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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Validation of Local Structural Loads Computed by OpenFAST Against Measurements From the FOCAL Experimental Campaign

This work presents the validation of the local structural load modeling capability in OpenFAST for floating substructures based on data from the FOCAL experimental campaign. Previously, OpenFAST could only represent the floating substructure as a rigid body, and though this approach can model the global response of the floater in most cases, it is not able to capture the structural loads within the floater's individual members. Consideration of local substructure loads is important for some floating designs, because the pursuit of cost reduction often results in lighter and more flexible structures. To address this limitation, the HydroDyn (hydrodynamics) and SubDyn (substructure dynamics) modules of OpenFAST have been recently extended to account for the flexibility of floating substructures. To validate this new capability, we compare the results obtained by OpenFAST with data measured during the FOCAL experimental campaign, which analyzed a 1:70 scale performance-matched model of the IEA 15-MW reference turbine atop a modified University of Maine VolturnUS-S semisubmersible in a wave basin under the action of both wind and waves. For the purposes of the present work, the most important feature of the experiment is the presence of load cells at the root of each pontoon, and our objective is to assess how well those loads are reproduced by OpenFAST. To model the distributed hydrodynamic and hydrostatic loads along the floating substructure, we adopt a strip-theory approach based on the Morison equation, and we discuss the impact of different hydrodynamic modeling options (wave stretching, MacCamy-Fuchs correction, and second-order wave kinematics) on both motions and loads. For simplicity, we focus on wave-only conditions, both regular and irregular. The results demonstrate good overall agreement for the loads at the root of the pontoons for the waves analyzed in this work, especially given the assumptions and simplifications inherent to a simple strip-theory model.

floating offshore wind turbine↗
DOE OSTI2021

Structural dynamics modeling of spent nuclear fuel during hypothetical package drop events

The response of spent nuclear fuel (SNF) to hypothetical package drop events is of particular interest in the scope of spent fuel storage and transportation because of the mechanical shock encountered in such scenarios. Previous testing and modeling by the U.S. Department of Energy has demonstrated that the shock and vibration environment of normal shipping and handling conditions (excluding package drop events) is relatively benign and does not challenge the integrity of spent nuclear fuel. Cask drop events are worth considering because SNF packages are required to withstand free drops onto unyielding surfaces as part of their licensing basis. The acceleration experienced during drop events can be orders of magnitude higher, and thus more advanced models are needed to encompass potential nonlinear behavior of the fuel, such as spacer grid buckling and rod-to-rod impact. This work describes a number of finite element models developed to calculate the response of spent nuclear fuel to various hypothetical drop events that have been validated by package and fuel assembly drop tests conducted in the last decade. Sensitivity of the model response to factors such as package drop orientation, secondary impacts, and irradiated material properties as well as their potential impacts to fuel cladding integrity, was also investigated. Cask drops are not expected as a regular occurrence during SNF transportation, but this work helps raise the understanding of SNF mechanical loads to the point of consistency with the package design requirements.

Kadooka, Kevin↗
DOE OSTI2021

Transition to Online Cable Insulation Condition Monitoring

Nuclear power plant cables were originally qualified for 40 year life and generally have not required specific test verification to assure service availability through the initial plant qualification period. However, license renewals to 60 and 80 years of operation require a cable aging management program that depends on some form of test and verification to assure fitness for service. Environmental stress (temperature, radiation, chemicals, water, and mechanical) varies dramatically within a nuclear power plant and, in some cases, cables have degraded and required repair or replacement before their qualified end-of-life period. In other cases, cable conditions have been mild and dependable cable performance confirmed to extend well beyond the initial qualified life. Most offline performance-based testing requires cables to be de-coupled and de-energized for specially trained technicians to perform testing. These offline tests constitute an expensive operational burden that limits the economic viability of nuclear power plants. Although initial investment may be higher, new online test practices are emerging as options or complements to offline testing that avoid or minimize the regularly scheduled offline test burden. These online methods include electrical and fiber-optic partial discharge measurement, spread spectrum time or frequency domain reflectometry, distributed temperature profile measurements, and local interdigital capacitance measurement of insulation characteristics. Introduction of these methods must be supported by research to confirm efficacy plus either publicly financed or market driven investment to support the start-up expense of cost-effective instrumentation to monitor cable condition and assure reliable operation. This work summarizes various online cable assessment technologies plus introduces a new cable motor test bed to assess some of these technologies in a controlled test environment.

Glass, Samuel W.↗
DOE OSTI2021

Shake loss intensities in x-ray photoelectron spectroscopy: Theory, experiment, and atomic composition accuracy for MgO and related compounds

The relative intensities of XPS core levels, scaled by their photoionization cross sections, are regularly used to determine sample atomic composition. Cross sections, however, give the intensity to all possible final states for the core ionizations, not just to the main peak. This includes all intrinsic satellite structure (shake states and, for open shell systems, the different ionic multiplets). In practice, for solids, this is usually experimentally impossible to determine accurately because such a satellite structure sits on the inelastically scattered electron background and cannot be easily separated. Therefore, usually, only the intensity of the main peak is used. This limits the ultimate possible accuracy of XPS composition determination. The purpose of the present paper is to examine the contributions that a theoretical analysis of losses of intensity can make to improve quantitation. For an MgO single crystal, we show that the correct stoichiometry of 1:1 can be recovered using the theoretical analysis of the experimental MgO peak ratio intensities. For materials with a sufficient bandgap for the XPS main peaks to be separated from the scattered background, the intensity of main peaks can often be accurately determined. Thus, if one uses theory to calculate that fraction of the total intensity lost from a main peak into all its satellite structure, the intensity of just main peaks could then be used to more accurately determine relative atom % composition. This work tests this approach using a single crystal MgO (50% Mg, 50% O) standard. Ab initio electronic structure theory of representative MgO clusters is used to determine Hartree–Fock wave functions for the ground state and final ionized states corresponding to the main Mg 2p and O1s XPS peaks of the oxide. The sudden approximation, SA, is used to determine the fractional losses from these main peaks to shake satellites, which is found to be greater for O1s than Mg2p. This results in predicted “apparent composition” for stoichiometric MgO of 55.2% Mg, 44.8% O instead of the true 50% Mg, 50% O. Equivalent theory for CaO results in a predicted apparent Ca value of 53.4%. Experimentally, using Mg2s or 2p intensity ratio to O1s, we find values between 52.2% and 56.0% Mg using two crystals and four different instrument electron pass energies. The average value of the measurements is 54.5% Mg when corrected for the presence of an adventitious carbon overlayer and slight surface hydroxide. Though this agreement with theory may be somewhat fortuitous, given the potential experimental errors, which are fully discussed, it is similar to that in our earlier study on LiF. We also present preliminary experimental data on Mg(OH) 2 and MgSO 4 , which show a similar trend of apparently higher than 50% Mg, but we have no theory values. We are not yet able to experimentally test for validation of the difference between apparent composition for MgO (55.2% Mg) and CaO (53.4% Ca), owing to significant carbonate formation at the surface of the single crystal CaO. Here, an important conclusion is that the theoretical determination of shake losses, obtained with ab initio wavefunctions and the SA, is likely to be a useful way to calibrate the accuracy and reliability of compositions obtained from XPS intensities and merits further study.

47 OTHER INSTRUMENTATION↗
DOE OSTI2022

Atomic-resolution lithography with an on-chip scanning tunneling microscope

In this work, atomic-resolution lithography with a Microelectromechanical-System (MEMS) based Scanning Tunneling Microscope (STM) is demonstrated for the first time. The microscope consists of a commercial UltraHigh-Vacuum (UHV) STM whose regular tip is replaced with a 1-Degree-of-Freedom (1-DOF) MEMS nanopositioner. This results in a hybrid STM system where XY-plane motions are provided by the piezotube of the original system and Z-axis motion by the MEMS with a higher bandwidth. Sharp tips made of Pt or W are added to the MEMS devices with postfabrication techniques. With this hybrid system, STM-based lithography is demonstrated on an H-passivated Si (100)-2×1 sample under UHV condition. Results prove the capability of the hybrid STM system for atomic-scale lithography. This capability, paired with the small footprint of the MEMS device, makes this approach a candidate for building a high-throughput parallel STM lithography platform by incorporating an array of 1-DOF MEMS devices that perform lithography in parallel.

Alipour, Afshin (ORCID:0000000263252067)↗
DOE OSTI2025

Thermodynamics of gallium-stabilized delta-plutonium: A high-temperature drop calorimetry study

Throughout the Cold War (1947–1991), both the United States and the former Soviet Union independently derived a phase diagram for the Pu-Ga system that has different implications on Pu phase stability. In the phase diagram produced by the United States, the Pu δ-phase is thermodynamically stable at room temperatures when Ga content is between 2 and 9 at. %. The diagram produced by the Soviet Union shows the δ-phase undergoing an eutectoid decomposition into the α-Pu + α-Pu 3 Ga at 7.9 at. % Ga and 370 K. This would suggest that Ga-stabilized δ-Pu is metastable with respect to α-Pu + α-Pu 3 Ga at 298 K. To investigate this, and the thermodynamic behavior of Ga in the FCC lattice of δ-Pu, we have utilized high-temperature drop calorimetry to study the enthalpy of formation of two δ-Pu 1−x Ga x compositions. In doing so, mixing models (regular and subregular) were developed to understand the thermodynamic behavior of Ga in the FCC lattice of δ-Pu and found a strong departure from ideal conditions, which suggests Ga ordering in the FCC lattice of δ-Pu. Overall, it was found that δ-Pu 1−x Ga x is enthalpically metastable with respect to α-Pu + Pu 3 Ga at 298 K.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Static metrology of the meter-scale deformable heliostat

This paper describes a heliostat metrology system which is developed based on deflectometry, utilizing a static perforated panel instead of conventional dynamic monitor displays to provide incident rays. The developed method is named static screen deflectometry (SSD). This robust and scalable method is especially valuable for outdoor tests of large reflectors used in concentrating solar-thermal power (CSP) systems. The developed method has been successfully demonstrated on a 2.4 𝑚 × 3.3 𝑚 float glass deformable reflector bent to focus sunlight at 113 𝑚 distance throughout a day. From images obtained from a camera at 50𝑚 distance, the reflector surface was measured to an accuracy of less than 1 𝑚𝑟𝑎𝑑 rms slope error in the full test scope.

14 SOLAR ENERGY↗
DOE OSTI2022

High grain boundary recombination velocity in polycrystalline metal halide perovskites

Understanding carrier recombination processes in metal halide perovskites is fundamentally important to further improving the efficiency of perovskite solar cells, yet the accurate recombination velocity at grain boundaries (GBs) has not been determined. Here, we report the determination of carrier recombination velocities at GBs (S GB ) of polycrystalline perovskites by mapping the transient photoluminescence pattern change induced by the nonradiative recombination of carriers at GBs. Charge recombination at GBs is revealed to be even stronger than at surfaces of unpassivated films, with average S GB reaching 2200 to 3300 cm/s. Regular surface treatments do not passivate GBs because of the absence of contact at GBs. We find a surface treatment using tributyl(methyl)phosphonium dimethyl phosphate that can penetrate into GBs by partially dissolving GBs and converting it into one-dimensional perovskites. It reduces the average S GB by four times, with the lowest SGB of 410 cm/s, which is comparable to surface recombination velocities after passivation.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Time-resolved atomic-resolution Brownian tomography of single nanocrystals reveals size-dependent dynamics

Atomic-resolution structure identification of nanocrystals by graphene liquid cell electron microscopy (GLC-EM) has revealed that small, solubilized platinum nanocrystals consist of an ordered crystalline core surrounded by mobile surface atoms, which dissociate during oxidative etching, resulting in distinct temporal structural states. Requirements imposed by the 3D reconstruction algorithm limit the number of structural states that can be resolved. We introduce a regularized 3D reconstruction algorithm that exploits the redundancy inherent in the experimental data, allowing us to improve the time resolution. Our developments provide a comprehensive molecular picture at unprecedented spatial and temporal resolution of the nonlinear, linear, and fluctuating dynamic phenomena that single nanocrystals undergo during the GLC-EM experiment. We determined atomic structures of 66 temporal structural states, extracted from 15 time trajectories of individual nanocrystals. Large (478 to 698 atoms) and small (<300 atoms) nanocrystals show etching that preserves a stable core, whereas mid-sized (351 to 571 atoms) nanocrystals present dynamics that change the coordination of the core.

Meana-Pañeda, Rubén↗
DOE OSTI2024

Tools for genetic engineering and gene expression control in Novosphingobium aromaticivorans and Rhodobacter sphaeroides

ABSTRACT Alphaproteobacteria have a variety of cellular and metabolic features that provide important insights into biological systems and enable biotechnologies. For example, some species are capable of converting plant biomass into valuable biofuels and bioproducts that have the potential to contribute to the sustainable bioeconomy. Among the Alphaproteobacteria, Novosphingobium aromaticivorans , Rhodobacter sphaeroides , and Zymomonas mobilis show promise as organisms that can be engineered to convert extracted plant lignin or sugars into bioproducts and biofuels. Genetic manipulation of these bacteria is needed to introduce engineered pathways and modulate expression of native genes with the goal of enhancing bioproduct output. Although recent work has expanded the genetic toolkit for Z. mobilis , N. aromaticivorans and R. sphaeroides still need facile, reliable approaches to deliver genetic payloads to the genome and to control gene expression. Here, we expand the platform of genetic tools for N. aromaticivorans and R. sphaeroides to address these issues. We demonstrate that Tn 7 transposition is an effective approach for introducing engineered DNA into the chromosome of N. aromaticivorans and R. sphaeroides . We screen a synthetic promoter library to identify isopropyl β-D-1-thiogalactopyranoside-inducible promoters with regulated activity in both organisms (up to ~15-fold induction in N. aromaticivorans and ~5-fold induction in R. sphaeroides ). Combining Tn 7 integration with promoters from our library, we establish CRISPR (Clustered Regularly Interspaced Short Palindromic Repeats) interference systems for N. aromaticivorans and R. sphaeroides (up to ~10-fold knockdown in N. aromaticivorans and R. sphaeroides ) that can target essential genes and modulate engineered pathways. We anticipate that these systems will greatly facilitate both genetic engineering and gene function discovery efforts in these species and other Alphaproteobacteria. IMPORTANCE It is important to increase our understanding of the microbial world to improve health, agriculture, the environment, and biotechnology. For example, building a sustainable bioeconomy depends on the efficient conversion of plant material to valuable biofuels and bioproducts by microbes. One limitation in this conversion process is that microbes with otherwise promising properties for conversion are challenging to genetically engineer. Here we report genetic tools for Novosphingobium aromaticivorans and Rhodobacter sphaeroides that add to the burgeoning set of tools available for genome engineering and gene expression in Alphaproteobacteria. Our approaches allow straightforward insertion of engineered pathways into the N. aromaticivorans or R. sphaeroides genome and control of gene expression by inducing genes with synthetic promoters or repressing genes using CRISPR interference. These tools can be used in future work to gain additional insight into these and other Alphaproteobacteria and to aid in optimizing yield of biofuels and bioproducts.

Hall, Ashley N.↗
DOE OSTI2020

Estimating the Timing of Early Simian-Human Immunodeficiency Virus Infections: a Comparison between Poisson Fitter and BEAST

Many HIV prevention strategies are currently under consideration where it is highly informative to know the study participants’ times of infection. These can be estimated using viral sequence data sampled early in infection. However, there are several scenarios that, if not addressed, can skew timing estimates. These include multiple transmitted/founder (TF) viruses, APOBEC (apolipoprotein B mRNA editing enzyme, catalytic polypeptide-like)-mediated mutational enrichment, and recombination. Here, we suggest a pipeline to identify these problems and resolve the biases that they introduce. We then compare two modeling strategies to obtain timing estimates from sequence data. The first, Poisson Fitter (PF), is based on a Poisson model of random accumulation of mutations relative to the TF virus (or viruses) that established the infection. The second uses a coalescence-based phylogenetic strategy as implemented in BEAST. The comparison is based on timing predictions using plasma viral RNA (cDNA) sequence data from 28 simian-human immunodeficiency virus (SHIV)-infected animals for which the exact day of infection is known. In this particular setting, based on nucleotide sequences from samples obtained in early infection, the Poisson method yielded more accurate, more precise, and unbiased estimates for the time of infection than did the explored implementations of BEAST. The inference of the time of infection is a critical parameter in testing the efficacy of clinical interventions in protecting against HIV-1 infection. For example, in clinical trials evaluating the efficacy of passively delivered antibodies (Abs) for preventing infections, accurate time of infection data are essential for discerning levels of the Abs required to confer protection, given the natural Ab decay rate in the human body. In such trials, genetic sequences from early in the infection are regularly sampled from study participants, generally prior to immune selection, when the viral population is still expanding and genetic diversity is low. In this particular setting of early viral growth, the Poisson method is superior to the alternative approach based on coalescent methods. This approach can also be applied in human vaccine trials, where accurate estimates of infection times help ascertain if vaccine-elicited immune protection wanes over time.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

The genetics of aerotolerant growth in an alphaproteobacterium with a naturally reduced genome

Reduced genome bacteria are genetically simplified systems that facilitate biological study and industrial use. The free-living alphaproteobacterium Zymomonas mobilis has a naturally reduced genome containing fewer than 2,000 protein-coding genes. Despite its small genome, Z. mobilis thrives in diverse conditions including the presence or absence of atmospheric oxygen. However, insufficient characterization of essential and conditionally essential genes has limited broader adoption of Z. mobilis as a model alphaproteobacterium. Here, we use genome-scale CRISPRi-seq (clustered regularly interspaced short palindromic repeats interference sequencing) to systematically identify and characterize Z. mobilis genes that are conditionally essential for aerotolerant or anaerobic growth or are generally essential across both conditions. Comparative genomics revealed that the essentiality of most “generally essential” genes was shared between Z. mobilis and other Alphaproteobacteria, validating Z. mobilis as a reduced genome model. Among conditionally essential genes, we found that the DNA repair gene, recJ, was critical only for aerobic growth but reduced the mutation rate under both conditions. Further, we show that genes encoding the F1FO ATP synthase and Rhodobacter nitrogen fixation (Rnf) respiratory complex are required for the anaerobic growth of Z. mobilis. Combining CRISPRi partial knockdowns with metabolomics and membrane potential measurements, we determined that the ATP synthase generates membrane potential that is consumed by Rnf to power downstream processes. Rnf knockdown strains accumulated isoprenoid biosynthesis intermediates, suggesting a key role for Rnf in powering essential biosynthetic reactions. Our work establishes Z. mobilis as a streamlined model for alphaproteobacterial genetics, has broad implications in bacterial energy coupling, and informs Z. mobilis genome manipulation for optimized production of valuable isoprenoid-based bioproducts.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

DNA Viral Diversity, Abundance, and Functional Potential Vary across Grassland Soils with a Range of Historical Moisture Regimes

Soil viruses are abundant, but the influence of the environment and climate on soil viruses remains poorly understood. Here, we addressed this gap by comparing the diversity, abundance, lifestyle, and metabolic potential of DNA viruses in three grassland soils with historical differences in average annual precipitation, low in eastern Washington (WA), high in Iowa (IA), and intermediate in Kansas (KS). Bioinformatics analyses were applied to identify a total of 2,631 viral contigs, including 14 complete viral genomes from three deep metagenomes (1 terabase [Tb] each) that were sequenced from bulk soil DNA. An additional three replicate metagenomes (~0.5 Tb each) were obtained from each location for statistical comparisons. Identified viruses were primarily bacteriophages targeting dominant bacterial taxa. Both viral and host diversity were higher in soil with lower precipitation. Viral abundance was also significantly higher in the arid WA location than in IA and KS. More lysogenic markers and fewer clustered regularly interspaced short palindromic repeats (CRISPR) spacer hits were found in WA, reflecting more lysogeny in historically drier soil. More putative auxiliary metabolic genes (AMGs) were also detected in WA than in the historically wetter locations. The AMGs occurring in 18 pathways could potentially contribute to carbon metabolism and energy acquisition in their hosts. Structural equation modeling (SEM) suggested that historical precipitation influenced viral life cycle and selection of AMGs. The observed and predicted relationships between soil viruses and various biotic and abiotic variables have value for predicting viral responses to environmental change.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

CRISPRi functional genomics in bacteria and its application to medical and industrial research

SUMMARY Functional genomics is the use of systematic gene perturbation approaches to determine the contributions of genes under conditions of interest. Although functional genomic strategies have been used in bacteria for decades, recent studies have taken advantage of CRISPR (clustered regularly interspaced short palindromic repeats) technologies, such as CRISPRi (CRISPR interference), that are capable of precisely modulating expression of all genes in the genome. Here, we discuss and review the use of CRISPRi and related technologies for bacterial functional genomics. We discuss the strengths and weaknesses of CRISPRi as well as design considerations for CRISPRi genetic screens. We also review examples of how CRISPRi screens have defined relevant genetic targets for medical and industrial applications. Finally, we outline a few of the many possible directions that could be pursued using CRISPR-based functional genomics in bacteria. Our view is that the most exciting screens and discoveries are yet to come.

Microbiology↗
DOE OSTI2024

Improved Zika virus plaque assay using Vero/TMPRSS2 cell line

Plaque assay is the gold standard for the quantification of viable cytopathic viruses like Zika virus (ZIKV). Some strains of ZIKV produce plaques that are very difficult to accurately visualize and count on the commonly used Vero cell line. From data generated in our lab, we became curious if Vero/TMPRSS2 cells may be a better alternative; therefore, we compared the plaque forming units of two strains of ZIKV on Vero/TMPRSS2 cells to those produced by Vero cells. We also compared the virus stock titer generated on Vero/TMPRSS2 cells to that generated by the Vero cell line. Although the Vero cells generated higher quantity of ZIKV stocks, the Vero/TMPRSS2 cells produced plaques with significantly improved morphology and visibility and may, therefore, be a better alternative to use for performing plaque assays for strains of ZIKV that are more difficult to titer on regular Vero cells.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2026

Predictive analytics to direct clinical attention to complex patients with elevated suicide risk: enhancement of the Veterans Health Administration REACH VET model

Suicide is a major public health concern, particularly among Veterans. The U.S. Department of Veterans Affairs Veterans Health Administration (VHA) employs the Recovery Engagement and Coordination for Health–Veterans Enhanced Treatment (REACH VET) model to prioritise high-risk patients for targeted clinical attention. REACH VET 1.0 (RV 1.0) was developed on 2008–2011 data. To reflect changes in clinical practice and populations, VHA updated it to REACH VET 2.0 (RV 2.0). This study describes its development and validation. RV 2.0 used longitudinal data from 7,248,170 VHA patients (4,967 suicide deaths) in 2018–2019, with 650 time-varying demographic, clinical and area-level predictors derived from a 2-year lookback (2016–2019). An ensemble of Elastic-Net logistic regression models was trained on 2018 data and evaluated monthly at the population level in 2019, focusing on the top 0.1% intervention risk tier. Analyses assessed model discrimination, suicide detection, risk concentration, subgroup consistency (sex, age and race/ethnicity) and performance relative to RV 1.0 using the same percentile-based risk strata. RV 2.0 outperformed RV 1.0 across all risk strata, with better discrimination (C-statistic 0.76 vs 0.69) and consistent performance across demographic subgroups. Within the top 0.1% of predicted risk, RV 2.0 identified more deaths, higher suicide rates and greater mortality risk concentration both when averaged across the 12 monthly 2019 test sets (5.6 vs 3.6; 83.6 vs 53.7 per 100,000 person-years; 21.0 vs 14.1) and when annualised for 2019 (67 vs 43; 2.7% vs 1.7%; 1,003 vs 644 per 100,000 person-years; 26.7 vs 17.1). RV 2.0 improves suicide risk stratification among Veterans, demonstrating better performance and consistent prediction across subgroups and highlighting the need for regular model updates and evaluation.

Peluso, Alina [Oak Ridge National Laboratory (ORNL↗
DOE OSTI2020

Efficient Low-Order Refined Preconditioners for High-Order Matrix-Free Continuous and Discontinuous Galerkin Methods

In this paper, we design preconditioners for the matrix-free solution of high-order continuous and discontinuous Galerkin discretizations of elliptic problems based on finite element method--spectral element method (FEM-SEM) equivalence and additive Schwarz methods. The high-order operators are applied without forming the system matrix, making use of sum factorization for efficient evaluation. The system is preconditioned using a spectrally equivalent low-order (p = 1) finite element operator discretization on a refined mesh. The low-order refined mesh is anisotropic and not shape regular in the polynomial degree of the high-order operator, requiring specialized solvers to treat the anisotropy. We make use of an element-structured, geometric multigrid V-cycle with ordered ILU(0) smoothing. The preconditioner is parallelized through an overlapping additive Schwarz method that is robust in h and p. The method is extended to interior penalty and Bassi and Rebay (BR2) discontinuous Galerkin discretizations, for which it is also robust in the size of the penalty parameter. Finally, numerical results are presented on a variety of examples, verifying the uniformity of the preconditioner.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A Fast Solver for the Fractional Helmholtz Equation

The purpose of this paper is to study a Helmholtz problem with a spectral fractional Laplacian, instead of the standard Laplacian. Recently, it has been established that such a fractional Helmholtz problem better captures the underlying behavior in Geophysical Electromagnetics. In this work, we establish the well-posedness and regularity of this problem. We introduce a hybrid spectral-finite element approach to discretize it and show well-posedness of the discrete system. In addition, we derive a priori discretization error estimates. Finally, we introduce an efficient solver that scales aswell as the best possible solver for the classical integer-order Helmholtz equation. We conclude withseveral illustrative examples that confirm our theoretical findings.

97 MATHEMATICS AND COMPUTING↗