as focal points of mechanical weakness, which complicate the coupled THMC processes in anisotropic EDZ rocks and challenge modeling predictions. Here, in this study, a series of core-scale experiments was conducted on three granite samples under repository-relevant conditions. These rock samples were obtained from the Grimsel Underground Research Laboratory (URL), featured by anisotropic minerals (represented by bedding layers) and microcrack distributions and coarse cm-scale grain sizes. During the experiments, samples were subjected to an elevated temperature at 90 °C and different triaxial loading conditions either by radial (normal to bedding layers) or axial (parallel to bedding layers) compaction. Water was injected into the samples, and the rock permeability evolutions and effluent water chemistry were monitored closely. For intact samples, thermal expansion of minerals at 90 °C resulted in a large, 75% irreversible permeability reduction and rock strengthening under radial compaction, while thermal impact was limited to a 15% permeability reduction under axial compaction. In contrast, for a sample containing open cracks, the growth of fractures during the experiment resulted in an abrupt permeability increase and fast failure at 90 °C. The effluent water chemistry indicates much more considerable mineral dissolution from large shear sliding than that in rocks dominated by mechanical compaction. These results helped better understand the coupled THMC processes in anisotropic rocks containing cracks, evaluate the behaviors of EDZ rocks, and predict the long-term evolution of EDZ for the performance of the repositories.

Coupled THMC processes↗
DOE OSTI2025

Environmental photosensitizers can exhibit enhanced actinic absorption in microhydrated clusters compared to solution

Brown carbon chromophores at environmental air-water interfaces often act as photosensitizers that absorb sunlight and subsequently transfer energy to nearby molecules, initiating a wide variety of chemical reactions. Despite their importance to understanding daytime chemistry at these airwater interfaces, little is known about the role of the solvation environment on the photophysical properties of these photosensitizers. In this work, we present a joint experimental-theoretical study of the vibrational and photophysical properties of microhydrated protonated and deprotonated 4-benzoylbenzoic acid (4-BBA), a key model system for environmental photosensitizers. We find that for protonated 4-BBAH + ∙(H 2 O) 0-1 , representing photosensitizers in very acidic conditions, a single bright state dominates the UV-Vis spectrum between 280 and 400 nm. Comparing the experimental UV-Vis spectra and quantum chemistry-predicted spectra of 4-BBA + ∙(H 2 O) 0-2 , we find that the degree of microhydration has little effect on the UV-Vis spectra or the orbitals of the dominant feature. For deprotonated 4-BBA ‒ , representing photosensitizers in basic conditions, quantum chemistry calculations predict that the UV-Vis spectra are ~3x weaker in intensity than the brightest 4-BBAH + ∙(H 2 O) 0-1 features and were not observed experimentally. Quantum chemistry calculations predict one dominant UV-Vis feature is present in the spectra of 4-BBA ‒ ∙(H 2 O) 0-2 , which exhibit minor shifts with degree of microhydration. While 4-BBA in bulk solution over a range of pH values has relatively weak absorption within the solar actinic region, we show that microhydrated 4-BBA has bright transitions within the actinic region. This indicates that the complex structure of environmental air-water interfaces can shift the absorption maximum of photosensitizers into the actinic region for enhanced absorption of sunlight and subsequent enhancement of photosensitizer-driven reactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Towards exascale for wind energy simulations

We examine large-eddy-simulation modeling approaches and computational performance of two open-source computational fluid dynamics codes for the simulation of atmospheric boundary layer flows that are of direct relevance to wind energy production. The first code, NekRS, is a high-order, unstructured-grid, spectral element code. The second code, AMR-Wind, is a second-order, block-structured, finite-volume code with adaptive mesh refinement capabilities. The objective of this study is to co-develop these codes in order to improve model fidelity and performance for each. These features will be critical for running ABL-based applications such as wind farm analysis on advanced computing architectures. To this end, we investigate the performance of NekRS and AMR-Wind on the Oak Ridge Leadership Facility supercomputers Summit, using 4 to 800 nodes (24 to 4,800 NVIDIA V100 GPUs), and Crusher, the testbed for the Frontier exascale system, using 18 to 384 Graphics Compute Dies on AMD MI250X GPUs. We compare strong- and weak-scaling capabilities, linear solver performance, and time to solution. We also identify leading inhibitors to parallel scaling.

17 WIND ENERGY↗
DOE OSTI2022

Energy-Storing Cryogenic Carbon Capture™ for Utility and Industrial-scale Processes (Final Report)

This project leverages work completed under funding from previous U.S. Department of Energy (DOE) projects and other sources of funding around the Cryogenic Carbon Capture Process™ (CCC). The purpose of this project is to further develop a perturbation of the CCC process that stores energy called the Cryogenic Carbon Capture™ Energy Storing (CCC-ES) process. The successful completion of the tasks in this project has prepared the CCC-ES process for scaling and developed initial plans and a feasibility analysis for an engineering-scale or small-commercial scale system that can store at least 10 MWh of energy. The specific areas of work in this project are: (1) Develop a conceptual, site-specific integrated process flow diagram: Sustainable Energy Solutions (SES) developed a conceptual, site-specific plan including a process flow diagram for integrating CCC-ES at a specific location. The proposed system was based on a typical engineering-scale CCC system designed to capture 30-50 metric tonnes of CO 2 per day (TPD), with modifications and additional changes and equipment put in place to add the energy storage element to the system. The 30-50 TPD scale corresponds to the required 10 MWh of stored energy. This task includes updating simulation software for transient analysis. SES also coordinated with the Jim Bridger Power Plant in Point of Rocks, Wyoming to get site-specific data. Using these data, SES completed site-specific preliminary process flow diagrams, estimated capital and operating costs for the CCC-ES system, and used the upgraded software package to estimate the primary figures of merit. (2) Complete a technoeconomic analysis (TEA): SES completed a full-scale TEA of the CCC-ES system to meet specific success criteria. This TEA used process information from the host site selected above. (3) Technology and data gap assessment for the CCC-ES process: As part of the technology gap assessment, SES performed an assessment of the best alternative energy storage solutions including figures of merit and operational strengths and weaknesses. SES then compared the proposed system with a discussion of how it addresses the weaknesses of alternative systems, showing for example a cost of stored energy at less than $50/MWh and with a roundtrip efficiency of greater than 95%. This assessment includes technical and other risk analyses and technology gaps with research and development needs to commercialize the process by 2030. Finally, work includes a commercialization roadmap/development pathway outlining the major milestones to move to a commercially operating CCC-ES system. (4) Phase II pre-FEED project plan: SES completed a project plan for the Phase II pre-FEED analysis using the same host site as in the Phase I conceptual study.

03 NATURAL GAS↗
DOE OSTI2020

Status of weak scale supersymmetry after LHC Run 2 and ton-scale noble liquid WIMP searches

After completion of LHC Run 2, the ATLAS and CMS experiments had collected of order 139 fb –1 of data at √s = 13 TeV. While discovering a very Standard Model-like Higgs boson of mass m h ≃ 125 GeV, no solid signal for physics beyond the Standard Model has emerged so far at LHC. In addition, no WIMP signals have emerged so far at ton-scale noble liquid WIMP search experiments. For the case of weak scale supersymmetry (SUSY), which is touted as a simple and elegant solution to the gauge hierarchy problem and likely low energy limit of compactified string theory, LHC has found rather generally that gluinos are beyond about 2.2 TeV whilst top squark must lie beyond 1.1 TeV. These limits contradict older simplistic notions of naturalness that emerged in the 1980s–1990s, leading to the rather pessimistic view that SUSY is now excluded except for perhaps some remaining narrow corners of parameter space. Yet, this picture ignores several important developments in SUSY/string theory that emerged in the 21st century: 1. the emergence of the string theory landscape and its solution to the cosmological constant problem, 2. a more nuanced view of naturalness including the notion of “stringy naturalness”, 3. the emergence of anomaly-free discrete R-symmetries and their connection to R-parity, Peccei-Quinn symmetry, the SUSY μ problem and proton decay and 4. the importance of including a solution to the strong CP problem. Rather general considerations from the string theory landscape favor large values of soft terms, subject to the vacuum selection criteria that electroweak symmetry is properly broken (no charge and/or color breaking (CCB) minima) and the resulting magnitude of the weak scale is not too far from our measured value. Then stringy naturalness predicts a Higgs mass m h ~ 125 GeV whilst sparticle masses are typically lifted beyond present LHC bounds. Lastly, in light of these refinements in theory perspective confronted by LHC and dark matter search results, we review the most likely LHC, ILC and dark matter signatures that are expected to arise from weak scale SUSY as we understand it today.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Water, Solute, and Ion Transport in De Novo-Designed Membrane Protein Channels

Biological organisms engineer peptide sequences to fold into membrane pore proteins capable of performing a wide variety of transport functions. Synthetic de novo-designed membrane pores can mimic this approach to achieve a potentially even larger set of functions. Here, in this work, we explore water, solute, and ion transport in three de novo designed β-barrel membrane channels in the 5–10 Å pore size range. We show that these proteins form passive membrane pores with high water transport efficiencies and size rejection characteristics consistent with the pore size encoded in the protein structure. Ion conductance and ion selectivity measurements also show trends consistent with the pore size, with the two larger pores showing weak cation selectivity. MD simulations of water and ion transport and solute size exclusion are consistent with the experimental trends and provide further insights into structure–function correlations in these membrane pores.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Comparison of vapour pressure osmometry, freezing point osmometry and direct membrane osmometry for determining the osmotic pressure of concentrated solutions

Osmometry is the analytical method of measuring osmotic pressure ($π$) and related colligative properties. Accurately measuring $π$ is essential for applications that use osmosis, including drug delivery systems and water filtration methods such as forward osmosis. The three most common forms of directly or indirectly measuring $π$ are vapour pressure osmometry (VPO), freezing point osmometry (FPO), and direct membrane osmometry (DMO). In this report, the performance of VPO, FPO, and DMO are compared for various aqueous solutions, including small molecule and polymer solutes, and potentially more difficult samples such as concentrated, carbonated, or viscous solutions. Furthermore, potential problems with each of the three methods are examined. Good practices can avoid inaccuracies in DMO due to external concentration polarization and solute diffusion through the membrane. Similarly, it is important to be aware of and avoid weaknesses in VPO and FPO in order to obtain reliable results. Even with care, however, the three methods still give different values of $π$ for concentrated aqueous solutions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

In situ Monitoring of Lanthanide Reactions with Oxide Species via Combined Absorption Spectroscopy and Electrochemical Methods

Molten salts for engineering scale applications of spent nuclear fuel pyrochemical processing will inevitably have some level of oxygen impurities which can form insoluble oxide and oxychloride species with fission products. This work demonstrates real-time concentration monitoring of two lanthanide (Ln3+) fission products, Nd3+ and Pr3+, and their reactions with oxygen (O2-) impurities to form insoluble products in LiCl-NaCl-KCl eutectic salt. Combined absorption spectroscopy and electrochemical testing were used to track lanthanide concentrations. O2- impurity levels were controlled by adding Li2O to lanthanide-salt solutions. After the introduction of O2- impurities, Ln3+ concentrations were monitored via time-resolved absorption spectroscopy. Concentrations of both Ln3+ species in solution decreased with time as insoluble products formed. The initial impurity concentration controlled whether insoluble products were predominantly oxychlorides or mixtures of oxychlorides and oxides. However, absorption spectroscopy is limited for weakly absorbing species, such as Pr3+, and under conditions of high impurity concentrations where solutions can be turbid. To circumvent this limitation, the concentrations of Pr3+ were monitored with square wave voltammetry (SWV). Reaction rates and extent of Pr3+ removal from solution as monitored by SWV agreed closely with results found from spectroscopic monitoring. This demonstrates that simultaneous electrochemical testing complements the capabilities of absorption spectroscopy to monitor reactions of fission products in molten salts.

absorption spectroscopy↗
DOE OSTI2025

In situ monitoring of lanthanide reactions with oxide species via combined absorption spectroscopy and electrochemical methods

Molten salts for engineering scale applications of spent nuclear fuel pyrochemical processing will inevitably have some level of oxygen impurities which can form insoluble oxide and oxychloride species with fission products. This work demonstrates real-time concentration monitoring of two lanthanide (Ln3+) fission products, Nd3+ and Pr3+, and their reactions with oxygen (O2-) impurities to form insoluble products in LiCl-NaCl-KCl eutectic salt. Combined absorption spectroscopy and electrochemical testing were used to track lanthanide concentrations. O2- impurity levels were controlled by adding Li2O to lanthanide-salt solutions. After the introduction of O2- impurities, Ln3+ concentrations were monitored via time-resolved absorption spectroscopy. Concentrations of both Ln3+ species in solution decreased with time as insoluble products formed. The initial impurity concentration controlled whether insoluble products were predominantly oxychlorides or mixtures of oxychlorides and oxides. However, absorption spectroscopy is limited for weakly absorbing species, such as Pr3+, and under conditions of high impurity concentrations where solutions can be turbid. To circumvent this limitation, the concentrations of Pr3+ were monitored with cyclic voltammetry (CV). Reaction rates and extent of Pr3+ removal from solution as monitored by CV agreed closely with results found from spectroscopic monitoring. This demonstrates that simultaneous electrochemical testing complements the capabilities of absorption spectroscopy to monitor reactions of fission products in molten salts.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

In situ monitoring of lanthanide reactions with oxide species via combined absorption spectroscopy and electrochemical methods

Molten salts for engineering scale applications of spent nuclear fuel pyrochemical processing will inevitably have some level of oxygen impurities which can form various insoluble oxide and oxychloride species with uranium and fission products. This work demonstrates real-time concentration monitoring of two trivalent lanthanide (Ln3+) fission products, Nd3+ and Pr3+, and their reactions with oxygen (O2-) impurities to form insoluble products in LiCl-NaCl-KCl eutectic salt. A combination of high-temperature absorption spectroscopy and electrochemical testing were used to track lanthanide concentrations. O2- impurity levels were controlled in the range of 0.001 M to 0.5 M by adding Li2O to lanthanide-salt solutions. After the introduction of O2- impurities, Ln3+ concentrations were monitored via time-resolved absorption spectroscopy. Concentrations of both Ln3+ species in solution decreased with time as insoluble products formed. The initial impurity concentration controlled whether insoluble products were predominantly oxychlorides (LnOCl) or mixtures of oxychlorides and oxides (Ln2O3). However, absorption spectroscopy is limited for weakly absorbing species, such as Pr3+, and under conditions of high impurity concentrations where solutions can be turbid. To circumvent this limitation, the concentrations of Pr3+ were monitored with square wave voltammetry (SWV). Estimated reaction rates and extent of Pr3+ removal from solution as monitored by SWV agreed to within ~10% of the results found from absorption spectroscopy monitoring. This demonstrates that simultaneous electrochemical testing complements and expands the capabilities of absorption spectroscopy to monitor reactions of fission products in molten salts.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

A FETI approach to domain decomposition for meshfree discretizations of nonlocal problems

We propose a domain decomposition method for the efficient simulation of nonlocal problems. Our approach is based on a multi-domain formulation of a nonlocal diffusion problem where the subdomains share “nonlocal” interfaces of the size of the nonlocal horizon. This system of nonlocal equations is first rewritten in terms of minimization of a nonlocal energy, then discretized with a meshfree approximation and finally solved via a Lagrange multiplier approach in a way that resembles the finite element tearing and interconnect method. Specifically, we propose a distributed projected gradient algorithm for the solution of the Lagrange multiplier system, whose unknowns determine the nonlocal interface conditions between subdomains. Several two-dimensional numerical tests on problems as large as 191 million unknowns illustrate the strong and the weak scalability of our algorithm, which outperforms the standard approach to the distributed numerical solution of the problem. Finally, this work is the first rigorous numerical study in a two-dimensional multi-domain setting for nonlocal operators with finite horizon and, as such, it is a fundamental step towards increasing the use of nonlocal models in large scale simulations.

42 ENGINEERING↗