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DOE OSTI2016

A multiscale coupled finite-element and phase-field framework to modeling stressed grain growth in polycrystalline thin films

A previously-developed finite-deformation- and crystal-elasticity-based constitutive theory for stressed grain growth in cubic polycrystalline bodies has been augmented to include a description of excess surface energy and grain-growth stagnation mechanisms through the use of surface effect state variables in a thermodynamically-consistent manner. The constitutive theory was also implemented into a multiscale coupled finite-element and phase-field computational framework. With the material parameters in the constitutive theory suitably calibrated, our three-dimensional numerical simulations show that the constitutive model is able to accurately predict the experimentally-determined evolution of crystallographic texture and grain size statistics in polycrystalline copper thin films deposited on polyimide substrate and annealed at high-homologous temperatures. In particular, our numerical analyses show that the broad texture transition observed in the annealing experiments of polycrystalline thin films is caused by grain growth stagnation mechanisms. - Graphical abstract: - Highlights: • Developing a theory for stressed grain growth in polycrystalline thin films. • Implementation into a multiscale coupled finite-element and phase-field framework. • Quantitative reproduction of the experimental grain growth data by simulations. • Revealing the cause of texture transition to be due to the stagnation mechanisms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Micro-Mechanically Guided High-Throughput Alloy Design Exploration Towards Metastability-Induced H Embrittlement Resistance

We develop a high-throughput approach for studying H embrittlement (HE)-resistance in alloys, which is based on combinatorial compositional screening of metastability effects by in situ scanning electron microscopy H-analyses. The project objective included: (i) technique development of high-throughput screening (HTS) for HE-resistance, (ii) discovery of new metallic materials with superior HE-resistance, (iii) Multiscale verification of HE-resistance of the new alloys and H-barrier layers, from atomic scale to an engineering scale. The investigation focused on a model system that enables exploration of different metastable states in Fe-based complex-concentrated alloys. Composition spread islands with hundreds of varying compositions are fabricated on a single substrate using a combinatorial co-sputtering technique. To screen these alloys, we developed and employed a home-built SEM-based integrated analysis system capable of characterizing H-permeability, H-trapping, H-influence on mechanical properties, and other material properties, as well as atomistic to continuum simulations to study the underlying physics.

08 HYDROGEN↗

DOE OSTI2022

Predicting and Controlling Corrosion (Abbreviated Final Report)

Corrosion accumulates significant replacement costs in the transportation, utility, manufacturing, and infrastructure sectors. It also underpins several of LLNL’s core missions in stockpile stewardship, defense, and energy security. Whereas most corrosion and aging models are empirically parameterized to describe well-defined conditions late in the reaction, the factors that determine the early stages of corrosion—during which mitigation could be most impactful— are poorly understood. This project addressed the critical need for new approaches to predict the kinetics of corrosion initiation based on firm physical and chemical understanding. The activities encompassed degradation of relevant metals in both hydrogen-rich and environmental corrosion scenarios. The team integrated state-of-the-art multiscale simulation, in situ characterization, and data science within three technical thrusts: hydriding of Ti alloys; aqueous corrosion of Al and Ni-Cr alloys; and degradation of additively manufactured 316L stainless steel. In each case, novel capabilities were developed to identify and track the impacts of key atomistic, compositional, and microstructural features on the metal systems. For hydriding, protocols were developed to tightly integrate multiscale models, advanced multimodal characterization, and machine learning to determine how hydrogen interacts with native passivating surface oxides and nucleates new undesired phases, shedding new light on the critical role of grain boundaries, interfaces, and atomically disordered regions. For aqueous corrosion, the project demonstrated methods to predict dissolution rates of metal surfaces in corrosive solutions, to measure and understand microstructural and grain orientation effects on corrosion susceptibility, and to investigate competing growth and dissolution kinetics of surface oxides. For additively manufactured metals, analysis using state-of-the-art microscopy techniques revealed the role of specific heterogeneities invoked during laser processing, including cellular structure, dislocations, and precipitates, on corrosion susceptibility. In addition to new capabilities and understanding, the project provided an avenue for workforce development, as well as key partnerships with stakeholders in corrosion science.

08 HYDROGEN↗

DOE OSTI2019

Multiscale additive manufacturing of polymers using 3D photo-printable self-assembling ionic liquid monomers

3D photoprinting of a self-assembled ionic liquid (IL) monomer based liquid-crystalline mesophase introduces high-resolution nanoscale features (2–5 nm) into otherwise low-resolution (microscale features) polymer builds. A wide variety of geometric builds possessing internal hexagonal perforated lamellar (HPL) nanostructure containing ~2.4 nm diameter pores are fabricated by the digital light processing 3D printing of an aqueous mixture (61(w/w%)) of an ionic liquid monomer, 1-decyl-3-vinylimidazolium chloride, a co-monomer, polyethylene diacrylate (PEGDA, M n 575), and a visible light photo-initiator (eosin Y and triethanolamine). Vibrational spectroscopy and thermal analysis proves acrylate moiety polymerization occurs during printing but incomplete consumption of the IL vinyl groups. Post-printing exposure to UV light (λ 350 nm) completes vinyl polymerization serving to further improve nanostructure ordering as determined by SAXS. Solvent swelling (ethanol) induces a structural transformation to a body center cubic architecture accompanied by slight pore expansion (to 3.2 nm). The introduction of nanoscale features into low-resolution photo-printed polymers establishes a low-cost strategy for the additive manufacturing of multi-scale, structured nanoporous polymer membranes.

36 MATERIALS SCIENCE↗

DOE OSTI2019

Mechanisms of Ion Transport in Block Copolymeric Polymerized Ionic Liquids

We present the results of a multiscale simulation framework investigating the ion transport mechanisms in multicomponent polymerized ionic liquids. Three different classes of polymeric ionic liquid systems, namely, random copolymers, lamellae forming block copolymers, and homopolymers, are constructed at the coarse-grained scale, and their atomistic counterparts are derived by using a reverse mapping method. Using such a framework, we investigate the influence of morphology on ion transport properties of such polymerized ionic liquids. Here, our results for ion mobilities are in qualitative agreement with experimental observations. Further analysis of random copolymer and block copolymer systems reveal that the reduced ion mobilities in such systems arise from the influence of architecture and morphology on ion coordination and intramolecular hopping events.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Isogeometric large-eddy simulations of turbulent particle-laden flows

In recent years, isogeometric analysis (IGA) has attracted significant attention from the computational mechanics community due to its ability to integrate design and analysis. Besides, IGA is also a higher-order discretization technique for solving partial differential equations, showing high approximation capability per degree of freedom. In this paper, we extend the application realm of IGA to particle-laden flows based on Eulerian–Eulerian description that couples Navier–Stokes equations with a density transport equation through a Boussinesq approximation. The coupled systems are solved by using quadratic non-uniform rational B-spline (NURBS) functions and a recently developed residual-based variational multiscale (VMS) formulation, which introduces coupling between the fine velocity scales and density equation residuals. We deploy the proposed approach to perform large-eddy simulations (LES) of dilute particle-laden flows over a flat surface at Reynolds number = 10,000. We compare the simulation results against direct numerical simulation (DNS) results from the literature. We find that combining VMS and IGA, the proposed approach enables accurate prediction of a wide range of flow/particle statistics with a relatively lower mesh resolution.

Mathematics↗

DOE OSTI2014

Multiscale Simulations of ALD in Cross Flow Reactors

In this study, we have developed a multiscale simulation code that allows us to study the impact of surface chemistry on the coating of large area substrates with high surface area/high aspect-ratio features. Our code, based on open-source libraries, takes advantage of the ALD surface chemistry to achieve an extremely efficient two-way coupling between reactor and feature length scales, and it can provide simulated quartz crystal microbalance and mass spectrometry data at any point of the reactor. By combining experimental surface characterization with simple analysis of growth profiles in a tubular cross flow reactor, we are able to extract a minimal set of reactions to effectively model the surface chemistry, including the presence of spurious CVD, to evaluate the impact of surface chemistry on the coating of large, high surface area substrates.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Observation-constrained kinetic modeling of isoprene SOA formation in the atmosphere

Isoprene has the largest global non-methane hydrocarbon emission, and the oxidation of isoprene plays a crucial role in the formation of secondary organic aerosol (SOA). Two primary processes are known to contribute to SOA formation from isoprene oxidation: (1) the reactive uptake of isoprene-derived epoxides on acidic or aqueous particle surfaces and (2) the absorptive gas–particle partitioning of low-volatility oxidation products. In this study, we developed a new multiphase condensed isoprene oxidation mechanism that includes these processes with key molecular intermediates and products. The new mechanism was applied to simulate isoprene gas-phase oxidation products and SOA formation from previously published chamber experiments under a variety of conditions and atmospheric observations during the Southern Oxidant and Aerosol Studies (SOAS) field campaign. Our results show that SOA formation from most of the chamber experiments is reasonably reproduced using our mechanism, except when the concentration ratios of initial nitric oxide to isoprene exceed ~ 2, the formed SOA is significantly underpredicted. The SOAS simulations also reasonably agree with the measurements regarding the diurnal pattern and concentrations of different product categories, while the total isoprene SOA remains underestimated. The molecular compositions of the modeled SOA indicate that multifunctional low-volatility products contribute to isoprene SOA more significantly than previously thought, with a median mass contribution of ~ 57 % to the total modeled isoprene SOA. However, this contribution is intricately intertwined with IEPOX-derived SOA (IEPOX: isoprene-derived epoxydiols), posing challenges for their differentiation using bulk aerosol composition analysis (e.g., the aerosol mass spectrometer with positive matrix factorization). Furthermore, the SOA from these pathways may vary greatly, mainly dependent on the volatility estimation and treatment of particle-phase processes (i.e., photolysis and hydrolysis). Our findings emphasize that the various pathways to produce these low-volatility species should be considered in models to more accurately predict isoprene SOA formation. The new condensed isoprene chemical mechanism can be further incorporated into regional-scale air quality models, such as the Community Multiscale Air Quality Modelling System (CMAQ), to assess isoprene SOA formation on a larger scale.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2016

Multiscale Evaluation of Catalytic Upgrading of Biomass Pyrolysis Vapors on Ni- and Ga-Modified ZSM-5

Metal-impregnated (Ni or Ga) ZSM-5 catalysts were studied for biomass pyrolysis vapor upgrading to produce hydrocarbons using three reactors constituting a 100 000x change in the amount of catalyst used in experiments. Catalysts were screened for pyrolysis vapor phase upgrading activity in two small-scale reactors: (i) a Pyroprobe with a 10 mg catalyst in a fixed bed and (ii) a fixed-bed reactor with 500 mg of catalyst. The best performing catalysts were then validated with a larger scale fluidized-bed reactor (using ~1 kg of catalyst) that produced measurable quantities of bio-oil for analysis and evaluation of mass balances. Despite some inherent differences across the reactor systems (such as residence time, reactor type, analytical techniques, mode of catalyst and biomass feed) there was good agreement of reaction results for production of aromatic hydrocarbons, light gases, and coke deposition. Relative to ZSM-5, Ni or Ga addition to ZSM-5 increased production of fully deoxygenated aromatic hydrocarbons and light gases. In the fluidized bed reactor, Ga/ZSM-5 slightly enhanced carbon efficiency to condensed oil, which includes oxygenates in addition to aromatic hydrocarbons, and reduced oil oxygen content compared to ZSM-5. Ni/ZSM-5, while giving the highest yield of fully deoxygenated aromatic hydrocarbons, gave lower overall carbon efficiency to oil but with the lowest oxygen content. Reaction product analysis coupled with fresh and spent catalyst characterization indicated that the improved performance of Ni/ZSM-5 is related to decreasing deactivation by coking, which keeps the active acid sites accessible for the deoxygenation and aromatization reactions that produce fully deoxygenated aromatic hydrocarbons. The addition of Ga enhances the dehydrogenation activity of the catalyst, which leads to enhanced olefin formation and higher fully deoxygenated aromatic hydrocarbon yields compared to unmodified ZSM-5. Catalyst characterization by ammonia temperature programmed desorption, surface area measurements, and postreaction temperature-programmed oxidation (TPO) also showed that the metal-modified zeolites retained a greater percentage of their initial acidity and surface area, which was consistent between the reactor scales. These results demonstrate that the trends observed with smaller (milligram to gram) catalyst reactors are applicable to larger, more industrially relevant (kg) scales to help guide catalyst research toward application.

09 BIOMASS FUELS↗

DOE OSTI2024

SQMS Quantum R&D in Machine Learning, Optimization and Sensing beyond Fundamental Physics Applications

This newly formed team at SQMS under the Ecosystem Thrust is looking to develop capabilities impacting societal advances outside the core domain of HEP and condensed matter physics. We explicitly leverage the experimental and algorithmic innovations developed across all groups as well as connect to broad-scope external projects of the diverse team of PIs. As the inaugural set of projects, we are studying numerically quantum machine learning models inspired by efficiently trainable echo-state and orthogonal neural networks and developing designs for related experiments to be performed on quantum processors based on SQMS SRF cQED technology and Rigetti s transmon arrays. Investigated models exploit ideas and lessons learned from multiple prior work by SQMS team members in a variety of internal and external activities [R1]. Target initial applications include noisy signal processing, potentially captured by quantum sensors or noisy QPUs, as well as simulation and classification of healthcare data. For instance, image reconstruction of the brain s electrical properties by solving the inverse Maxwell equation problem with uncertainty [R2] through a hybrid quantum-classical physics-informed architecture for time-dependent processes [R3]. The group is also investigating the application and development of novel quantum sensors based on magnetic levitation of a superconducting sphere coupled to a superconducting qubit. This coupling enables high-precision measurements of the position of the sphere, which can be used for sensitive detection of forces, enabling practical applications such as gravimetry for geophysics analysis, or accelerometry for GPS-denied navigation [R4] [R1] Rieffel, Eleanor G., Ata Akbari Asanjan, M. Sohaib Alam, Namit Anand, David E. Bernal Neira, Sophie Block, Lucas T. Brady et al. "Assessing and advancing the potential of quantum computing: A NASA case study." Future Generation Computer Systems (2024). [R2] Yu, X., Serrall s, J.E., Giannakopoulos, I.I., Liu, Z., Daniel, L., Lattanzi, R. and Zhang, Z., 2023. Pifon-ept: Mr-based electrical property tomography using physics-informed fourier networks. IEEE Journal on Multiscale and Multiphysics Computational Techniques. [R3] Wudarski, Filip, Daniel OConnor, Shaun Geaney, Ata Akbari Asanjan, Max Wilson, Elena Strbac, P. Aaron Lott, and Davide Venturelli. "Hybrid quantum-classical reservoir computing for simulating chaotic systems." arXiv preprint arXiv:2311.14105 (2023). [R4] Higgins, Gerard, Saarik Kalia, and Zhen Liu. "Maglev for dark matter: Dark-photon and axion dark matter sensing with levitated superconductors." Physical Review D 109.5 (2024): 055024.

Venturelli, Davide↗

DOE OSTI2023

Multiscale Temporal Variability of the Global Air‐Sea CO 2 Flux Anomaly

Abstract The global air‐sea CO 2 flux (F) impacts and is impacted by a plethora of climate‐related processes operating at multiple time scales. In bulk mass transfer formulations, F is driven by physico‐ and bio‐chemical factors such as the air‐sea partial pressure difference (∆pCO 2 ), gas transfer velocity, sea surface temperature, and salinity–all varying at multiple time scales. To de‐convolve the impact of these factors on variability in F at different time scales, time‐resolved estimates of F were computed using a global data set assembled between 1988 and 2015. The F anomalies were defined as temporal deviations from the 28‐year time‐averaged value. Spectral analysis revealed four dominant timescales of variability in F–subseasonal, seasonal, interannual, and decadal with relative amplitude differences varying across regions. A second‐order Taylor series expansion was then conducted along these four timescales to separate drivers across differing regions. The analysis showed that on subseasonal timescales, wind speed variability explains some 66% of the global F anomaly and is the dominant driver. On seasonal, interannual, and decadal timescales, the ∆pCO 2 effect controlled by the ∆pCO 2 anomaly, explained much of the F anomaly. On decadal timescales, the F anomaly was almost entirely governed by the ∆pCO 2 effect with large contributions from high latitudes. The main drivers across timescales also dominate the regional F anomaly, particularly in the mid‐high latitude regions. Finally, the driver of the ∆pCO 2 effect was closely connected with the relative strength of atmospheric pCO 2 and the nonthermal component of oceanic pCO 2 anomaly associated with dissolved inorganic carbon and alkalinity.

Environmental Sciences & Ecology↗

DOE OSTI2026

MATEY: multiscale adaptive transformer models for spatiotemporal physical systems

Accurate representation of the multiscale features in spatiotemporal physical systems using vision transformer architectures requires extremely long, computationally prohibitive token sequences. To address this issue, we propose two novel adaptive tokenization schemes that dynamically adjust patch sizes based on local features: one ensures convergent behavior to uniform patch refinement, while the other offers better computational efficiency. Moreover, we present a set of spatiotemporal attention schemes, where the temporal or axial spatial dimensions are decoupled, to evaluate their baseline computational and data efficiencies and to determine whether adaptive tokenization can improve this performance. We assess the performance of the proposed multiscale adaptive model, MATEY, in a sequence of experiments. Compared to a full spatiotemporal attention scheme or a scheme that decouples only the temporal dimension, we find that fully decoupled axial attention is less efficient and expressive, requiring more training time and model parameters to achieve the same accuracy. The experiments on the adaptive tokenization schemes show that, compared to a uniformly refined model, the proposed schemes achieve comparable or improved accuracy at a much lower cost in the tested two-dimensional settings. While the asymptotic analysis suggests the potential for favorable scaling, empirical validation at substantially longer sequence lengths remains to be performed in future work. Finally, we demonstrate in two fine-tuning tasks featuring different physics that models pretrained on PDEBench data outperform the ones trained from scratch, especially in the low data regime with frozen attention.

adaptive tokenization↗

DOE OSTI2024

Purification Techniques for Actinide Radiolysis Studies

Our fundamental understanding of actinide radiation-induced redox chemistry is crucial due to their unavoidable exposure to ionizing radiation fields, both inherent and from in-process applications. Plutonium (Pu) and americium (Am) both possess multiple oxidation states, the careful manipulation of which are essential in the study and utilization of their rich chemistry, developing new technologies, and securing the long-term sustainability of nuclear power. However, knowledge in this area is far from complete. We have studied the radiation-induced chemistry of both Pu and Am through a variety of techniques, including gamma irradiation, in-situ alpha irradiation and pulse radiolysis experiments. However, for the collection of accurate data, thorough purification and quantification of actinide-containing solutions is required. This presentation will cover the purification and quantification techniques employed for the radiolysis experiments described in our recent publications: Kynman et al., Multiscale Modeling of Plutonium Radiation Chemistry in Nitric Acid Solutions. 1. Cobalt-60 Gamma Irradiation of Pu(IV) [https://pubs.acs.org/doi/10.1021/acs.inorgchem.4c00138] and Kynman et al., Generation and Study of Am(IV) by Temperature-Controlled Electron Pulse Radiolysis [https://doi.org/10.1039/D4DT00991F].

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

DOE OSTI2025

SynopFrame: Multiscale time-dependent visual abstraction framework for analyzing DNA nanotechnology simulations

We present an open-source framework, SynopFrame, that allows DNA nanotechnology (DNA-nano) experts to analyze and understand molecular dynamics simulation trajectories of their designs. We use a multiscale multi-dimensional abstraction space, connect the representations to a projected conformational space plot of the structure’s temporal sequence, and thus enable experts to analyze the dynamics of their structural designs and, specifically, failure cases of the assembly. In addition, our time-dependent abstraction representation allows the biologists, for the first time in a smooth and structurally clear way, to identify and observe temporal transitions of a DNA-nano design from one configuration to another, and to highlight important periods of the simulation for further analysis. We realize SynopFrame as a dashboard of the different synchronized 3D spatial and 2D schematic visual representations, with a color overlay to show essential properties such as the status of hydrogen bonds. The linking of the spatial, schematic, and abstract views ensures that users can effectively analyze the high-frequency motion. We also categorize the status of the hydrogen bonds into a new format to allow us to color-encode it and overlay it on the representations. To demonstrate the utility of SynopFrame, we describe example usage scenarios and report user feedback.

Abstraction space↗

DOE OSTI2026

Revealing EDL-driven reduction mechanisms in binary, ternary, and quaternary fluorinated electrolytes via an integrated MD–DFT–ML framework

Accurately predicting solid electrolyte interphase (SEI) formation requires explicitly resolving the electric double layer (EDL) structure, which deviates significantly from that of the bulk electrolyte. Although an established molecular dynamics (MD) and Density Functional Theory (DFT) framework can model SEI formation by evaluating reduction reactions of local clusters in the EDL, it suffers from a combinatorial computational bottleneck. To overcome this limitation, we introduce a machine-learning-accelerated simulation workflow (MD–DFT–ML), integrating a gradient-boosted regression model trained on EDL composition data to efficiently predict reduction potentials. We apply this framework to seven fluorinated electrolytes comprising fluorinated anions, a fluorinated ester solvent, two types of diluent (ion-solvating ester vs. non-solvating ether), and an FEC additive. The analysis shows that the EDL selectively accumulates cation-binding species; consequently, the non–cation-binding ether diluent rarely enters the EDL and makes minimal contributions to SEI formation. DFT calculations on statistically representative EDL clusters provide reduction potentials and fluorine-release pathways, while the ML model, which substantially reduces the DFT workload, predicts cluster reduction energies with a mean absolute error of 0.1 eV. The combined MD–DFT–ML approach also quantifies contributions from different sources to LiF formation in the SEI. This methodology establishes a generalizable route for multiscale modeling electrolyte and interphase design for next-generation electrochemical energy-storage systems.

DFT-MD-ML workflow↗

DOE OSTI2022

Ion Correlations and Partial Ionicities in the Lamellar Phases of Block Copolymeric Ionic Liquids

Recently, significant interest has arisen on the impact of dynamical ion correlations on the conductivity and transport properties of polymeric electrolyte materials. It has been hypothesized that confining ion motion to narrow channels may reduce such ion correlations and enhance the resulting ionic conductivity. Motivated by such considerations, in this study we used a multiscale simulation framework to study the dynamical ion correlations in the microphase-separated lamella phase of block copolymeric ionic liquids and compare with the corresponding results for homopolymeric systems. We probed the influence of ion correlations through the partial ionicity, Δ, which quantifies the ratio of true conductivity to the ideal, Nernst–Einstein conductivity for the anion-related contributions. Consistent with our original hypothesis, our results demonstrate that the partial ionicity relating to the mobile anions is much larger in the lamella phases of block copolymers compared to that in homopolymers. Analysis of the distinct conductivity contributions demonstrates that such results arise as a result of an intricate compensation among the nonideal dynamical correlations relating to anions in lamella phases. Overall, our results suggest that self-assembled phases of block copolymers may provide an avenue to tune the dynamical ion correlations in polymer electrolyte systems.

36 MATERIALS SCIENCE↗

DOE OSTI2024

A multiscale model of immune surveillance in micrometastases gives insights on cancer patient digital twins

Abstract Metastasis is the leading cause of death in patients with cancer, driving considerable scientific and clinical interest in immunosurveillance of micrometastases. We investigated this process by creating a multiscale mathematical model to study the interactions between the immune system and the progression of micrometastases in general epithelial tissue. We analyzed the parameter space of the model using high-throughput computing resources to generate over 100,000 virtual patient trajectories. We demonstrated that the model could recapitulate a wide variety of virtual patient trajectories, including uncontrolled growth, partial response, and complete immune response to tumor growth. We classified the virtual patients and identified key patient parameters with the greatest effect on the simulated immunosurveillance. We highlight the lessons derived from this analysis and their impact on the nascent field of cancer patient digital twins (CPDTs). While CPDTs could enable clinicians to systematically dissect the complexity of cancer in each individual patient and inform treatment choices, our work shows that key challenges remain before we can reach this vision. In particular, we show that there remain considerable uncertainties in immune responses, unreliable patient stratification, and unpredictable personalized treatment. Nonetheless, we also show that in spite of these challenges, patient-specific models suggest strategies to increase control of clinically undetectable micrometastases even without complete parameter certainty.

Mathematical & Computational Biology↗

DOE OSTI2016

Conservative tightly-coupled simulations of stochastic multiscale systems

Multiphysics problems often involve components whose macroscopic dynamics is driven by microscopic random fluctuations. The fidelity of simulations of such systems depends on their ability to propagate these random fluctuations throughout a computational domain, including subdomains represented by deterministic solvers. When the constituent processes take place in nonoverlapping subdomains, system behavior can be modeled via a domain-decomposition approach that couples separate components at the interfaces between these subdomains. Its coupling algorithm has to maintain a stable and efficient numerical time integration even at high noise strength. We propose a conservative domain-decomposition algorithm in which tight coupling is achieved by employing either Picard's or Newton's iterative method. Coupled diffusion equations, one of which has a Gaussian white-noise source term, provide a computational testbed for analysis of these two coupling strategies. Fully-converged (“implicit”) coupling with Newton's method typically outperforms its Picard counterpart, especially at high noise levels. This is because the number of Newton iterations scales linearly with the amplitude of the Gaussian noise, while the number of Picard iterations can scale superlinearly. At large time intervals between two subsequent inter-solver communications, the solution error for single-iteration (“explicit”) Picard's coupling can be several orders of magnitude higher than that for implicit coupling. Increasing the explicit coupling's communication frequency reduces this difference, but the resulting increase in computational cost can make it less efficient than implicit coupling at similar levels of solution error, depending on the communication frequency of the latter and the noise strength. This trend carries over into higher dimensions, although at high noise strength explicit coupling may be the only computationally viable option.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗