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At least 541 records · Page 30
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Linear Combination of Atomic Dipoles to Calculate the Bond and Molecular Dipole Moments of Molecules and Molecular Liquids

Here we report a linear combination of atomic dipole (LCAD) method for calculating the bond dipole moments of molecules. We show that the LCAD method reproduces the known molecular dipole moments of small to large molecules with a small error with respect to experimental and benchmark ab initio calculations, and molecular dipole distributions of bulk water that agree with maximally localized Wannier functions. The bond dipole moments derived from LCAD are also chemically interpretable in terms of the trend in bond ionicity in going from neutral to charged molecules. Moreover, the LCAD method accurately captures the influence of electric fields, supported by the correct trend in the change of the dipole moment under a uniform external electric field. The better grounding of bond dipole calculations indicates that it should also serve as a useful approach to bond dipole-field models used in catalysis or to reconstruct the small dipole of a H-terminated graphene flake.

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

Hydrolysis-Induced Morphology Evolution of Linear and Bottlebrush Block Copolymers in Thin Films with Acid Vapor or Photoacid Generators

The self-assembly of high-χ low-N block copolymers (BCPs) can give patterns with sub-10 nm full pitch, serving as a promising alternative to photolithographic methods. Here, in this work, we synthesized poly(solketal methacrylate)-block-polystyrene copolymers, PSM-b-PS, with various volume ratios of the two blocks. After hydrolysis of the PSM block into poly(glycerol monomethacrylate), PGM, the BCPs had both lamellar and cylindrical microdomain morphologies in the bulk phase and in thin films. In addition to our previously developed solid-state hydrolysis strategy involving trifluoroacetic acid vapor, we developed a new photoinduced solid-state hydrolysis using photoacid generators, PAGs, embedded within the polymer films. After exposure to UV followed by a postexposure baking or solvent vapor annealing, the BCPs transitioned from the disordered, phase-mixed state into laterally ordered cylindrical patterns. In comparison to linear BCPs that rely on a random copolymer layer to modify interfacial interactions with the substrate to promote an orientation of the microdomains normal to the interface, we found that the microdomains in bottlebrush multiblock copolymers oriented normal to the interface absent substrate modification due to the chain architecture.

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

Mechanically Accelerated Depolymerization of Entangled Linear Polymer Melts

Mechanical forces can enhance the chemical depolymerization of synthetic polymers when shear flow accelerates chain scission. To quantify the extent of mechanically-accelerated scission, the effect of simple shear flow (duration and strength) with low Weissenberg and Deborah numbers was investigated by considering the impact of applied work in both simple shear and shear dominated mixed flows. Hydrogenated polyisoprene was chosen as a model linear, entangled system. The conditions (strain amplitude, frequency, and shearing time) necessary to increase chain scission were assessed in the rubbery melt. Shear flow accelerated chain scission at higher temperatures, suggesting an activated process. Isothermal scission versus work curves were superposed by applying shift factors a T,S , whose Arrhenius-like temperature dependence gave an apparent activation energy for chain scission of ~ 110 kJ/mol, which is likely a combination of the activation energy of viscosity and bond energy. This work provides a base for quantifying the impact of shear on depolymerization of polymer melts and highlight the connection between viscous dissipation and scission chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Chemically Recyclable Analogs of Styrene–Butadiene Copolymers Enabling Perfectly Linear Ethylene–Styrene Materials with Random Phenyl Distribution

Copolymerization of cyclopentene (CP) and 4-phenylcyclopentene (4PCP) at a full range of comonomer feed ratios is reported using Ru-based ring-opening metathesis polymerization (ROMP) yielding homogeneous copolymers analogous to poly(styrene-ran-1,4-butadiene) and poly(ethylene-ran-styrene) copolymers following hydrogenation under mild conditions. In all cases, total monomer conversions of 86%–92% yielded copolymers with compositions within 4% of monomer feeds. Analysis of equilibrium copolymerization thermodynamics, rarely performed on two cycloolefin monomers with low ring strain energies, provides rational design strategies for negotiating two monomers with different equilibrium monomer concentrations. Inverse-gated decoupled 13 C NMR analysis of dyad sequences on the resulting copolymer microstructures concludes a near-random distribution of comonomer units. The copolymers produced from ROMP have number-average molar masses up to 60 kg mol –1 , moderate dispersities (1.5 ± 0.1), and high trans olefin content (86% ± 2%) while glass-transitions temperatures follow the Fox equation and span the full range between homopolymer extremities of PCP (−96 °C) and P4PCP (17 °C). Unlike most prevulcanized elastomers, these materials undergo facile chemical recycling to monomer, producing complete ring-closing metathesis depolymerization (RCMD) of the polymer back to the CP comonomers. Quantitative olefin hydrogenation produced perfectly linear polyethylene with 4%–16% of the backbone carbons containing a phenyl pendant, analogous to ES copolymers with up to 71.5% w/w styrene units but with random distribution of the aromatic pendants. Thermal properties of these materials are discussed, which span from semicrystalline to amorphous, and with T g values notably less than the reported ES copolymer analogs at similar compositions.

animal feed↗
DOE OSTI2021

Observation of Giant Optical Linear Dichroism in a Zigzag Antiferromagnet FePS 3

Direct optical probing of the antiferromagnetic order parameter in atomically thin samples is challenging, for example, via magneto-optical spectroscopy, due to the lack of net magnetization. Here, we report zigzag-antiferromagnetism (AFM) induced optical linear dichroism (LD) in layered transition-metal thiophosphate FePS3 down to the monolayer limit. The observed LD is giant despite having the optical wave vector parallel to the Neel vector. The LD is at least one order of magnitude larger than those reported in other antiferromagnetic systems, where the optical wave vector is orthogonal to the Neel vector. The large LD enables the probe of 60 degrees orientated zigzag-AFM domains. The optical anisotropy in FePS 3 originates from an electronic anisotropy associated with the zigzag direction of the AFM order and is independent of the spin-pointing direction. Furthermore, our findings point to a new optical approach for the investigation and control of zigzag or stripe magnetic order in strongly correlated systems.

2D magnet↗
DOE OSTI2023

Carbon Dioxide Insertion into Rhenium Hydrides as a Probe for the Impact of Solvent on Linear Free Energy Relationships between Thermodynamic and Kinetic Hydricity

The kinetics of CO 2 insertion into electronically different Re( R bpy)(CO) 3 H ( R bpy = 4,4'-R-2,2'- bipyridine; R = OMe, t Bu, Me, H, Br, COOMe, CF 3 ) complexes to form Re( R bpy)(CO) 3 {OC(H)O} compounds were determined in acetone, dimethylacetamide (DMAc), dimethylformamide (DMF), dimethylsulfoxide (DMSO), and 3-methoxypropionitrile (3-MPN) and compared with previous data in acetonitrile (MeCN). The rates of CO 2 insertion for any one complex of the type Re(Rbpy)(CO) 3 H in different solvents correlates with the Dimroth-Reichardt (E T (30)) solvent parameter. Hammett plots in each solvent indicate that insertion reactions are faster for bpy ligands with electron-donating groups. There is, however, no correlation between the slope of the Hammett plot in different solvents and any common solvent parameter. Similarly, the enthalpies and entropies of activation and kinetic isotope effects associated with CO 2 insertion into Re(bpy)(CO) 3 H in different solvents do not correlate with any common solvent parameters. Theoretical calculations were used to determine the relative thermodynamic hydricities of Re( R bpy)(CO) 3 H type complexes in MeCN, acetone, DMF, and DMSO and in each solvent complexes with more electron-donating substituents on the bpy ligand are stronger hydride donors. Linear Free Energy Relationships (LFERs) between calculated thermodynamic and experimental kinetic hydricity, as measured through CO 2 insertion reactions, were observed in MeCN, acetone, DMF, and DMSO. Furthermore, the slopes of the LFERs correlate with the dielectric constant of the solvent. Overall, this work provides fundamental information about the thermodynamics and kinetics of hydride transfer reactions in different solvents, which is valuable for catalyst design.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Effect of Extended Aging and Oxidation on Linear Poly(propylenimine)-Mesoporous Silica Composites for CO 2 Capture from Simulated Air and Flue Gas Streams

Physical aging or degradation of amine-containing polymers and supported amine adsorbents is a critical issue that could limit practical application of such materials for CO 2 capture. However, to date, there is a scarcity of studies that evaluate the long-term stability of amine-based sorbents without the exclusive use of accelerated aging tests. Here, we demonstrate that extended aging (~2 years) of linear poly(propylenimine) (LPPI) confined in mesoporous silica (SBA-15) supports does not drastically impact the CO 2 adsorption performance under simulated flue gas (10% CO 2 ) and direct air capture (DAC, 400 ppm CO 2 ) conditions, although the behavior of the aged sorbents and polymers in the two CO 2 concentration regimes differs. Sorbents made with aged LPPI had modestly decreased CO 2 uptake performance (<~20% lower) compared to the fresh polymers, with overall good CO 2 cycling performance. The data indicate that only slow degradation occurs under the deployed ambient storage conditions. Even after extended aging, the LPPI-based sorbents preserved their ability to display stable temperature-swing cycling performance. In parallel, the impact of blending LPPI polymers of different number-average molecular weights, M n , is evaluated, seeking to understand its impact on adsorbent performance. We find that the results demonstrate that blends of two M n aged LPPI give similar CO 2 adsorption performance to adsorbents made from a single M n LPPI, suggesting that molecular weight will not negatively impact adsorbent performance in the studied M n range. After an accelerated oxidation experiment, the aged LPPI sorbents retained a larger portion of the samples’ original performance when cycling under simulated flue gas conditions than under DAC conditions. However, in each case, the oxidized sorbents could be cycled repeatedly with consistent uptake performance. Overall, these first of their kind extended aging tests suggest that LPPI-based amine adsorbents offer promise for long term, stable use in carbon capture applications.

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

Increasing Branching and Functionalization Decreases Crystallinity and Crystallization Rate in Linear EVOH

Here, we report the crystallization behavior of a linear poly(ethylene-co-vinyl alcohol) (LEVOH) under isothermal crystallization as a function of both OH incorporation and undercooling, and compare the results to conventional branched EVOH. This LEVOH is synthesized by post-polymerization functionalization of polycyclooctene, and it exhibits a half-crystallization time and primary crystallization rate nearly an order of magnitude faster than branched EVOH at ~ 6 mol% OH incorporation. While the LEVOH obtains approximately twice the extent of crystallization compared to the branched equivalent, as OH incorporation increases, the crystallization kinetics and crystallinity of LEVOH decrease. The crystal structure of LEVOH is orthorhombic at low functionalization (≤ 11 mol% OH), a mixture of orthorhombic and hexagonal at moderate functionalization (17 - 21 mol%), and hexagonal at high functionalization (23 %). The LEVOH crystallizes into plates, with crystallite widths ~ 20 - 60 times the crystallite thickness. Ultimately, we show LEVOH crystallizes faster and to a greater extent than commercial branched EVOH, a potential advantage of post-polymerization functionalization as part of polymer-to-polymer upcycling.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Full Exclusion of Branched Hexanes from Their Linear Isomer by a Robust Aluminum Metal–Organic Framework with Tailored Pore Structure

High-efficiency separation of hexane isomers through selective molecular exclusion represents an important yet challenging task in the petrochemical industry. It has stringent requirements on the adsorbents' pore shape and dimensions. Here we report the complete exclusion of branched hexanes from their linear isomer by an aluminum metal-organic framework, CAU-21-ODB (ODB = 4,4'-oxydibenzoate) with high stability. The unique gourd-shaped channels with suitable pore aperture lead to substantial uptake of nHEX (141 mg/g at 30 °C) but negligible adsorption of its branched isomers under identical conditions. Furthermore, the capability of CAU-21-ODB for the separation of hexane isomers has been verified by multicomponent breakthrough experiments. DFT calculations further confirm the size-exclusion based separation mechanism.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Exploring Causal Physical Mechanisms via Non-Gaussian Linear Models and Deep Kernel Learning: Applications for Ferroelectric Domain Structures

Rapid emergence of multimodal imaging in scanning probe, electron, and optical microscopies has brought forth the challenge of understanding the information contained in these complex data sets, targeting the intrinsic correlations between different channels, and further exploring the underpinning causal physical mechanisms. Here, we develop such an analysis framework for Piezoresponse Force Microscopy. We argue that under certain conditions, we can bootstrap experimental observations with the prior knowledge of materials structure to get information on certain nonobserved properties, and demonstrate linear causal analysis for PFM observables. We further demonstrate that the strength of individual causal links between complex descriptors can be ascertained using the deep kernel learning (DKL) model. In this DKL analysis, we use the prior information on domain structure within the image to predict the physical properties. This analysis demonstrates the correlative relationships between morphology, piezoresponse, elastic property, etc., at nanoscale. The prediction of morphology and other physical parameters illustrates a mutual interaction between surface condition and physical properties in ferroelectric materials. Overall, this analysis is universal and can be extended to explore the correlative relationships of other multichannel data sets, and allow for high-fidelity reconstruction of underpinning functionalities and physical mechanisms.

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

Tunable Semiconducting Behavior and Linear-Nonlinear Optical Properties of Ag–Sn Dual-Doped Nanocrystalline CdO Thin Films for Optoelectronics

Semiconductor-based thin films have a great impact on determining the anticipated optoelectronic device construction and the advancement of cutting-edge applications. Herein, Ag and Sn dual-doped nanocrystalline transparent conducting CdO thin films were prepared on glass substrates using a cost-effective spray coating method, and their structural, morphological, optical, and semiconducting behaviors were investigated. The successful incorporation of Ag and Sn resulted in the polycrystalline nature of the deposited films without the additional peaks, as verified by X-ray diffraction (XRD) analysis. The XRD report also revealed the enhanced crystallinity (65%) at the higher doping level (3 wt % Ag and Sn-doped CdO film). All the deposited CdO films exhibited homogeneous, spherical, or round-shaped grains, with agglomeration revealed by scanning electron microscopy analysis. UV–visible spectroscopy was utilized to determine the linear and nonlinear optical properties of the deposited CdO thin films, and a reduction in the band gap from 3.891 to 3.772 eV was observed. A significant enhancement in the first- and third-order nonlinear susceptibility and nonlinear refractive index of the doped CdO films was also observed with increasing doping concentration. Hall effect data were collected at room temperature to investigate the electrical properties of all of the CdO films. The charge carrier concentration of CdO thin films was increased from 142.08 × 10 18 to 169.10 × 10 18 cm –3 , and the highest conductivity was found to be 192 s/cm on doping 3 wt % Ag–Sn. All the CdO thin films exhibited n-type conductivity, while an incredible n-type to p-type charge carrier transition was noticed at a higher doping level (3 wt % Ag–Sn). The findings of the current work are expected to advance the synthesis of semiconductor thin films through cost-effective spray coating methods for optoelectronic device applications.

deposition↗
DOE OSTI2022

Tolerance Factor for Stabilizing 3D Hybrid Halide Perovskitoids Using Linear Diammonium Cations

Three-dimensional (3D) halide perovskites have attracted enormous research interest, but the choice of the A-site cations is limited by the Goldschmidt tolerance factor. In order to accommodate cations that lie outside the acceptable range of the tolerance factor, low-dimensional structures usually form. To maintain the favorable 3D connection, the links among the metal-halide octahedra need to be rearranged to fit the large cations. This can result in a departure from the proper corner-sharing perovskite architectures and lead to distinctly different perovskitoid motifs with edge- and face-sharing. In this work, we report four new 3D bromide perovskitoids incorporating linear organic diammonium cations, A'Pb 2 Br 6 (A' is a +2 cation). We propose a rule that can guide the further expansion of this class of compounds, analogous to the notion of Goldschmidt tolerance factor widely adopted for 3D AMX 3 perovskites. The fundamental building blocks in A'Pb 2 Br 6 consist of two edge-shared octahedra, which are then connected by corner-sharing to form a 3D network. Different compounds adopt different structural motifs, which can be transformed from one to another by symmetry operations. Electronic structure calculations suggest that they are direct bandgap semiconductors, with relatively large band dispersions created by octahedra connected by corner-sharing. They exhibit similar electronic band structures and dynamic lattice characteristics to the regular 3D AMX 3 perovskites. Structures with smaller Pb–Br–Pb angles and larger octahedra distortion exhibit broad photoluminescence at room temperature. Furthermore, the emerging structure–property relationships in these 3D perovskitoids set the foundation for designing and investigating these compounds for a variety of optoelectronic applications.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Cyclic versus Linear Alkylammonium Cations: Preventing Phase Transitions at Operational Temperatures in 2D Perovskites

Two-dimensional lead halide perovskites offer numerous attractive features for optoelectronics owing to their soft, deformable lattices and high degree of chemical tunability. While alteration of the metal and halide ions gives rise to significant modification of the bandgap energy, the organic spacer cations offer in-roads to tuning phase behavior and more subtle functionalities in ways that remain to be understood. Here, we study six variations of 2D perovskites changing only the organic spacer cations and demonstrate that these components intrinsically impact material response in important ways such as altering crystallographic structure, temperature-induced phase transitions, and photoluminescence emission. Two-dimensional perovskites containing commonly utilized aliphatic linear spacers, such as butylammonium, undergo phase transitions near room temperature. These transitions and temperature changes induce spacer-dependent variations in the emission spectra. Conversely, 2D perovskites comprising cyclic aliphatic spacers, such as cyclobutylammonium, are found to lack first-order phase transitions. These cyclic molecules are more sterically hindered within the crystal lattice, leading to temperature-induced contraction or expansion along certain crystallographic planes but no other significant thermal effects; additionally, they undergo changes in their emission spectra that cannot be explained by simple thermal expansion. Finally, given the similarities in the dielectric and chemical makeup of this set of six alkylammonium molecules, these results are unexpected and suggest a large structural and thermal phase space via spacer manipulation that could lead to improved 2D perovskite functionalization.

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

Chemical Framework to Design Linear-like Relaxors toward Capacitive Energy Storage

ABO 3 -type perovskite relaxor ferroelectrics (RFEs) have emerged as the preferred option for dielectric capacitive energy storage. However, the compositional design of RFEs with high energy density and efficiency poses significant challenges owing to the vast compositional space and the absence of general rules. Here, we present an atomic-level chemical framework that captures inherent characteristics in terms of radius and ferroelectric activity of ions. By categorizing A/B-site ions as host framework, rattling, ferroelectrically active, and blocking ions and assembling these four types of ions with specific criteria, linear-like relaxors with weak locally correlated and highly extendable unit-cell polarization vectors can be constructed. As example, we demonstrate two new compositions of Bi 0.5 K 0.5 TiO 3- based and BaTiO 3- based relaxors, showing extremely high recoverable energy densities of 17.3 and 12.1 J cm –3 , respectively, both with a high efficiency of about 90%. Further, the role of different types of ions in forming heterogeneous polar structures is identified through element-specific local structure analysis using neutron total scattering combined with reverse Monte Carlo modeling. Further, our work not only opens up new avenues toward rational compositional design of high energy storage performance lead-free RFEs but also sheds light on atomic-level manipulation of functional properties in compositionally complex ferroelectrics.

25 ENERGY STORAGE↗
DOE OSTI2026

Mechanism of O 2 /NO-Promoted Oxidative C–C Bond Cleavage in Linear Alkanes

Selective oxidation of alkanes to oxygenated products remains a fundamental challenge, particularly if the goal is to promote C−C bond cleavage while minimizing formation of CO 2 . Oxidation conditions that use O 2 and nitrogen oxides (NO x ) have been shown to be very effective in promoting radical-mediated functionalization and oxidative carbon−carbon cleavage in saturated hydrocarbon polymers, such as polyethylene. Here, we investigate the mechanism of O 2 /NO-mediated oxidation of ndecane as a prototypical linear alkane substrate. These reactions enable identification and quantification of reactive intermediates, including nitrites, nitrates, alcohols, and ketones. Under the reaction conditions, these species convert into common ketone intermediates that evolve into α-diketones and other α-functionalized ketones, which undergo further conversion into carboxylic acids. Infrared (IR) spectroscopy indicates that HDPE oxidation proceeds through similar key intermediates. Together, these findings establish a mechanistic framework for NO x -mediated alkane oxidation and provide a foundation for the development of broadly applicable oxidative transformations.

Anions↗
DOE OSTI2025

Toward an Understanding of Linear Scaling Relations through Energy Decomposition Analysis

The discovery of linear scaling relations has fundamentally changed the field of heterogeneous catalysis. The scaling relations have been rationalized based on the d-band theory, specifically a separation of sp and d electron contributions to adsorption energies. Within the framework of energy decomposition analysis, a full understanding of such a separation would require one to further break down the adsorption energy into distinct energy components such as electrostatics, polarization, charge transfer, and van der Waals interactions, and to examine the sp and d contributions to each of them. As a step in this direction, we analyzed the interaction energy between CH x (x = 1–4) adsorbates and fcc(100) transition metal surfaces (M = Cu, Ag, Au, Rh, and Pt), with the surfaces represented both as slabs in plane-wave density functional theory (pw-DFT) calculations and as atomic clusters in atomic-orbital basis density functional theory (ao-DFT) calculations. Through an absolutely localized molecular orbital (ALMO) based energy decomposition analysis of the ao-DFT adsorption energy, each of the interaction energy components (electrostatics, polarization, van der Waals, and charge transfer) was found to follow its own scaling relations, with an intricate interplay among these energy components yielding the overall scaling relations for the total adsorption energies. Using the recently introduced ALMO-based polarization and charge-transfer analysis schemes, we further dissected polarization into metal surface and adsorbate contributions, and charge transfer into metal → adsorbate and adsorbate → metal contributions. The contributions from the sp and d electrons of the metal to these terms were further quantified, and the dominant role of the metal d electrons was reaffirmed. These results shed light on how CHx adsorbates interact with metal surfaces and further reveal the physical origin of the scaling relations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Does Regional Hydroclimate Change Scale Linearly With Global Warming?

Many aspects of climate change scale linearly with global warming. However, nonlinear changes are possible, especially in the context of hydroclimate, and under emissions scenarios with stabilized global temperature, as aspired to by current climate targets. In CMIP5 and 6, a progressively larger land area shows nonlinear changes as a function of global warming when considering precipitation, evaporation, and soil moisture, with the latter showing nonlinearity over ~50% of global land. Here, using ensemble simulations with the Community Earth System Model 1, in which individual forcing factors are held constant, we illustrate how nonadditive responses to anthropogenic greenhouse gases and industrial and fire-related aerosols can yield complex soil moisture changes in certain regions. This complexity contributes to uncertainty in regional soil moisture projections and suggests that the timing of, as well as model response uncertainty to, future aerosol reductions will have significant impacts on regional hydroclimate change as global temperatures stabilize.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

A Comparison of Linear Solvers for Resolving Flow in Three-Dimensional Discrete Fracture Networks

We compare various methods for resolving steady flow within three-dimensional discrete fracture networks, including direct methods, Krylov subspace methods with and without preconditioning, and multi-grid methods. We compared the performance of the methods based on compute times and scaling of the solution as a function of the number of grid nodes and log-variance of the hydraulic aperture. The methods are applied to three test cases: (a) variable density of networks with a truncated power-law distribution of fracture lengths, (b) a fixed network composed of monodisperse fracture sizes but varied permeability/aperture heterogeneity, (c) and a network based on field site in Nevada, US. We chose these cases to allow us to study the impact of the mesh size and flow properties, as well as to demonstrate our conclusions on a large-scale, realistic problem (more than 40 million mesh nodes). A direct solution using Cholesky factorization outperformed other methods for every example but was closely followed in performance by some algebraic multigrid (AMG) preconditioned Krylov subspace methods. Among the Krylov methods, conjugate gradients (CG) with an AMG preconditioner performs the best. Generally, Cholesky factorization is recommended, but CG with an AMG preconditioner may be suitable for very large problems beyond 40 million nodes where the entire linear system cannot reside in memory.

58 GEOSCIENCES↗