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DOE OSTI2025

Enriched immersed finite element and isogeometric analysis: algorithms and data structures

Immersed finite element methods provide a convenient analysis framework for problems involving geometrically complex domains, such as those found in topology optimization and microstructures for engineered materials. However, their implementation remains a major challenge due to, among other things, the need to apply nontrivial stabilization schemes and generate custom quadrature rules. This article introduces the robust and computationally efficient algorithms and data structures comprising an immersed finite element preprocessing framework. The input to the preprocessor consists of a background mesh and one or more geometries defined on its domain. The output is structured into groups of elements with custom quadrature rules formatted such that common finite element assembly routines may be used without or with only minimal modifications. The key to the preprocessing framework is the construction of material topology information, concurrently with the generation of a quadrature rule, which is then used to perform enrichment and generate stabilization rules. While the algorithmic framework applies to a wide range of immersed finite element methods using different types of meshes, integration, and stabilization schemes, the preprocessor is presented within the context of the extended isogeometric analysis. This method utilizes a structured B-spline mesh, a generalized Heaviside enrichment strategy considering the material layout within individual basis functions’ supports, and face-oriented ghost stabilization. Using a set of examples, the effectiveness of the enrichment and stabilization strategies is demonstrated alongside the preprocessor’s robustness in geometric edge cases. Additionally, the performance and parallel scalability of the implementation are evaluated.

Computer implementation↗

DOE OSTI2018

Crank–Nicolson WSGI difference scheme with finite element method for multi-dimensional time-fractional wave problem

In this article, a second-order Crank–Nicolson weighted and shifted Grünwald integral (WSGI) time-discrete scheme combined with finite element method is studied for finding the numerical solution of the multi-dimensional time-fractional wave equation. The time-fractional wave equation with Caputo-fractional derivative is transformed into the time-fractional integral equation by integral technique, then the second-order Crank–Nicolson finite element scheme with a time second-order WSGI discrete approximation for fractional integral is formulated. The analysis of stability is made, then a priori error estimate is given by making use of the conversion technique between the WSGI formula and fractional integral. At the end of the article, some numerical examples covering two two-dimensional cases with rectangular element and triangular element and a three-dimensional case with tetrahedral element are shown to test and verify our theoretical results.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Matrix-free subcell residual distribution for Bernstein finite element discretizations of linear advection equations

In this work, we introduce a new residual distribution (RD) framework for the design of bound-preserving high-resolution finite element schemes. The continuous and discontinuous Galerkin discretizations of the linear advection equation are modified to construct local extremum diminishing (LED) approximations. To that end, we perform mass lumping and redistribute the element residuals in a manner which guarantees the LED property. The hierarchical correction procedure for high-order Bernstein finite element discretizations involves localization to subcells and definition of bound-preserving weights for subcell contributions. Using strong stability preserving (SSP) Runge–Kutta methods for time integration, we prove the validity of discrete maximum principles under CFL-like time step restrictions. The low-order version of our method has roughly the same accuracy as the one derived from a piecewise (multi)-linear approximation on a submesh with the same nodal points. In high-order extensions, we use an element-based flux-corrected transport (FCT) algorithm which can be interpreted as a nonlinear RD scheme. The proposed LED corrections are tailor-made for matrix-free implementations which avoid the rapidly growing cost of matrix assembly for high-order Bernstein elements. The results for 1D, 2D, and 3D test problems compare favorably to those obtained with the best matrix-based approaches.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Stress-hybrid virtual element method on six-noded triangular meshes for compressible and nearly-incompressible linear elasticity

In this paper, we present a first-order Stress-Hybrid Virtual Element Method (SH-VEM) on six-noded triangular meshes for linear plane elasticity. Here, we adopt the Hellinger–Reissner variational principle to construct a weak equilibrium condition and a stress based projection operator. In each element, the stress projection operator is expressed in terms of the nodal displacements, which leads to a displacement based formulation. This stress-hybrid approach assumes a globally continuous displacement field while the stress field is discontinuous across each element. The stress field is initially represented by divergence-free tensor polynomials based on Airy stress functions, but we also present a formulation that uses a penalty term to enforce the element equilibrium conditions, referred to as the Penalty Stress-Hybrid Virtual Element Method (PSH-VEM). Numerical results are presented for PSH-VEM and SH-VEM, and we compare their convergence to the composite triangle FEM and B-bar VEM on benchmark problems in linear elasticity. The SH-VEM converges optimally in the L 2 norm of the displacement, energy seminorm, and the L 2 norm of hydrostatic stress. Furthermore, the results reveal that PSH-VEM converges in most cases at a faster rate than the expected optimal rate, but it requires the selection of a suitably chosen penalty parameter.

42 ENGINEERING↗

DOE OSTI2019

Multilayered triangular and quadrilateral flat shell elements based on the Refined Zigzag Theory

The paper presents a class of C 0 -continuous, flat shell elements based on the Refined Zigzag Theory (RZT) for the analysis of multilayered and curved composite and sandwich structures. In this study, the use of the interdependent interpolation strategy allows eliminating the shear-locking phenomenon and introducing the drilling rotation necessary to complete the set of classical nodal degrees of freedom (three displacements and three rotations). Additional kinematic variables are present in RZT, the zigzag rotations around the in-plane axes that measure the normal distortion typical of multilayered structures. An additional “drilling” zigzag rotation is therefore included among the nodal degrees of freedom in order to properly model curved and built-up structures. A stabilization procedure is adopted to suppress spurious zero-energy modes. A three-node triangular and a four-node quadrilateral flat shell element are formulated with 9 degrees of freedom per node. Example problems involving flat and curved multilayered structures are presented and discussed in order to assess the accuracy and convergence properties of the presented elements. Both static response predictions and free vibrations analyses are considered and the comparison is made with analytic RZT solutions, high-fidelity 3D finite element models and FSDT-based flat shell elements.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

An automated micro-separation system for the chromatographic removal of uranium matrix for trace element analysis by ICP-OES

An automated, miniaturized, off-line separation technique is presented here using an Elemental Scientific Inc. microFAST MC system with UTEVA resin to extract the uranium matrix from its trace element impurities in aqueous media. The collected fractions were analyzed for ~30 trace elements using inductively coupled plasma – optical emission spectroscopy. Ten replicate samples were processed with a single column resulting in precision ranging from 3.3% to 6.2% relative standard deviation with regards to the trace element recoveries. Accuracy, with respect to trace element concentrations in the U 3 O 8 Certified Reference Material 124-1, resulted in an average of 13.9% relative deviation while accuracy to the Canadian U3O8 reference material, CUP-2, resulted in an average relative deviation of 8.6%. In conclusion, the total separation time of this automated process was reduced to ~30 min per sample while employing a 0.5 mL UTEVA chromatographic resin bed and 2.5 mg of uranium.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2018

Geochemical Evidence for Rare-Earth Element Mobilization during Kaolin Diagenesis

This study investigates how saprolization influences inherent rare-earth element (REE) source rock signatures and how depositional environment(s) and diagenetic reactions ultimately impact the REE signature within sedimentary kaolin bodies. Rare-earth element geochemistry signatures are particularly useful for tracking element sources and mobility and are, therefore, powerful tools in the investigation of clay mineral formation and diagenesis. Rare-earth element and bulk chemical compositions were determined using discrete chemical analyses and chemical imaging. Saprolitic materials show an enrichment in the light and heavy REEs, compared with the parent material, with enhanced Ce/Eu anomalies. Light REEs within sedimentary kaolins are associated with phosphate mineralogy and have experienced variable degrees of diagenetic fractionation and mobilization. Cretaceous kaolins display more light REE mobility compared with Tertiary kaolins, which show very little REE fractionation. Degrees of REE fractionation are driven primarily by differences in sedimentary kaolin physical properties and the presence of organic acids in groundwater. Unfortunately, the provenance of the Georgia kaolins could not be determined based solely on the trace-element and REE compositions because fractionations during saprolization and diagenesis mask much of the inherent provenance signatures. Lastly, implications for the REEs as an economic deposit and their beneficiation are discussed.

58 GEOSCIENCES↗

DOE OSTI2014

Diversity of abundance patterns of neutron-capture elements in very metal-poor stars

Observations of Very Metal-Poor stars indicate that there are at least two sites to r-process; “weak r-process” and “main r-process”. A question is whether these two are well separated or there exists a variation in the r-process. We present the results of abundance analysis of neutron-capture elements in the two Very Metal-Poor stars HD107752 and HD110184 in the Milky Way halo observed with the Subaru Telescope HDS. The abundance patterns show overabundace at light n-capture elements (e.g. Sr, Y), inferring the element yielding of weak r-process, while heavy neutron-capture elements (e.g. Ba, Eu) are deficient; however, the overabundance of light ones is not as significant as that previously found in stars representing the weak r-process (e.g. HD122563; Honda et al. 2006). Our study show diversity in the abundance patterns from light to heavy neutron-capture elements in VMP stars, suggesting a variation in r-process, which may depend on electron fraction of environment.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

Matrix elements and duality for type 2 unitary representations of the Lie superalgebra gl(m|n)

The characteristic identity formalism discussed in our recent articles is further utilized to derive matrix elements of type 2 unitary irreducible gl(m|n) modules. In particular, we give matrix element formulae for all gl(m|n) generators, including the non-elementary generators, together with their phases on finite dimensional type 2 unitary irreducible representations which include the contravariant tensor representations and an additional class of essentially typical representations. Remarkably, we find that the type 2 unitary matrix element equations coincide with the type 1 unitary matrix element equations for non-vanishing matrix elements up to a phase.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

Elemental analysis of different varieties of rice samples using XRF technique

Rice is most consumed staple food in the world providing over 21% of the calorie intake of world’s population having high yielding capacity. Elements detected in rice are Al, As, Br, Cd, Cl, Co, Cs, Cu, Fe, Hg, K, Mg, Mn, Mo, Rb, Se and Zn by using Instrumental Neutron Activation with k0 standardization (R. Jayasekera etal,2004). Some of these trace elements are C, H, O, N, S, Ca, P, K, Na, Cl, Mn, Ti, Mg, Cu, Fe, Ni, Si and Zn are essential for growth of human physique The deficiency or excess of these elements in food is known to cause a variety of malnutrition or health disorders in the world. Every year, various varieties of rice are launched by Punjab Agriculture University, Ludhiana. The main purpose of which is to increases the yield to attain the maximum profit. But this leads to changing the elemental concentration in them, which may affect the human health according to variation in the nutrition values. The main objective is to study the presence of elemental concentration in various varieties of rice using EDXRF technique.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2019

Spatial changes in trace element and strontium isotope water chemistry in a temperate river system with application to sturgeon movement

Understanding patterns in trace element concentrations and water quality within river systems provides a foundation to evaluate retrospective movements and habitat use of fish. Because trace elements are incorporated into calcified structures of fishes relative to water concentrations, baseline maps have application for fisheries management, including for rare species such as sturgeons. Therefore, trace elements [strontium (Sr), barium (Ba), manganese (Mn), zinc (Zn), and magnesium (Mg)], strontium isotopes ( 87 Sr/ 86 Sr), dissolved oxygen and salinity were measured in the Pearl River and Lake Pontchartrain watersheds, within Mississippi and Louisiana, USA for application in assessing riverine use by Gulf Sturgeon Acipenser oxyrinchus desotoi. Water samples were collected during the summer-fall period when juvenile Gulf Sturgeon were anticipated to be present and analyzed by solution and multi-collector inductively coupled plasma mass spectrometry. Trace element to calcium (Ca) ratios in Sr, Ba, Zn, and Mg were distinguishable between the upper Pearl River and the Bogue Chitto River tributary, and the upper Pearl River and lower Pearl River. For most trace elements and 87 Sr/ 86 Sr, there was a gradual increase from upper river regions to lower river regions, and large differences between freshwater and saline areas. Lake Pontchartrain watershed rivers were not easily differentiated, but regions of low dissolved oxygen concentrations in the lower reaches suggest available Gulf Sturgeon habitat may be seasonally limited. Therefore, maps of water microchemistry in the Pearl River watershed allow for retrospective analyses of fish watershed use.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2015

THE COMPOSITION OF INTERSTELLAR GRAINS TOWARD ζ OPHIUCHI: CONSTRAINING THE ELEMENTAL BUDGET NEAR THE DIFFUSE-DENSE CLOUD TRANSITION

We investigate the composition of interstellar grains along the line of sight toward ζ Ophiuchi, a well-studied environment near the diffuse-dense cloud transition. A spectral decomposition analysis of the solid-state absorbers is performed using archival spectroscopic observations from the Spitzer Space Telescope and Infrared Space Observatory. We find strong evidence for the presence of sub-micron-sized amorphous silicate grains, principally comprised of olivine-like composition, with no convincing evidence of H{sub 2}O ice mantles. However, tentative evidence for thick H{sub 2}O ice mantles on large (a ≈ 2.8 μm) grains is presented. Solid-state abundances of elemental Mg, Si, Fe, and O are inferred from our analysis and compared to standard reference abundances. We find that nearly all of the Mg and Si atoms along the line of sight reside in amorphous silicate grains, while a substantial fraction of the elemental Fe resides in compounds other than silicates. Moreover, we find that the total abundance of elemental O is largely inconsistent with the adopted reference abundances, indicating that as much as ∼156 ppm of interstellar O is missing along the line of sight. After taking into account additional limits on the abundance of elemental O in other O-bearing solids, we conclude that any missing reservoir of elemental O must reside on large grains that are nearly opaque to infrared radiation.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Giant Starship Elements Mobilize Accessory Genes in Fungal Genomes

Accessory genes are variably present among members of a species and are a reservoir of adaptive functions. In bacteria, differences in gene distributions among individuals largely result from mobile elements that acquire and disperse accessory genes as cargo. In contrast, the impact of cargo-carrying elements on eukaryotic evolution remains largely unknown. Here, we show that variation in genome content within multiple fungal species is facilitated by Starships, a newly discovered group of massive mobile elements that are 110 kb long on average, share conserved components, and carry diverse arrays of accessory genes. We identified hundreds of Starship-like regions across every major class of filamentous Ascomycetes, including 28 distinct Starships that range from 27 to 393 kb and last shared a common ancestor ca. 400 Ma. Using new long-read assemblies of the plant pathogen Macrophomina phaseolina, we characterize four additional Starships whose activities contribute to standing variation in genome structure and content. One of these elements, Voyager, inserts into 5S rDNA and contains a candidate virulence factor whose increasing copy number has contrasting associations with pathogenic and saprophytic growth, suggesting Voyager’s activity underlies an ecological trade-off. We propose that Starships are eukaryotic analogs of bacterial integrative and conjugative elements based on parallels between their conserved components and may therefore represent the first dedicated agents of active gene transfer in eukaryotes. Our results suggest that Starships have shaped the content and structure of fungal genomes for millions of years and reveal a new concerted route for evolution throughout an entire eukaryotic phylum.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2018

On the Possibility of Delayed Fission of Nuclei in the Region of Superheavy Transuranium Elements

Delayed fission of atomic nuclei was discovered in 1966. It is observed primarily in odd–odd nuclei for which the energy released in beta decay (K capture) is commensurate with the fission barrier in the nucleus formed after this process. Delayed fission was found in four nuclide regions: neutrondeficient isotopes in the Pb region, neutron-deficient isotopes in the Ac and Pa regions, and neutrondeficient and neutron-rich isotopes of transuranium elements. In the wake of investigations into the properties of isotopes of superheavy transuranium elements, numerous calculations were performed in order to determine the masses of new nuclei and to predict their decay properties. Explored and predicted properties of superheavy-element nuclides, where, for some odd–odd nuclei of transuranium elements, the K-capture energy is commensurate with the fission barriers in the corresponding daughter nuclei formed after K capture, are analyzed. Estimates of the delayed-fission probability are presented for some isotopes of elements whose charge number Z ranges from 103 to 107.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2018

Nonlocal and Mixed-Locality Multiscale Finite Element Methods

In many applications the resolution of small-scale heterogeneities remains a significant hurdle to robust and reliable predictive simulations. In particular, while material variability at the mesoscale plays a fundamental role in processes such as material failure, the resolution required to capture mechanisms at this scale is often computationally intractable. Multiscale methods aim to overcome this difficulty through judicious choice of a subscale problem and a robust manner of passing information between scales. One promising approach is the multiscale finite element method, which increases the fidelity of macroscale simulations by solving lower-scale problems that produce enriched multiscale basis functions. Here, in this study, we present the first work toward application of the multiscale finite element method to the nonlocal peridynamic theory of solid mechanics. This is achieved within the context of a discontinuous Galerkin framework that facilitates the description of material discontinuities and does not assume the existence of spatial derivatives. Analysis of the resulting nonlocal multiscale finite element method is achieved using the ambulant Galerkin method, developed here with sufficient generality to allow for application to multiscale finite element methods for both local and nonlocal models that satisfy minimal assumptions. Finally, we conclude with preliminary results on a mixed-locality multiscale finite element method in which a nonlocal model is applied at the fine scale and a local model at the coarse scale.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Nonconforming Mesh Refinement for High-Order Finite Elements

In this study, we propose a general algorithm for nonconforming adaptive mesh refinement (AMR) of unstructured meshes in high-order finite element codes. Our focus is on $h$-refinement with a fixed polynomial order. The algorithm handles triangular, quadrilateral, hexahedral, and prismatic meshes of arbitrarily high-order curvature, for any order finite element space in the de Rham sequence. We present a flexible data structure for meshes with hanging nodes and a general procedure to construct the conforming interpolation operator, both in serial and in parallel. The algorithm and data structure allow anisotropic refinement of tensor product elements in two and three dimensions and support unlimited refinement ratios of adjacent elements. We report numerical experiments verifying the correctness of the algorithms and perform a parallel scaling study to show that we can adapt meshes containing billions of elements and run efficiently on 393,000 parallel tasks. Finally, we illustrate the integration of dynamic AMR into a high-order Lagrangian hydrodynamics solver.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Toward a least-effort principle for evaluating prices of elements as indicators of sustainability

In this article, we explore simplifying mechanisms in materials economics for conceptionally organizing the flows of chemical elements into society. We use the concept of rank, which plays a crucial role in information theory where power laws are involved, and is a useful measure for seeking extremal principles. Borrowing from an analogy to Zipf’s law leads to a power-law relationship between abundance and rank that—pressing the Zipf’s law analogy further—may suggest that the price paid for elemental materials optimizes efficient utilization. Factors such as weight, volume, and moles in the earth's crust or in global mining production of elements are used in our analysis. For this research, 42 elements with price and production data for the year 2010 (a relatively typical year) were considered. We observe that the role of the volume from global mining production dominates in materials economics and indicate that elements such as Te and He should be sold at prices at leas ~ 100–1000 times more than their present price for efficient utilization.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2021

Probabilistic Data Association for Orbital-Element Estimation Using Multistage Expectation–Maximization

Tracking space objects is important for managing space traffic and predicting collisions, but is difficult in part due to data association and orbit model uncertainty. Expectation–maximization (EM) is a commonly used tracking method that has not been widely considered for tracking space objects. The technique consists of iteratively computing data association probabilities with a set of current element estimates, and updating estimates of the elements by solving a nonlinear weighted least-squares regression problem where the weights are the data association probabilities. In this paper, we demonstrate the use of EM for probabilistic data association and orbital-element estimation by applying the technique to simulated data from two angles-only tracking scenarios. In both scenarios, EM provides correct data associations and accurate maximum likelihood estimates of orbital elements. One scenario considers tracking a single object in clutter and quantifies the improvement of the orbital-element estimates and data associations as the detection probability increases. However, standard application of EM requires knowing the number of objects or may fail when a large number of objects are present. To address these issues, this paper employs a multistage version of EM that is applicable when there are a large and possibly unknown number of objects.

97 MATHEMATICS AND COMPUTING↗