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At least 595 records · Page 33

Catalytic Resonance Theory: Forecasting the Flow of Programmable Catalytic Loops

Chemical transformations on catalyst surfaces occur through series and parallel reaction pathways. These complex networks and their behavior can be most simply evaluated through a three-species surface reaction loop (A* to B* to C* to A*) that is internal to the overall chemical reaction. Application of an oscillating dynamic catalyst to this reactive loop has been shown to exhibit one of three types of behavior: (1) a positive net flux of molecules about the loop in the clockwise direction, (2) a negative net flux of molecules about the loop in the counterclockwise direction, or (3) negligible flux of molecules about the loop at the limit cycle of reaction. Three-species surface loops were simulated with microkinetic modeling to assess the reaction loop behavior resulting from a catalytic surface oscillating between two or more catalyst surface energy states. Selected input parameters for the simulations spanned an 11-dimensional parameter space using 127 688 different parameter combinations. Their converged limit cycle solutions were analyzed for their loop turnover frequencies, the majority of which were found to be approximately zero. Classification and regression machine learning models were trained to predict the sign and magnitude of the loop turnover frequency and successfully performed above accessible baselines. Notably, the classification models exhibited a baseline weighted F1 score of 0.49, whereas trained models achieved weighted F1 scores of 0.94 and 0.96 when trained on the parameters used to define the simulations and derived rate constants, respectively. The trained models successfully predicted catalytic loop behavior, and interpretation of these models revealed all input parameters to be important for the prediction and performance of each model.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Substantial reduction of the anisotropy in the critical current densities J c of Ni-doped CaKFe 4 As 4 single crystals by chemical and irradiation-induced disorder

Here, we demonstrate that the anisotropy in the critical current densities, J c , of CaK(Fe 1–x Ni x ) 4 As 4 (x = 0, 0.015, 0.025, and 0.030) single crystals reduces with increasing chemical and irradiation-induced disorder. The magnetic field dependences of J c are analyzed by performing magnetization measurements with H applied parallel and perpendicular to the crystallographic c-axis. The results show that undoped crystals display large anisotropies in Jc due to an enhancement of the vortex pinning with H applied parallel to the crystallographic ab-planes. This anisotropy reduces substantially as Ni addition increases. Moreover, we found that random disorder introduced by proton irradiation enhances mainly the vortex pinning for H parallel to the c-axis. Consequently, using adequate fluencies, the vortex pinning at low temperatures in both undoped and doped samples becomes close to isotropic. These results make the CaKFe 4 As 4 system promising for applications that require isotropic J c under magnetic fields.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Revealing Phase Heterogeneity in Vertically Aligned Nanocomposites via Plan-View Electron Energy Loss Spectroscopy

Hydrogen utilization in clean energy technologies is challenged by limited storage and transport within materials, owing to the complex hydrogen kinetics at interfaces [1]. Understanding these interfacial mechanisms at the nanoscale is crucial for developing improved materials for hydrogen applications, particularly proton-conducting fuel cells (PCFCs). Vertically aligned nanocomposites (VANs) grown by pulsed laser deposition (PLD) offer a unique platform for investigating the interfacial effects on hydrogen transport due to their well-defined interfaces parallel to the direction of charge transport [2-4]. To investigate hydrogen transport, the two phases within the VANs were chosen as BaZr 0.9 Y 0.1 O 3-x (BZY), a known proton conductor, and Pr 0.1 Ce 0.9 O 2-x (PCO), a mixed ionic-electronic conductor [5]. This PCO-BZY VANs architecture allows the investigation of how the interface between a proton conductor and a mixed conductor influences hydrogen transport. However, because of the small size of hydrogen, it is difficult to discern the nature of its interactions with interfaces from bulk measurements at the macroscale, thus necessitating nanoscale measurements [6]. Electron energy loss spectroscopy (EELS) allows for nanometer-resolution probing of the local atomic structure and chemistry at the BZY/PCO interface. In this study, plan-view analysis of PCO-BZY VANs films was employed to characterize the structure and phase distribution of the VANs and investigate the interface between the nanostructures. The films were imaged using scanning electron microscopy (SEM) in the Hitachi S-4800 SEM, collecting secondary electron images using mixed upper and lower detectors. Then, plan-view transmission electron microscopy (TEM) and scanning transmission electron microscopy (STEM) EELS were employed using a JEOL ARM300 microscope operated at 300kV with a Gatan K3 GIF Continuum detector to study the distribution of the BZY and PCO phases through the film. As a result, spectrum images were acquired at a dispersion of 0.18eV per channel and denoised afterward by principal component analysis (PCA) method.

Griffin, Elizabeth [Northwestern University, Evans↗

Containers for Massive Ensemble of I/O Bound Hierarchical Coupled Simulations

We present our experience using containers to scale up a massive ensemble of coupled I/O bound workloads on the NERSC Cori supercomputer. We describe the design of a hierarchical simulation structure using the Integrated Plasma Simulator (IPS) that enables the flexible execution of coupled simulations at the system, node, and core level using the same coupling abstraction and API. The hierarchical design allows for the node-level execution to be efficiently executed using containers while not impacting the structure of the simulation at the system level. We demonstrate the viability of the approach by presenting experimental results from applications in coupled fusion plasma simulations that illustrate the performance impact of using containers to deploy the node-level workloads, in conjunction with the user mountable XFS file systems to ameliorate the load on the Lustre parallel file system. We also present results from production runs showing the ability of the ensemble simulations to scale to hundreds of Cori Haswell nodes, with little or no overhead.

Elwasif, Wael↗

Auxin‐induced actin cytoskeleton rearrangements require AUX1

Summary The actin cytoskeleton is required for cell expansion and implicated in cellular responses to the phytohormone auxin. However, the mechanisms that coordinate auxin signaling, cytoskeletal remodeling and cell expansion are poorly understood. Previous studies examined long‐term actin cytoskeleton responses to auxin, but plants respond to auxin within minutes. Before this work, an extracellular auxin receptor – rather than the auxin transporter AUXIN RESISTANT 1 (AUX1) – was considered to precede auxin‐induced cytoskeleton reorganization. In order to correlate actin array organization and dynamics with degree of cell expansion, quantitative imaging tools established baseline actin organization and illuminated individual filament behaviors in root epidermal cells under control conditions and after indole‐3‐acetic acid (IAA) application. We evaluated aux1 mutant actin organization responses to IAA and the membrane‐permeable auxin 1‐naphthylacetic acid (NAA). Cell length predicted actin organization and dynamics in control roots; short‐term IAA treatments stimulated denser and more parallel, longitudinal arrays by inducing filament unbundling within minutes. Although AUX1 is necessary for full actin rearrangements in response to auxin, cytoplasmic auxin (i.e. NAA) stimulated a lesser response. Actin filaments became more ‘organized’ after IAA stopped elongation, refuting the hypothesis that ‘more organized’ actin arrays universally correlate with rapid growth. Short‐term actin cytoskeleton response to auxin requires AUX1 and/or cytoplasmic auxin.

AUX1↗

1D model of SOL with self consistent calculation of non-coronalradiation and applications to shallow field line angles

A 1D model of the scrape off layer (SOL) is created with a physics based calculation of the impurity radiation and the inclusion of the perpendicular heat flux q ⊥ compared to previous 1D models. The calculation of the impurity radiation includes the addition of a model using parallel and perpendicular motion to calculate the impurity confinement time τ and the inclusion of charge exchange between neutral hydrogen and impurity ions. Reasonable agreement is found between the model and the 2D fluid code SOLPS-ITER. Additionally, an improvement is shown over the constant τ used in previous works The model is used to examine the effects of shallow field line angles at ITER levels of parallel heat flux (q || ). A large increase in radiation results in an increase in the upstream parallel heat flux which can still be in detachment at shallow field line angles for both q ⊥ and the calculated τ for traditional impurities (argon and nitrogen) as well as boron. The physics behind this increase in radiation at shallow field line angles is shown to be a decrease in τ and a change in the temperature profile with the inclusion of q ⊥ .

ITER↗

MEUMAPPS (Microstructure Evolution Using Massively Parallel Phase-field Simulations)

The software “MEUMAPPS” is a h high-performance computing code used to simulate microstructure evolution associated with diffusional solid-state transformations in structural alloys. Understanding microstructure evolution during thermo-mechanical processing of structural alloys is the first step towards designing and processing alloys for specific applications by meeting property requirements demanded by the application. In this instance, the code is an important component in predicting processing-structure linkages during additive manufacturing of structural alloys as a function of processing parameters and alloy composition used in an additive manufacturing process. The code provides a detailed three-dimensional distribution of different types of phases / constituents and their morphologies, as well as the compositions of these phases that make up the microstructure. The microstructure is simulated by solving the governing partial differential equations using a Fourier Spectral Method.

Radhakrishnan, Balasubram↗

Discovery and Synthesis of a Family of Boride Altermagnets

Borides are a rich material family. To push the boundaries of borides’ properties and applications into broader fields, we have conducted systematic theoretical and experimental searches for synthesizable phases in ternary borides TM 2 B 2 (T = 3d, M = 4d/5d transition metals). We find that TM 2 B 2 in the FeMo 2 B 2 -type and CoW 2 B 2 -type structures form a large family of stable/metastable materials of 120 members. Among them, we identify 40 materials with stable magnetic solutions. Further, we discover 11 altermagnets in the FeMo 2 B 2 -type structure. So far, boride altermagnets are rare. In these altermagnets, T = Fe or Mn atoms are arranged in parallel T-chains with strong ferromagnetic intrachain couplings and antiferromagnetic interchain couplings. They simultaneously exhibit electronic band spin splitting, typical of ferromagnetism, and zero net magnetization, typical of antiferromagnetism. They also exhibit magnonic band chiral splitting. Both effects originate from the unique altermagnetic symmetries crucially constrained by the nonmagnetic atoms in the structure. Transport properties of relevance to spintronic applications, including the strain-induced spin-splitter effect and anomalous Hall effect, are predicted. An iodine-assisted synthesis method for TM 2 B 2 is developed, using which 7 of the predicted low-energy phases are experimentally synthesized and characterized, including 4 altermagnets. This work expands the realm of borides by offering new opportunities for studying altermagnetism and altermagnons in borides. It also provides valuable insights into the discovery and design of altermagnets. Here, by demonstrating that altermagnets can exist as families sharing a common motif, this work paves a feasible route for discovering altermagnets by elemental substitutions and high-throughput computations.

Chemical structure↗

Deep Learning Approaches to Surrogates for Solving the Diffusion Equation for Mechanistic Real-World Simulations

In many mechanistic medical, biological, physical, and engineered spatiotemporal dynamic models the numerical solution of partial differential equations (PDEs), especially for diffusion, fluid flow and mechanical relaxation, can make simulations impractically slow. Biological models of tissues and organs often require the simultaneous calculation of the spatial variation of concentration of dozens of diffusing chemical species. One clinical example where rapid calculation of a diffusing field is of use is the estimation of oxygen gradients in the retina, based on imaging of the retinal vasculature, to guide surgical interventions in diabetic retinopathy. Furthermore, the ability to predict blood perfusion and oxygenation may one day guide clinical interventions in diverse settings, i.e., from stent placement in treating heart disease to BOLD fMRI interpretation in evaluating cognitive function (Xie et al., 2019; Lee et al., 2020). Since the quasi-steady-state solutions required for fast-diffusing chemical species like oxygen are particularly computationally costly, we consider the use of a neural network to provide an approximate solution to the steady-state diffusion equation. Machine learning surrogates, neural networks trained to provide approximate solutions to such complicated numerical problems, can often provide speed-ups of several orders of magnitude compared to direct calculation. Surrogates of PDEs could enable use of larger and more detailed models than are possible with direct calculation and can make including such simulations in real-time or near-real time workflows practical. Creating a surrogate requires running the direct calculation tens of thousands of times to generate training data and then training the neural network, both of which are computationally expensive. Often the practical applications of such models require thousands to millions of replica simulations, for example for parameter identification and uncertainty quantification, each of which gains speed from surrogate use and rapidly recovers the up-front costs of surrogate generation. We use a Convolutional Neural Network to approximate the stationary solution to the diffusion equation in the case of two equal-diameter, circular, constant-value sources located at random positions in a two-dimensional square domain with absorbing boundary conditions. Such a configuration caricatures the chemical concentration field of a fast-diffusing species like oxygen in a tissue with two parallel blood vessels in a cross section perpendicular to the two blood vessels. To improve convergence during training, we apply a training approach that uses roll-back to reject stochastic changes to the network that increase the loss function. The trained neural network approximation is about 1000 times faster than the direct calculation for individual replicas. Because different applications will have different criteria for acceptable approximation accuracy, we discuss a variety of loss functions and accuracy estimators that can help select the best network for a particular application. We briefly discuss some of the issues we encountered with overfitting, mismapping of the field values and the geometrical conditions that lead to large absolute and relative errors in the approximate solution.

60 APPLIED LIFE SCIENCES↗

Exciton Delocalization in Indolenine Squaraine Aggregates Templated by DNA Holliday Junction Scaffolds

Exciton delocalization plays a prominent role in the photophysics of molecular aggregates, ultimately governing their particular function or application. DNA is a compelling scaffold in which to template molecular aggregates and promote exciton delocalization. As individual dye molecules are the basis of exciton delocalization in molecular aggregates, their judicious selection is important. Motivated by their excellent photostability and spectral properties, here we examine the ability of squaraine dyes to undergo exciton delocalization when aggregated via a DNA Holliday junction (HJ) template. A commercially available indolenine squaraine dye was chosen for the study given its strong structural resemblance to Cy5, a commercially available cyanine dye previously shown to undergo exciton delocalization in DNA HJs. Three types of DNA-dye aggregate configurations—transverse dimer, adjacent dimer, and tetramer—were investigated. Signatures of exciton delocalization were observed in all squaraine-DNA aggregates. Specifically, strong blue shift and Davydov splitting were observed in steady-state absorption spectroscopy and exciton-induced features were evident in circular dichroism spectroscopy. Strongly suppressed fluorescence emission provided additional, indirect evidence for exciton delocalization in the DNA-templated squaraine dye aggregates. To quantitatively evaluate and directly compare the excitonic Coulombic coupling responsible for exciton delocalization, the strength of excitonic hopping interactions between the dyes were obtained by simultaneous fitting the experimental steady-state absorption and CD spectra via a Holstein-like Hamiltonian in which, following the theoretical approach of Kühn, Renger, and May, the dominant vibrational mode is explicitly considered. The excitonic hopping strength within indolenine squaraines was found to be comparable to that of the analogous Cy5 DNA-templated aggregate. The squaraine aggregates adopted primarily an H-type (dyes oriented parallel to each other) spatial arrangement. Extracted geometric details of dye mutual orientation in the aggregates enabled close comparison of aggregate configurations and the elucidation of the influence of dye angular relationship on excitonic hopping interactions in squaraine aggregates. Furthermore, these results encourage the application of squaraine-based aggregates in next generation systems driven by molecular excitons.

36 MATERIALS SCIENCE↗

Proximity Spin–Orbit Torque on a Two-Dimensional Magnet within van der Waals Heterostructure: Current-Driven Antiferromagnet-to-Ferromagnet Reversible Nonequilibrium Phase Transition in Bilayer CrI 3

The recently discovered two-dimensional magnetic insulator CrI 3 is an intriguing case for basic research and spintronic applications since it is a ferromagnet in the bulk but an antiferromagnet in bilayer form, with its magnetic ordering amenable to external manipulations. Using the first-principles quantum transport approach, we predict that injecting unpolarized charge current parallel to the interface of the bilayer-CrI 3 /monolayer-TaSe 2 van der Waals (vdW) heterostructure will induce spin–orbit torque and thereby drive the dynamics of magnetization on the first monolayer of CrI 3 in direct contact with TaSe 2 . By combining the calculated complex angular dependence of spin–orbit torque with the Landau-Lifshitz-Gilbert equation for classical dynamics of magnetization, we demonstrate that current pulses can switch the direction of magnetization on the first monolayer to become parallel to that of the second monolayer, thereby converting CrI 3 from antiferromagnet to ferromagnet while not requiring any external magnetic field. We explain the mechanism of this reversible current-driven nonequilibrium phase transition by showing that first monolayer of CrI 3 carries current due to evanescent wave functions injected by metallic transition metal dichalcogenide TaSe 2 , while concurrently acquiring strong spin–orbit coupling via such a proximity effect, whereas the second monolayer of CrI 3 remains insulating. Furthermore, the transition can be detected by passing vertical read current through the vdW heterostructure, encapsulated by a bilayer of hexagonal boron nitride and sandwiched between graphite electrodes, where we find a tunneling magnetoresistance of ≃240%.

2D magnetic materials↗

Statistical Analysis of Intertube Tunneling Contacts in the Macroscopic Electrical Conductivity of Carbon Nanotube Fibers

Here, this study investigates the influence of tunneling contact resistances between carbon nanotubes (CNTs) on electron transport and electrical conductivity of macroscopic carbon nanofibers (CNFs), which profoundly impacts the performance of CNT thin film electronics, CNF electron emitters and cathodes, and energy conversion and storage devices. Utilizing a self-consistent electrical contact model coupling a transmission line model with tunneling current, we calculate the contact resistances of a plethora of CNT-CNT contacts within a CNF fiber, which consists of aligned, densely packed CNTs. A statistical analysis is conducted, using Gaussian distributions to account for variations in contact lengths, tunneling gap distances, and single CNT aspect ratios, to calculate the CNT-CNT contact resistance and the overall resistance of CNT fiber. By scaling our model to a macroscopic level, our results are in good agreement with experimental measurements. Our calculation suggests that while increasing the contact overlap length diminishes individual CNT-CNT contact resistance, it could paradoxically increase macroscopic CNT fiber resistance for a given constant CNF mass density, which is due to that fact that a larger overlap length allows more CNTs to pack along an electrical conduction path per unit length, leading to more tunneling contact junctions connected in series and thus less number of parallel conduction paths within the fiber cross section. Increasing tunneling gap distance increases both individual contact and overall fiber resistance. This research provides a simple design tool for tailoring CNT fiber electrical properties to promote real-world applications using CNTs or similar low-dimensional materials.

36 MATERIALS SCIENCE↗

Analytical model for drag reduction on liquid-infused structured non-wetting surfaces

Liquid-infused structured non-wetting surfaces provide alternating no-slip and partial slip boundary conditions to the fluid flow, resulting in reduced friction at the interface. In this paper, an analytical model is developed for the evaluation of effective slip and, in turn, friction factor and drag reduction on liquid-infused structured non-wetting surfaces. By considering the entire range of anisotropy and heterogeneity of the surface structures as well as the full range of partial slip offered by the infusion liquid, the present model eliminates empirical fitting or correlations that are inherent in previous studies. Based on the effective slip length, drag reduction and skin friction coefficient values for Newtonian flow between two infinite parallel plates and flow in round tubes are presented. Extension of Moody charts for non-wetting surfaces and design maps of surface meso/micro/nano texturing for achieving desired drag reduction are presented for a broad range of engineering applications. The paper further presents independent validation of the model across experimental and computational data from the literature and brings together several previous studies in a unified manner.

36 MATERIALS SCIENCE↗

Entanglement engineering of optomechanical systems by reinforcement learning

Entanglement is fundamental to quantum information science and technology, yet controlling and manipulating entanglement—so-called entanglement engineering—for arbitrary quantum systems remains a formidable challenge. There are two difficulties: the fragility of quantum entanglement and its experimental characterization. We develop a model-free deep reinforcement-learning (RL) approach to entanglement engineering, in which feedback control together with weak continuous measurement and partial state observation is exploited to generate and maintain desired entanglement. We employ quantum optomechanical systems with linear or nonlinear photon–phonon interactions to demonstrate the workings of our machine-learning-based entanglement engineering protocol. In particular, the RL agent sequentially interacts with one or multiple parallel quantum optomechanical environments, collects trajectories, and updates the policy to maximize the accumulated reward to create and stabilize quantum entanglement over an arbitrary amount of time. The machine-learning-based model-free control principle is applicable to the entanglement engineering of experimental quantum systems in general.

97 MATHEMATICS AND COMPUTING↗

Picasso: Memory-Efficient Graph Coloring Using Palettes With Applications in Quantum Computing

A coloring of a graph is an assignment of colors to vertices such that no two neighboring vertices have the same color. The need for memory-efficient coloring algorithms is motivated by their application in computing clique partitions of graphs arising in quantum computations where the objective is to map a large set of Pauli strings into a compact set of unitaries. We present Picasso, a randomized memory-efficient iterative parallel graph coloring algorithm with theoretical sublinear space guarantees under practical assumptions. The parameters of our algorithm provide a trade-off between coloring quality and resource consumption. To assist the user, we also propose a machine learning model to predict the coloring algorithm’s parameters considering these trade-offs. We provide a sequential and a parallel implementation of the proposed algorithm. We perform an experimental evaluation on a 64-core AMD CPU equipped with 512 GB of memory and an Nvidia A100 GPU with 40GB of memory. For a small dataset where existing coloring algorithms can be executed within the 512 GB memory budget, we show up to 68× memory savings. On massive datasets we demonstrate that GPU-accelerated Picasso can process inputs with 49.5× more Pauli strings (vertex set in our graph) and 2,478× more edges than state-of-the-art parallel approaches.

artificial intelligence, quantum computing↗

Progress Report of Alloy 709 Performance in Liquid Sodium

With improved high-temperature properties, Alloy 709 shows great potential for advanced reactor applications. To understand the effects of sodium on A709, small tensile specimens were machined from two commercial heats and subject to sodium exposure in two forced convection loops operated by Argonne. Thermal aging experiments were also conducted in parallel to isolate any sodium-specific effects. An increasing trend in yield strength and a decrease trend in ultimate tensile strength can be seen with the increasing exposure time, suggesting microstructural changes at these temperatures. Nonetheless, the thermally aged and sodium exposed samples behaved similarly, implying no sodium-specific effect at these temperatures. In contrast, 316H SS exposed to sodium at 650°C showed a strong sodium effect. The different responses of A709 and 316H SS to sodium exposure is of interest and requires additional effort to understand. The cold traps of the sodium loop were replaced early in FY23. During a maintenance operation, an unexpected sodium leak incident occurred at one of the sodium loops, triggering an emergency response. An investigation into the incident revealed that the leak happened at a VCR fitting on the recently replaced cold trap. The metal gasket of the leaked VCR fitting was not compressed sufficiently. A dimensional mismatch between the new component and old piping configuration was responsible for a significant misalignment. A new cold trap with improved design is in production. The new design provides additional flexibility and an access point for post-installation helium leak check and for venting of trapped gas. These design features will make the system more error-tolerant and the installation quality verifiable. A thermodynamic analysis was performed to understand the carburization-decarburization behavior of A709 in sodium environment. The equilibrium carbon activity in the alloy was evaluated with M 23 C 6 , TiC, and NbC. The carburization-decarburization boundary was calculated with different methods developed previously. The results suggests that A709 will be carburized in SMT-1 and SMT-2, and can be decarburized in low-carbon-activity environments such as EBR-II at temperatures above 620-650°C. Nonetheless, A709 should be less likely to be decarburized than 316H SS when exposed to the same low-carbon-activity environment.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Neural network methods for radiation detectors and imaging

Recent advances in image data proccesing through deep learning allow for new optimization and performance-enhancement schemes for radiation detectors and imaging hardware. This enables radiation experiments, which includes photon sciences in synchrotron and X-ray free electron lasers as a subclass, through data-endowed artificial intelligence. We give an overview of data generation at photon sources, deep learning-based methods for image processing tasks, and hardware solutions for deep learning acceleration. Most existing deep learning approaches are trained offline, typically using large amounts of computational resources. However, once trained, DNNs can achieve fast inference speeds and can be deployed to edge devices. A new trend is edge computing with less energy consumption (hundreds of watts or less) and real-time analysis potential. While popularly used for edge computing, electronic-based hardware accelerators ranging from general purpose processors such as central processing units (CPUs) to application-specific integrated circuits (ASICs) are constantly reaching performance limits in latency, energy consumption, and other physical constraints. These limits give rise to next-generation analog neuromorhpic hardware platforms, such as optical neural networks (ONNs), for high parallel, low latency, and low energy computing to boost deep learning acceleration (LA-UR-23-32395).

edge computing↗

Parallel Algebraic Multigrid for Fusion and Higher-Order PDEs

Multigrid methods play a key role in large-scale scientific simulation because they are among the fastest and most scalable approaches for solving the underlying sparse linear systems of equations that arise from a wide array of Partial Differential Equation (PDE) discretizations. Algebraic multigrid (AMG) is a special type of multigrid method that depends only on the description of the linear system, giving it better portability and broader applicability than geometric multigrid, as it requires no explicit knowledge of the problem geometry. Even though these methods are widely used today, there are still applications where further development is needed. In this report, we focus on PDEs with higher-order terms (e.g., fourth order), concentrating on a PDE that arises in tokamak edge plasma simulations (a tokamak is a machine that confines a plasma using magnetic fields and is believed to be the leading plasma confinement concept for future fusion power plants). General multigrid relaxes a linear system on coarser grids and reverses this process with interpolation, but standard AMG methods struggle with the aforementioned higher-order PDEs. We investigate cyclic coarsening and interpolation heuristics, as well as new iterative approximation methods of refining the solution at each grid to improve the existing multigrid approach. To this end, we ensure that these techniques are transferable to a parallelized setting with LLNL’s supercomputers.

97 MATHEMATICS AND COMPUTING↗