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DOE OSTI2021

Antimicrobial properties of nanostructured surfaces – demonstrating the need for a standard testing methodology

Bioinspired nanostructured materials that exhibit antimicrobial properties are being synthesized and tested at increasing rates for use in healthcare, manufacturing processes, and diagnostics. Although progress has been made in improving and understanding their bactericidal activity, arguably, the biggest problem currently in the field is the lack of a standard testing methodology that allows for optimal characterization and better comparison of emerging nanostructures. In this work, we examine two forms of nanostructured silicon that vary in their ability to kill certain bacterial species due to different physical mechanisms and derive guidelines for the comparative testing. We perform a comprehensive evaluation of methodologies used extensively in the field (e.g., colony counting and live dead analysis) and the novel application of high-throughput flow cytometry. The data reveal how the techniques are complementary but not always directly equivalent or correlative. Therefore, comparison of results obtained using different methodologies on different materials can be grossly misleading. We report significant variations in bactericidal efficiencies depending on experimental environments (medium type, etc.) and methodologies employed. In addition, we demonstrate how cytometry is yet another powerful complementary tool that can aid the mechanistic understanding of antimicrobial activities of rough surfaces. Besides standardization for comparison, ultimately, evaluation methods need to consider anticipated applications. Then and only then can the true potential (or limitation) of a novel material be determined for its suitability for advancement in a particular field of use.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2020

Planck 2018 results

We report on the implications for cosmic inflation of the 2018 release of the Planck cosmic microwave background (CMB) anisotropy measurements. The results are fully consistent with those reported using the data from the two previous Planck cosmological releases, but have smaller uncertainties thanks to improvements in the characterization of polarization at low and high multipoles. Planck temperature, polarization, and lensing data determine the spectral index of scalar perturbations to be n s = 0.9649 ± 0.0042 at 68% CL. We find no evidence for a scale dependence of n s , either as a running or as a running of the running. The Universe is found to be consistent with spatial flatness with a precision of 0.4% at 95% CL by combining Planck with a compilation of baryon acoustic oscillation data. The Planck 95% CL upper limit on the tensor-to-scalar ratio, r0.002 < 0.10, is further tightened by combining with the BICEP2/Keck Array BK15 data to obtain r 0.002 < 0.056. In the framework of standard single-field inflationary models with Einstein gravity, these results imply that: (a) the predictions of slow-roll models with a concave potential, V"(Φ) < 0, are increasingly favoured by the data; and (b) based on two different methods for reconstructing the inflaton potential, we find no evidence for dynamics beyond slow roll. Three different methods for the non-parametric reconstruction of the primordial power spectrum consistently confirm a pure power law in the range of comoving scales 0.005 Mpc -1 ≲ k ≲ 0.2 Mpc -1 . A complementary analysis also finds no evidence for theoretically motivated parameterized features in the Planck power spectra. For the case of oscillatory features that are logarithmic or linear in k, this result is further strengthened by a new combined analysis including the Planck bispectrum data. The new Planck polarization data provide a stringent test of the adiabaticity of the initial conditions for the cosmological fluctuations. In correlated, mixed adiabatic and isocurvature models, the non-adiabatic contribution to the observed CMB temperature variance is constrained to 1.3%, 1.7%, and 1.7% at 95% CL for cold dark matter, neutrino density, and neutrino velocity, respectively. Planck power spectra plus lensing set constraints on the amplitude of compensated cold dark matter-baryon isocurvature perturbations that are consistent with current complementary measurements. The polarization data also provide improved constraints on inflationary models that predict a small statistically anisotropic quadupolar modulation of the primordial fluctuations. However, the polarization data do not support physical models for a scale-dependent dipolar modulation. All these findings support the key predictions of the standard single-field inflationary models, which will be further tested by future cosmological observations.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Development of a platform for experimental and computational studies of magnetic and radiative effects on astrophysically relevant jets at OMEGA

Accurate modeling of astrophysical jets is critical for understanding accretion systems and their impact on the interstellar medium. While astronomical observations can validate models, they have limitations. Controlled laboratory experiments offer a complementary approach for qualitative and quantitative demonstration. Laser experiments offer a complementary approach. This article introduces a new platform on the OMEGA laser facility for high-velocity (1500 kms−1), high-aspect-ratio (∼36) jet creation with strong cylindrical symmetry. This platform's capabilities bridge observational gaps, enabling controlled initial conditions and direct measurements of plasma characteristics, crucial for refining astrophysical jet dynamics and improving the models accuracy.

Rigon, G. (ORCID:0000000256664725)↗

DOE OSTI2021

Soil metabolome response to whole-ecosystem warming at the Spruce and Peatland Responses under Changing Environments experiment

In this study, a suite of complementary environmental geochemical analyses, including NMR and gas chromatography-mass spectrometry (GC-MS) analyses of central metabolites, Fourier transform ion cyclotron resonance mass spectrometry (FTICR-MS) of secondary metabolites, and lipidomics, was used to investigate the influence of organic matter (OM) quality on the heterotrophic microbial mechanisms controlling peatland CO2, CH4, and CO2:CH4 porewater production ratios in response to climate warming. Our investigations leverage the Spruce and Peatland Responses under Changing Environments (SPRUCE) experiment, where air and peat warming were combined in a whole-ecosystem warming treatment. We hypothesized that warming would enhance the production of plant-derived metabolites, resulting in increased labile OM inputs to the surface peat, thereby enhancing microbial activity and greenhouse gas production. Because shallow peat is most susceptible to enhanced warming, increases in labile OM inputs to the surface, in particular, are likely to result in significant changes to CO2 and CH4 dynamics and methanogenic pathways. In support of this hypothesis, significant correlations were observed between metabolites and temperature consistent with increased availability of labile substrates, which may stimulate more rapid turnover of microbial proteins. An increase in the abundance of methanogenic genes in response to the increase in the abundance of labile substrates was accompanied by a shift toward acetoclastic and methylotrophic methanogenesis. Our results suggest that as peatland vegetation trends toward increasing vascular plant cover with warming, we can expect a concomitant shift toward increasingly methanogenic conditions and amplified climate–peatland feedbacks.

Wilson, Rachel M.↗

DOE OSTI2022

Mechanism of tethered agonist-mediated signaling by polycystin-1

Mutations of polycystin-1 (PC1) are the major cause (85% of cases) of autosomal dominant polycystic kidney disease (ADPKD), which is the fourth leading cause of kidney failure. PC1 is thought to function as an atypical G protein-coupled receptor, yet the mechanism by which PC1 regulates G-protein signaling remains poorly understood. A significant portion of ADPKD mutations of PC1 encode a protein with defects in maturation or reduced function that may be amenable to functional rescue. In this work, we have combined complementary biochemical and cellular assay experiments and accelerated molecular simulations, which revealed an allosteric transduction pathway in activation of the PC1 C-terminal fragment. Our findings will facilitate future rational drug design efforts targeting the PC1 signaling function. Polycystin-1 (PC1) is an important unusual G protein-coupled receptor (GPCR) with 11 transmembrane domains, and its mutations account for 85% of cases of autosomal dominant polycystic kidney disease (ADPKD). PC1 shares multiple characteristics with Adhesion GPCRs. These include a GPCR proteolysis site that autocatalytically divides these proteins into extracellular, N-terminal, and membrane-embedded, C-terminal fragments (CTF), and a tethered agonist (TA) within the N-terminal stalk of the CTF that is suggested to activate signaling. However, the mechanism by which a TA can activate PC1 is not known. Here, we have combined functional cellular signaling experiments of PC1 CTF expression constructs encoding wild type, stalkless, and three different ADPKD stalk variants with all-atom Gaussian accelerated molecular dynamics (GaMD) simulations to investigate TA-mediated signaling activation. Correlations of residue motions and free-energy profiles calculated from the GaMD simulations correlated with the differential signaling abilities of wild type and stalk variants of PC1 CTF. They suggested an allosteric mechanism involving residue interactions connecting the stalk, Tetragonal Opening for Polycystins (TOP) domain, and putative pore loop in TA-mediated activation of PC1 CTF. Key interacting residues such as N3074–S3585 and R3848–E4078 predicted from the GaMD simulations were validated by mutagenesis experiments. Together, these complementary analyses have provided insights into a TA-mediated activation mechanism of PC1 CTF signaling, which will be important for future rational drug design targeting PC1.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Comparing multi-source urban flood indicators: satellite, simulation, and citizen-reported data

Urban flooding arises from complex mechanisms, making it challenging to capture accurately with a single detection method. This study evaluates three complementary approaches to detect flooding across three Chicago neighborhoods: (i) Sentinel-1 synthetic aperture radar (SAR), offering weather-independent, high-resolution (10 m) imagery of surface inundation; (ii) the storm water management model (SWMM), simulating combined sewer overflow and drainage performance; and (iii) citizen-generated 311 service requests, capturing observed flooding impacts. By analyzing six storms ranging from severe to mild, we examine how each source uniquely contributes to identifying urban flood events. SAR imagery effectively identifies standing water but can miss brief flooding due to satellite revisit constraints. SWMM provides detailed insights into system-wide drainage behavior yet may underestimate localized street-level flooding. Meanwhile, 311 calls reflect real-world flooding impacts but are vulnerable to underreporting. Statistical overlap analysis highlights chronic flood hotspots repeatedly identified across multiple detection methods, indicating persistent infrastructure and topographic vulnerabilities. Temporal analysis further reveals that while SWMM flooding aligns closely with rainfall peaks, 311 calls typically precede or persist beyond these peaks. Our findings emphasize the value of using satellite observations, hydrological modeling, and resident-reported data in a complementary manner to better interpret patterns in flood timing, severity, and spatial distribution—providing insights that can inform targeted infrastructure improvements and contribute to urban flood resilience planning.

311↗

DOE OSTI2024

The Interplay of Binary and Quantitative Structure on the Stability of Mutualistic Networks

Synopsis Understanding how the structure of biological systems impacts their resilience (broadly defined) is a recurring question across multiple levels of biological organization. In ecology, considerable effort has been devoted to understanding how the structure of interactions between species in ecological networks is linked to different broad resilience outcomes, especially local stability. Still, nearly all of that work has focused on interaction structure in presence-absence terms and has not investigated quantitative structure, i.e., the arrangement of interaction strengths in ecological networks. We investigated how the interplay between binary and quantitative structure impacts stability in mutualistic interaction networks (those in which species interactions are mutually beneficial), using community matrix approaches. We additionally examined the effects of network complexity and within-guild competition for context. In terms of structure, we focused on understanding the stability impacts of nestedness, a structure in which more-specialized species interact with smaller subsets of the same species that more-generalized species interact with. Most mutualistic networks in nature display binary nestedness, which is puzzling because both binary and quantitative nestedness are known to be destabilizing on their own. We found that quantitative network structure has important consequences for local stability. In more-complex networks, binary-nested structures were the most stable configurations, depending on the quantitative structures, but which quantitative structure was stabilizing depended on network complexity and competitive context. As complexity increases and in the absence of within-guild competition, the most stable configurations have a nested binary structure with a complementary (i.e., anti-nested) quantitative structure. In the presence of within-guild competition, however, the most stable networks are those with a nested binary structure and a nested quantitative structure. In other words, the impact of interaction overlap on community persistence is dependent on the competitive context. These results help to explain the prevalence of binary-nested structures in nature and underscore the need for future empirical work on quantitative structure.

Zoology↗

DOE OSTI2025

Protoplast fusion as a strategy to increase ploidy in Rhodotorula toruloides for strain development

Rhodotorula toruloides is a red oleaginous yeast with growing commercial interest because of its hardiness and exceptional lipid production capacity. Because it is a basidiomycete yeast with a complex life cycle, many of the classical breeding methods used with ascomycetes are unavailable for strain improvement. However, we have been able to construct polyploid yeast by fusing protoplasts of parents with the same mating type. Fusing of Y-6985 (A2) and Y-48190 (A2), which had been transformed with complementary antibiotic markers, led to the recovery of two diploids and one triploid. The stability of the fusion yeasts was tested by plating them on non-selective medium after several growth cycles under antibiotics and then testing five colonies per strain for nuclear DNA contents using flow cytometry and standard cell cycle analysis: the triploid and one diploid were stable. Fusants inherited their mitochondria from a single parent, which was demonstrated using restriction fragment length polymorphism (RFLP) of mitochondrial DNA. The phenotypic properties of the parents and fusants were compared in glucose fed-batch bioreactor studies and cellulosic sugar batch cultures. The final lipid titers for the fed-batch cultures were 24.9–39.7 g/L with Y-6985 and the diploid and triploid performing the best and worst, respectively. The fusants demonstrated intermediate hardiness for growth on hydrolysate prepared with dilute-acid pretreated switchgrass and were outperformed by Y-48190. Unlike one of the haploid parents, the fusants grew in 70% v/v concentrated hydrolysate. Furthermore, they did not grow as fast as the other haploid. In this study, a modernized protoplast fusion method is resurrected a useful tool for strain development in this yeast, which is complementary with other available methods.

Lignocellulose↗

DOE OSTI2026

Characterizing radial flow fluctuations in relativistic heavy-ion collisions at top RHIC and LHC energies

This study presents a systematic investigation of the transverse-momentum differential radial flow fluctuations observable 𝑣 0 ⁡ (𝑝 𝑇 ) in relativistic heavy-ion collisions at top Relativistic Heavy Ion Collider ($\sqrt{s_{NN}}$ = 200 GeV) and Large Hadron Collider ($\sqrt{s_{NN}}$ = 2.76 and 5.02 TeV) energies. Using a multistage hydrodynamic model, this study assesses the sensitivity of 𝑣 0 ⁡(𝑝 𝑇 ) to a wide range of physical effects, including bulk and shear viscosities, off-equilibrium corrections at particlization, the presence of a hadronic afterburner, and the nucleon size in the initial conditions. By employing complementary rescaling strategies, this study demonstrates how different physical effects leave distinct imprints on the shape of 𝑣 0 ⁡(𝑝 𝑇 ). A combined double-rescaling of 𝑣 0 ⁡(𝑝 𝑇 )/𝑣 0 versus 𝑝 𝑇 /⟨𝑝 𝑇 ⟩ reveals a universality across a wide range of energies and model assumptions in the low-𝑝 𝑇 regime, a robust signature of collective behavior. This allows us to disentangle the universal dynamics of the bulk medium from model-specific features that emerge at higher 𝑝 𝑇 . These results establish 𝑣 0⁡ (𝑝 𝑇 ) as a powerful and complementary observable for constraining quark-gluon plasma transport properties and initial-state granularity, offering a unique probe of the created QCD medium.

Du, Lipei [University of California, Berkeley, CA ↗

DOE OSTI2020

High-Energy Coherent X-Ray Dffraction Microscopy of Polycrystal Grains: First Steps Towards a Multi-Scale Approach

Here, we present proof-of-concept imaging measurements of a polycrystalline material that integrate the elements of conventional high-energy x-ray diffraction microscopy with coherent diffraction-imaging techniques, and that can enable in situ strain-sensitive imaging of lattice structure in ensembles of deeply embedded crystals over five decades of length scale upon full realization. We demonstrate that the combination of these two characterization methods enables a more complete picture of the crystal-lattice strain than either method is capable of providing individually. Such complementary imaging capabilities are critical to addressing questions in a variety of research areas such as materials science and engineering, chemistry, and solid-state physics. Towards this eventual goal, the following key aspects are demonstrated: (1) high-energy Bragg coherent diffraction imaging (HE BCDI) of submicron-scale crystallites at 52 keV at current third-generation synchrotron light sources, (2) HE BCDI performed in conjunction with far-field high-energy diffraction microscopy (FF HEDM) on the grains of a polycrystalline sample in a smoothly integrated manner, and (3) the orientation information of an ensemble of grains obtained via FF HEDM used to perform complementary HE BCDI on multiple Bragg reflections of a single targeted grain. The imaged structures are seen to be 477 ± 50 nm or smaller in size, with an estimated strain resolution of 2.5 x 10 -4 . These steps lay the foundation for integration of HE BCDI, which typically provides a spatial resolution tens of nanometers, into a broad suite of well-established HEDM methods, extending HEDM beyond the few-micrometer resolution bound and into the nanoscale, and positioning the approach to take full advantage of the orders-of-magnitude improvement of x-ray coherence expected at fourth-generation light sources presently being built and commissioned worldwide.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Theory of thermal properties of magnetic materials with unknown entropy

Theoretical approaches to study thermal properties of magnetic materials typically require accurate models of magnetic interactions in order to define the entropy. Here we introduce a complementary approach for examining thermal properties in magnetic systems where an accepted model for such interactions does not exist. In place of a specific model for magnetic interactions, the approach integrates measurements of temperature dependent magnetization of the studied material into a first principles computational scheme. The approach calculates system pressure from thermally disordered microstates that properly incorporate vibrational and spin subsystems at each temperature as well as the coupling between these subsystems. We apply the approach to calculate phonon modes and to investigate the anomalously low thermal expansion of the classical Invar alloy, Fe 0.65 Ni 0.35 . Here, the calculated phonon dispersions for Invar are in excellent agreement with measured data. The Invar thermal expansion is shown to remain small between 50 K and room temperature, consistent with the experimentally observed low thermal expansion value in this same temperature range. This anomalously small thermal expansion is directly connected to a small positive contribution from lattice thermal disorder that is nearly canceled by a large negative magnetic disorder contribution. By contrast, calculations for bcc Fe show a much larger thermal expansion, consistent with experiment, which is dominated by a large contribution from lattice thermal disorder that is reduced only slightly by a small negative contribution from that of magnetism. These findings give insights into the unusual nature of magnetism and spin-lattice coupling in Invar and Fe. In addition, they give promising preliminary support to the presented new methodology as a complementary way to investigate thermal properties of magnetic materials. The success achieved on Invar and Fe motivates future testing of the approach on other magnetic materials.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Experimental study of 53 Cr via the (𝑑, 𝑝⁢𝛾) reaction

Excited states in 53 Cr were studied via the 52 Cr ⁢(𝑑, 𝑝⁢𝛾) reaction up to the neutron-separation threshold. Proton-𝛾 angular correlations and 𝛾 decay branching ratios were measured in particle-𝛾 coincidences between the Super-Enge Split-Pole Spectrograph (SE-SPS) and CeBr 3 Array (CeBrA) demonstrator of the John D. Fox Accelerator Laboratory at Florida State University. Previous spin-parity assignments from a (𝑑,𝑝) singles experiment at the SE-SPS are supported and 𝛾-ray transitions in 53 Cr are reported. We firmly assign higher-lying excited states to 53 Cr because overlapping excited states and contaminants could be identified better due to the complementary 𝛾-decay information. We also correct some of the previously reported excitation energies and present a reanalysis of previously measured 52 Cr (𝑑, 𝑝)⁢ 53 Cr angular distributions guided by the complementary 𝛾-ray information. Based on this reanalysis, the fragmentation of the neutron 2⁢𝑝 3/2 , 2⁢𝑝 1/2 , 1⁢𝑓 5/2 , 1⁢𝑔 9/2 , and 2⁢𝑑 5/2 single-particle strengths is reassessed for 53 Cr. Here, a comparison to the corresponding strengths in 55 Fe is presented.

39 ≤ A ≤ 58↗

DOE OSTI2023

Hybrid Cyber-attack Detection in Photovoltaic Farms

Here, to address the cyber-physical security in PV farms, a hybrid cyber-attack detection is proposed in this manuscript. To secure PV farms, the proposed method integrates model-based and data-driven methods by fusing the detection score at the device and system levels. First, a model-based cyber-attack detection method is developed for each PV inverter. A residual between the estimation of the Kalman filter and measurement is calculated. By leveraging the calculated residual from all inverters, a squared Mahalanobis distance is developed for device detection score generation. At the system level, a convolutional neural network (CNN) is proposed to detect cyber-attack using the waveform data at the point of common coupling (PCC) in PV farms. To improve the CNN detection accuracy, a set of well-designed features are extracted from the raw waveform data. Finally, a weighted detection score fusion method is proposed to combine device and system detection scores by using their complementary strength. The feasibility and robustness of the proposed method are validated by testing cases and a comparative experiment.

14 SOLAR ENERGY↗

DOE OSTI2025

Securing 3D NAND Without Density Loss via In-Situ Encryption Using a Single Transistor XOR Cell

In this article, we push lightweight XOR-based in-situ encryption to extreme density by proposing a singletransistor XOR memory cell and applying it to 3D NAND, enabling secure data storage without density loss. Using a ferroelectric field-effect transistor (FeFET) as an example technology, we demonstrate that: i) a single-transistor memory can realize the XOR function by exploiting the ability to charge the source and drain separately and control current flow direction, eliminating the need for conventional encrypted cells that rely on complementary devices; ii) with a XOR-based cipher, encryption and decryption can be mapped to in-situ array operations, where ciphertext is stored as the threshold voltage (VTH) states of FeFETs in a NAND string, and decryption is achieved through read operations using key-dependent complementary source/drain bias; iii) the proposed technique is scalable to multi-level cell (MLC) storage by encrypting and decrypting data bit by bit; iv) using an integrated NAND FeFET array, we experimentally demonstrate encryption and decryption operations for both single-level cell (SLC) and MLC storage; v) systemlevel benchmarking shows that the proposed technique achieves 48× and 278× improvements in encryption and decryption throughput, respectively, compared to AES.

36 MATERIALS SCIENCE↗

DOE OSTI2020

A Strategy for Forced Oscillation Suppression

Wide-area time-synchronized measurements have recently revealed troublesome forced oscillations (FOs) within modern synchronized power grids. In some cases, these FOs represent a dangerous hazard to the system. Recent research has focused on locating the source of FOs to provide operators with knowledge for mitigating their impact locally. This paper presents a complementary mitigation strategy, which is to purposely induce a second oscillation into the grid which cancels the impact of the FO. Such a strategy is complementary in that it may provide valuable time to operators attempting to locate the FOs source and to determine how to rectify it. This paper presents a suppression control strategy which modulates controllable devices to automatically cancel the impact of the FO without the need for locating the source of the original FO. The strategy is based upon tuned feedback control. In this study, the approach is demonstrated on a simulation system via modulation of inverter-based generation.

42 ENGINEERING↗

DOE OSTI2023

Development of genetic tools for heterologous protein expression in a pentose‐utilizing environmental isolate of Pseudomonas putida

Abstract Pseudomonas putida has emerged as a promising host for the conversion of biomass‐derived sugars and aromatic intermediates into commercially relevant biofuels and bioproducts. Most of the strain development studies previously published have focused on P. putida KT2440, which has been engineered to produce a variety of non‐native bioproducts. However, P. putida is not capable of metabolizing pentose sugars, which can constitute up to 25% of biomass hydrolysates. Related P. putida isolates that metabolize a larger fraction of biomass‐derived carbon may be attractive as complementary hosts to P. putida KT2440. Here we describe genetic tool development for P. putida M2, a soil isolate that can metabolize pentose sugars. The functionality of five inducible promoter systems and 12 ribosome binding sites was assessed to regulate gene expression. The utility of these expression systems was confirmed by the production of indigoidine from C6 and C5 sugars. Chromosomal integration and expression of non‐native genes was achieved by using chassis‐independent recombinase‐assisted genome engineering (CRAGE) for single‐step gene integration of biosynthetic pathways directly into the genome of P. putida M2. These genetic tools provide a foundation to develop hosts complementary to P. putida KT2440 and expand the ability of this versatile microbial group to convert biomass to bioproducts.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

Analytical Sensitivity Analysis of a Spent Nuclear Fuel Cask

Here, we report nuclear science and engineering is a field increasingly dominated by computational studies resulting from increasingly powerful computational tools. As a result, analytical studies, which previously pioneered nuclear engineering, are increasingly viewed as secondary or unnecessary. However, analytical solutions to reduced-fidelity models can provide important information concerning the underlying physics of a problem and aid in guiding computational studies. Similarly, there is increased interest in sensitivity analysis studies. These studies commonly use computational tools. However, providing a complementary sensitivity study of relevant analytical models can lead to a deeper analysis of a problem. This work provides the analytical sensitivity analysis of the one-dimensional (1D) cylindrical mono-energetic neutron diffusion equation using the forward sensitivity analysis procedure (FSAP) developed by Cacuci. Further, these results are applied to a reduced-fidelity model of a spent nuclear fuel cask, demonstrating how computational analysis might be improved with a complementary analytic sensitivity analysis.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2024

On Compatible Transfer Operators in Nonsymmetric Algebraic Multigrid

The standard goal for an effective algebraic multigrid (AMG) algorithm is to develop relaxation and coarse-grid correction schemes that attenuate complementary error modes. In the nonsymmetric setting, coarse-grid correction Π will almost certainly be nonorthogonal (and divergent) in any known standard product, meaning ∥Π∥ > 1. This introduces a new consideration, that one wants coarse-grid correction to be as close to orthogonal as possible, in an appropriate norm. In addition, due to nonorthogonality, Π may actually amplify certain error modes that are in the range of interpolation. Relaxation must then not only be complementary to interpolation, but also rapidly eliminate any error amplified by the nonorthogonal correction, or the algorithm may diverge. Here this paper develops analytic formulae on how to construct “compatible” transfer operators in nonsymmetric AMG such that ∥Π∥ = 1 in some standard matrix-induced norm. Discussion is provided on different options for the norm in the nonsymmetric setting, the relation between “ideal” transfer operators in different norms, and insight into the convergence of nonsymmetric reduction-based AMG.

97 MATHEMATICS AND COMPUTING↗