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At least 199 records · Page 11

Accurate computational design of three-dimensional protein crystals

Protein crystallization plays a central role in structural biology. Despite this, the process of crystallization remains poorly understood and highly empirical, with crystal contacts, lattice packing arrangements and space group preferences being largely unpredictable. Programming protein crystallization through precisely engineered side-chain-side-chain interactions across protein-protein interfaces is an outstanding challenge. Here, in this study, we develop a general computational approach for designing three-dimensional protein crystals with prespecified lattice architectures at atomic accuracy that hierarchically constrains the overall number of degrees of freedom of the system. We design three pairs of oligomers that can be individually purified, and upon mixing, spontaneously self-assemble into >100 µm three-dimensional crystals. The structures of these crystals are nearly identical to the computational design models, closely corresponding in both overall architecture and the specific protein-protein interactions. The dimensions of the crystal unit cell can be systematically redesigned while retaining the space group symmetry and overall architecture, and the crystals are extremely porous and highly stable. Our approach enables the computational design of protein crystals with high accuracy, and the designed protein crystals, which have both structural and assembly information encoded in their primary sequences, provide a powerful platform for biological materials engineering.

59 BASIC BIOLOGICAL SCIENCES↗

In situ coherent x-ray scattering reveals polycrystalline structure and discrete annealing events in strongly coupled nanocrystal superlattices

Solution-phase bottom up self-assembly of nanocrystals into superstructures such as ordered superlattices is an attractive strategy to generate functional materials of increasing complexity, including very recent advances that incorporate strong interparticle electronic coupling. While the self-assembly kinetics in these systems have been elucidated and related to the product characteristics, the weak interparticle bonding interactions suggest the superstructures formed could continue to order within the solution long after the primary nucleation and growth have occurred, even though the mechanism of annealing remains to be elucidated. Here, we use a combination of Bragg coherent diffractive imaging and x-ray photon correlation spectroscopy to create real-space maps of supercrystalline order along with a real-time view of the strain fluctuations in aging strongly coupled nanocrystal superlattices while they remain suspended and immobilized in solution. By combining the results, we deduce that the self-assembled superstructures are polycrystalline, initially comprising multiple nucleation sites, and that shear avalanches at grain boundaries continue to increase crystallinity long after growth has substantially slowed. This multimodal approach should be generalizable to characterize a breadth of materials in their native chemical environments, thus extending the reach of high-resolution coherent x-ray characterization to the benefit of a much wider range of physical systems. Published by the American Physical Society 2024

36 MATERIALS SCIENCE↗

2D k -th nearest neighbour statistics: a highly informative probe of galaxy clustering

ABSTRACT Beyond standard summary statistics are necessary to summarize the rich information on non-linear scales in the era of precision galaxy clustering measurements. For the first time, we introduce the 2D k-th nearest neighbour (kNN) statistics as a summary statistic for discrete galaxy fields. This is a direct generalization of the standard 1D kNN by disentangling the projected galaxy distribution from the redshift-space distortion signature along the line-of-sight. We further introduce two different flavours of 2D kNNs that trace different aspects of the galaxy field: the standard flavour which tabulates the distances between galaxies and random query points, and a ‘DD’ flavour that tabulates the distances between galaxies and galaxies. We showcase the 2D kNNs’ strong constraining power both through theoretical arguments and by testing on realistic galaxy mocks. Theoretically, we show that 2D kNNs are computationally efficient and directly generate other statistics such as the popular two-point correlation function (2PCF), voids probability function, and counts-in-cell statistics. In a more practical test, we apply the 2D kNN statistics to simulated galaxy mocks that fold in a large range of observational realism and recover parameters of the underlying extended halo occupation distribution (HOD) model that includes velocity bias and galaxy assembly bias. We find unbiased and significantly tighter constraints on all aspects of the HOD model with the 2D kNNs, both compared to the standard 1D kNN, and the classical redshift-space 2PCF.

79 ASTRONOMY AND ASTROPHYSICS↗

Corrosion Engineering of Part‐Per‐Million Single Atom Pt 1 /Ni(OH) 2 Electrocatalyst for PET Upcycling at Ampere‐Level Current Density

The plastic waste issue has posed a series of formidable challenges for the ecological environment and human health. While conventional recycling strategies often lead to plastic down-cycling, the electrochemical strategy of recovering valuable monomers enables an ideal, circular plastic economy. Here a corrosion synthesized single atom Pt 1 /Ni(OH) 2 electrocatalyst with part-per-million noble Pt loading for highly efficient and selective upcycling of polyethylene terephthalate (PET) into valuable chemicals (potassium diformate and terephthalic acid) and green hydrogen is reported. Electro-oxidation of PET hydrolysate, ethylene glycol (EG), to formate is processed with high Faraday efficiency (FE) and selectivity (>90%) at the current density close to 1000 mA cm −2 (1.444 V vs RHE). The in situ spectroscopy and density functional theory calculations provide insights into the mechanism and the understanding of the high efficiency. Remarkably, the electro-oxidation of EG at the ampere-level current density is also successfully illustrated by using a membrane-electrode assembly with high FEs to formate integrated with hydrogen production for 500 h of continuous operation. In conclusion, this process allows valuable chemical production at high space-time yield and is highly profitable (588–700 $\$$ ton −1 PET), showing an industrial perspective on single-atom catalysis of electrochemical plastic upcycling.

36 MATERIALS SCIENCE↗

Coarse-grained simulation of colloidal self-assembly, cation exchange, and rheology in Na/Ca smectite clay gels

Knowledge Gap: The aggregation of clay minerals—layered silicate nanoparticles—strongly impacts fluid flow, solute migration, and solid mechanics in soils, sediments, and sedimentary rocks. Experimental and computational characterization of clay aggregation is inhibited by the delicate water-mediated nature of clay colloidal interactions and by the range of spatial scales involved, from 1 nm thick platelets to flocs with dimensions up to micrometers or more. Simulations: Using a new coarse-grained molecular dynamics (CGMD) approach, we predicted the microstructure, dynamics, and rheology of hydrated smectite (more precisely, montmorillonite) clay gels containing up to 2,000 clay platelets on length scales up to 0.1 μm. Further, simulations investigated the impact of simulation time, platelet diameters (6 to 25nm), and the ratio of Na to Ca exchangeable cations on the assembly of tactoids (i.e., stacks of parallel clay platelets) and larger aggregates (i.e., assemblages of tactoids). We analyzed structural features including tactoid size and size distribution, basal spacing, counterion distribution in the electrical double layer, clay association modes, and the rheological properties of smectite gels. Findings: Our results demonstrate new potential to characterize and understand clay aggregation in dilute suspensions and gels on a scale of thousands of particles with explicit representation of counterion clouds and with accuracy approaching that of all-atom molecular dynamics (MD) simulations. For example, our simulations predict the strong impact of Na/Ca ratio on clay tactoid formation and the shear-thinning rheology of clay gels.

42 ENGINEERING↗

Quantitative SANS and multi-model analysis of spacer-dependent micellization of urea-based gemini surfactants

The micellization behavior of urea-based cationic gemini surfactants was investigated using small-angle neutron scattering (SANS) with multi-model form factor analysis. A homologous series of surfactants with urea group included in the hydrophobic tail and polymethylene spacers consisting of two to ten methylene units was analyzed using three form factor models: a core–shell ellipsoid and two variants of homogeneous ellipsoids. The results from all models show a consistent trend of the micelle structures, confirming that the spacer length critically influences micellar geometry, aggregation number, and hydration. The surfactant with four CH 2 groups in the spacer formed the largest micelles with the highest aggregation number, while longer spacers led to progressively smaller, more compact aggregates. The shell hydration—quantified as the volume fraction of heavy water within the hydrophilic region—decreased systematically with increasing spacer length due to enhanced hydrophobicity of the headgroup-spacer region. Intermicellar interactions, modeled as screened Coulomb interaction using the rescaled mean spherical approximation (RMSA), revealed the strongest electrostatic repulsion for the case of four methylene groups in the spacer, corresponding to the highest micellar charge and largest interparticle spacing. The observed spacer-dependent trends were robust across all modeling approaches, demonstrating that the spacer length serves as a key structural determinant of self-assembly in this type of urea-based gemini systems. These findings provide insight into the design of gemini surfactants with tailored aggregation behavior for applications in drug delivery, nanostructure templating, and solubilization technologies.

Core–shell ellipsoid model↗

How Do Uncertainties in Galaxy Formation Physics Impact Field-level Galaxy Bias?

Our ability to extract cosmological information from galaxy surveys is limited by uncertainties in the galaxy–dark matter halo relationship for a given galaxy population, which are governed by the intricacies of galaxy formation. To quantify these uncertainties, we examine quenched and star-forming galaxies using two distinct approaches to modeling galaxy formation: U$\scriptsize{NIVERSE}$M$\scriptsize{ACHINE}$, an empirical semianalytic model, and the I$\scriptsize{llustris}$TNG hydrodynamical simulation. We apply a second-order hybrid N-body perturbative bias expansion to each galaxy sample, enabling direct comparison of modeling approaches and revealing how uncertainties in the galaxy–halo connection affect bias parameters and non-Poisson noise across number densities and redshifts. Notably, we find that quenched and star-forming galaxies occupy distinct parts of the bias parameter space, and that the scatter induced from these different galaxy formation models is small when conditioned on similar selections of galaxies. We also detect the signature of assembly bias in our samples; this leads to small but significant deviations from analytic bias predictions, while assembly bias-removed samples match these predictions well. This work indicates that galaxy samples from a spectrum of reasonable, physically motivated models for galaxy formation give a relatively small range of field-level galaxy bias parameters. We estimate a set of priors from these models that should be useful in extracting cosmological constraints from luminous red galaxy– and emission line galaxy–like samples. Looking forward, careful estimates of the range of impacts of galaxy formation, for a given sample and cosmological analysis, will be an essential ingredient for extracting the most precise cosmological information from current and future large galaxy surveys.

79 ASTRONOMY AND ASTROPHYSICS↗

Hard carbon with an opened pore structure for enhanced sodium storage performance

The pore structure of hard carbon has a significant impact on its Na + storage capacity. Herein, a waste wood-derived hard carbon with opened pores (OP-HC) was fabricated with polyvinyl pyrrolidone (PVP) as an additive. Ex situ SAXS and HR-TEM testing results indicate that OP-HC with opened pores and enlarged d 002 interlayer spacing facilitates the reversible (de)sodiation of Na + ions. In situ TEM and XRD testing results demonstrate that OP-HC shows excellent structure stability during the (de)sodiation process. Thus, OP-HC delivers a high reversible charge capacity of 350.7 mA h g −1 at 0.05 C and an ultra-high initial Coulombic efficiency (ICE) of 94.9%. Moreover, OP-HC exhibits excellent cycling stability, and the assembled 18650 full cell with an OP-HC anode can achieve a high capacity retention of 94.5% after 400 cycles at 1.0 A. Furthermore, the excellent electrochemical performance and deep insights into OP-HC with opened pores and increased d 002 interlayer spacing offer a new strategy to design high-performance HC anodes for SIBs.

You, Shunzhang↗

Directed self-assembly of block copolymers for high-precision patterning in the era of extreme ultraviolet lithography

Extreme ultraviolet (EUV) lithography enables unprecedented resolution in semiconductor patterning but faces critical challenges in developing resist materials that achieve high-precision at economically viable throughput. Directed self-assembly (DSA) of block copolymers (BCPs) offers a promising solution for pattern rectification by leveraging thermodynamically determined domain structures to decouple BCP pattern quality from the imperfect original lithographic pattern. This prospective presents an overview of recent progress on the EUV + DSA strategy, covering advances in BCP material design, processing, metrology, and pattern transfer. We highlight recent advances in high-χ BCPs with perpendicular orientation and domain spacings compatible with EUV dimensions, leveraging A-b-(B-r-C) architectures. We also discuss progress in chemical pre-pattern fabrication using both positive- and negative tone resists, along with processing strategies to minimize defects and roughness based on BCP thermodynamics and assembly kinetics. We further examine metrology platforms for characterizing the thermodynamics of BCP materials and quantifying the size and shape of BCP domains. Lastly, we review pattern transfer strategies for generating functional inorganic masks suitable for semiconductor manufacturing. Together, these advances highlight the potential of DSA to complement EUV lithography, offering a pathway to address critical challenges in achieving high-precision patterning for the semiconductor industry.

Lee, Kyunghyeon [Univ. of Chicago, IL (United Stat↗

AEDGE: Atomic Experiment for Dark Matter and Gravity Exploration in Space

We propose in this White Paper a concept for a space experiment using cold atoms to search for ultra-light dark matter, and to detect gravitational waves in the frequency range between the most sensitive ranges of LISA and the terrestrial LIGO/Virgo/KAGRA/INDIGO experiments. This interdisciplinary experiment, called Atomic Experiment for Dark Matter and Gravity Exploration (AEDGE), will also complement other planned searches for dark matter, and exploit synergies with other gravitational wave detectors. We give examples of the extended range of sensitivity to ultra-light dark matter offered by AEDGE, and how its gravitational-wave measurements could explore the assembly of super-massive black holes, first-order phase transitions in the early universe and cosmic strings. AEDGE will be based upon technologies now being developed for terrestrial experiments using cold atoms, and will benefit from the space experience obtained with, e.g., LISA and cold atom experiments in microgravity. This paper is based on a submission (v1) in response to the Call for White Papers for the Voyage 2050 long-term plan in the ESA Science Programme. ESA limited the number of White Paper authors to 30. However, in this version (v2) we have welcomed as supporting authors participants in the Workshop on Atomic Experiments for Dark Matter and Gravity Exploration held at CERN: ({\tt https://indico.cern.ch/event/830432/}), as well as other interested scientists, and have incorporated additional material.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Supramolecular meso -Trick: Ambidextrous Mirror Symmetry Breaking in a Liquid Crystalline Network with Tetragonal Symmetry

Bicontinuous and multicontinuous network phases are among nature's most complex structures in soft matter systems. Here, a chiral bicontinuous tetragonal phase is reported as a new stable liquid crystalline intermediate phase at the transition between two cubic phases, the achiral double gyroid and the chiral triple network cubic phase with an I 23 space group, both formed by dynamic networks of helices. The mirror symmetry of the double gyroid, representing a meso -structure of two enantiomorphic networks, is broken at the transition to this tetragonal phase by retaining uniform helicity only along one network while losing it along the other one. This leads to a conglomerate of enantiomorphic tetragonal space groups, P 4 1 2 1 2 and P 4 3 2 1 2. Phase structures and chirality were analyzed by small-angle X-ray scattering (SAXS), grazing-incidence small-angle X-ray scattering (GISAXS), resonant soft X-ray scattering (RSoXS) at the carbon K-edge, and model-dependent SAXS/RSoXS simulation. In conclusion, our findings not only lead to a new bicontinuous network-type three-dimensional mesophase but also reveal a mechanism of mirror symmetry breaking in soft matter by partial meso -structure racemization at the transition from enantiophilic to enantiophobic interhelical self-assembly.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Gripper Test Assembly Status Report (FY2020)

Refueling systems for fast reactors are designed to handle fresh and used core assemblies (fuel, reflector, and shield core assemblies) within the reactor vessel in an opaque coolant environment without visual reference. These refueling machines are designed to work in a sodium (or other fast reactor coolant) and argon vapor space environment and are engineered with the rotatable plug system to allow for the movement of fresh and spent fuel into and out of the reactor core. The refueling machines are a critical component in any reactor and thus need to undergo extensive testing in a prototypic environment to ensure that they will meet all of the system functions and requirements. Argonne has developed an innovative compact refueling system design for the Advanced Fast Reactor-100 that is based upon some mechanisms used in previous reactor designs, such as the U.K.’s Prototype Fast Reactor (PFR) and some mechanisms that have not been used in sodium. This compact refueling machine supports the reduction in size of the AFR-100’s reactor vessel, and if fully developed, would support and inform the development of the in-vessel refueling machines for such commercial reactors as the GEH PRISM reactor plant, the ARC Clean Energy’s ARC-100 reactor, and the Natrium reactor, among others. This refueling system is a vital component of a fast reactor that supports reducing the cost of the reactor and increasing its reliability. During the development of the compact fuel handling machine conceptual design for the AFR-100, a lack of testing data for many mechanical components in sodium under typical in-reactor loads and conditions was discovered. The reduction in lifetime of the various mechanical components in the liquid sodium environment needs to be quantified versus the calculated component lifetimes under normal conditions in the testing while they are subjected to typical loading profiles experienced in the past. The Gripper Test Assembly discussed here includes a full-size gripper device with appropriate mechanical features that will be tested in sodium to provide this testing data. The Gripper Test Assembly is used to test various mechanical fuel handling components submerged in high temperature liquid sodium. These mechanisms are gears, bearings, gripper jaws and head, universal joints and shafts, ball screws, among others. These components will be tested under the typical sodium environmental conditions experienced during refueling operations with appropriate loading conditions that simulate the removal and insertion of core assemblies into a fast reactor grid plate structure. This Gripper Test Assembly is the second in a series of refueling system mechanisms developed for testing in sodium. The first test assembly is the Gear Test Assembly (GTA) which was used to test the performance of gears and bearings operating in sodium. Because of the successful testing conducted with the GTA, it was decided to continue with the development of the Gripper Test Assembly which uses the same gears and bearings tested in GTA. Using the data collected during operation of this gripper test assembly, lifetime reduction factors of the various mechanical components can be calculated for the material combinations selected. These lifetime reduction factors can be used in the design of future mechanical systems which operate in these environments to accurately predict component end of life. In addition, an understanding of the ability of these components and mechanisms to operate under-sodium with the chosen materials will be accomplished. Again, this Gripper Test Assembly is the follow-on test article to the Gear Test Assembly which was testing the ability of gears and bearings operating in a sodium environment. Once fabricated and qualified, it will be tested in the Mechanism Engineering Test Loop (METL) facility located in Building 308 at Argonne National Laboratory.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

SPHERE Assembly and Operation Demonstration

The objective of the current scope was to complete single primary heat extraction and removal emulator (SPHERE) assembly and demonstrate the operation of the SPHERE facility. The initial testing consisted of vacuum operation of a sodium heat pipe. The temperature was measured at 10 evenly spaced points along the heat pipe. Additional exterior thermocouple measurements were also taken on the exterior of the heat pipe to confirm the similarity of thermowell temperatures to exterior heat pipe temperature measurements. The initial test was successfully completed and results measured at INL are consistent with the data from the manufacturer.

42 ENGINEERING↗

Impact of the numerical solution approach of a plant hydrodynamic model (v0.1) on vegetation dynamics

Abstract. Numerous plant hydrodynamic models have started to be implemented in vegetation dynamics models, reflecting the central role of plant hydraulic traits in driving water, energy, and carbon cycles, as well as plant adaptation to climate change. Different numerical approximations of the governing equations of the hydrodynamic models have been documented, but the numerical accuracy of these models and its subsequent effects on the simulated vegetation function and dynamics have rarely been evaluated. Using different numerical solution methods (including implicit and explicit approaches) and vertical discrete grid resolutions, we evaluated the numerical performance of a plant hydrodynamic module in the Functionally Assembled Terrestrial Ecosystem Simulator (FATES-HYDRO version 0.1) based on single-point and global simulations. Our simulation results showed that when near-surface vertical grid spacing is coarsened (grid size >10 cm), the model significantly overestimates aboveground biomass (AGB) in most of the temperate forest locations and underestimates AGB in the boreal forest locations, as compared to a simulation with finer vertical grid spacing. Grid coarsening has a small effect on AGB in the tropical zones of Asia and South America. In particular, coarse surface grid resolution should not be used when there are large and prolonged water content differences among soil layers at depths due to long dry-season duration and/or well-drained soil or when soil evaporation is a dominant fraction of evapotranspiration. Similarly, coarse surface grid resolution should not be used when there is lithologic discontinuity along the soil depth. This information is useful for uncertainty quantification, sensitivity analysis, or the training of surrogate models to design the simulations when computational cost limits the use of ensemble simulations.

54 ENVIRONMENTAL SCIENCES↗

Confocal Raman Microscopy Investigation of Phospholipid Monolayers Deposited on Nitrile-Modified Surfaces in Porous Silica Particles

Phospholipid bilayers deposited on a variety of surfaces offer models for investigation of the lipid membrane structure and supports for biocompatible sensors. Hybrid-supported phospholipid bilayers (HSLBs) are stable membrane models for these investigations, typically prepared by self-assembly of a lipid monolayer over an n-alkane-modified surface. HSLBs have been prepared on n-alkyl chain-modified silica and used for lipophilicity-based chromatographic separations. The structure of these hybrid bilayers differs from vesicle membranes where the lipid head group spacing is greater due to interdigitation of the lipid acyl chains with the underlying n-alkyl chains bound to the silica surface. This interdigitated structure exhibits a broader melting transition at a higher temperature due to strong interactions between the lipid acyl chains and the immobile n-alkyl chains bound to silica. In the present work, we seek to reduce the interactions between a lipid monolayer and its supporting substrate by self-assembly of 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) on porous silica functionalized with nitrile-terminated surface ligands. The frequency of Raman scattering of the surface -C≡N stretching mode at the lipid–nitrile interface is consistent with an n-alkane-like environment and insensitive to lipid head group charge, indicating that the lipid acyl chains are in contact with the surface nitrile groups. The head group area of this lipid monolayer was determined from the within-particle phospholipid concentration and silica specific surface area and found to be 54 ± 2 Å 2 , equivalent to the head group area of a DMPC vesicle bilayer. The structure of these nitrile-supported phospholipid monolayers was characterized below and above their melting transition by confocal Raman microscopy and found to be nearly identical to DMPC vesicle bilayers. Their narrow gel-to-fluid-phase melting transition is equivalent to dispersed DMPC vesicles, indicating that the acyl chain structure on the nitrile support mimics the outer leaflet structure of a vesicle membrane.

36 MATERIALS SCIENCE↗

Symmetry-specific orientational order parameters for complex structures

A comprehensive framework of characterizing complex self-assembled structures with a set of orientational order parameters is presented. It is especially relevant in the context of using anisotropic building blocks with various symmetries. Two classes of tensor order parameters are associated with polyhedral nematic and bond orientational order. For the latter, a variation of classical bond order parameters (BOPs) is introduced, which takes advantage of the symmetry of constituent particles and/or expected crystalline phases. These symmetrized BOPs can be averaged over an entire system or assigned locally to an individual bond. By combining that with the bond percolation procedure, one is able to identify coherent domains within a self-assembled structure. As a demonstration of the proposed framework, we apply it to a simulated hybrid system that combines isotropic and patchy particles with octahedral symmetry. In conclusion, not only does the methodology allow one to identify individual crystalline domains but also it detects coherent clusters of a peculiar compact amorphous structure that is not space-filling and lacks any long-range order.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Turbo‐charging crop improvement: harnessing multiplex editing for polygenic trait engineering and beyond

Multiplex CRISPR editing has emerged as a transformative platform for plant genome engineering, enabling the simultaneous targeting of multiple genes, regulatory elements, or chromosomal regions. This approach is effective for dissecting gene family functions, addressing genetic redundancy, engineering polygenic traits, and accelerating trait stacking and de novo domestication. Its applications now extend beyond standard gene knockouts to include epigenetic and transcriptional regulation, chromosomal engineering, and transgene‐free editing. These capabilities are advancing crop improvement not only in annual species but also in more complex systems such as polyploids, undomesticated wild relatives, and species with long generation times. At the same time, multiplex editing presents technical challenges, including complex construct design and the need for robust, scalable mutation detection. We discuss current toolkits and recent innovations in vector architecture, such as promoter and scaffold engineering, that streamline workflows and enhance editing efficiency. High‐throughput sequencing technologies, including long‐read platforms, are improving the resolution of complex editing outcomes such as structural rearrangements—often missed by standard genotyping—when targeting repetitive or tandemly spaced loci. To fully realize the potential of multiplex genome engineering, there is growing demand for user‐friendly, synthetic biology‐compatible, and scalable computational workflows for gRNA design, construct assembly, and mutation analysis. Experimentally validated inducible or tissue‐specific promoters are also highly desirable for achieving spatiotemporal control. As these tools continue to evolve, multiplex CRISPR editing is poised to become a foundational technology of next‐generation crop improvement to address challenges in agriculture, sustainability, and climate resilience.

59 BASIC BIOLOGICAL SCIENCES↗

Spectral Equivalence of Low-Order Discretizations for High-Order H(curl) and H(div) Spaces

In this paper, we present spectral equivalence results for high-order tensor product edge- and face-based finite elements for the H(curl) and H(div) function spaces. Specifically, we show for certain choices of shape functions that the mass and stiffness matrices of the high-order elements are spectrally equivalent to those for an assembly of low-order elements on the associated Gauss--Lobatto--Legendre mesh. Based on this equivalence, efficient preconditioners can be designed with favorable computational complexity. Numerical results are presented which confirm the theory and demonstrate the benefits of the equivalence results for overlapping Schwarz preconditioners.

97 MATHEMATICS AND COMPUTING↗