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At least 469 records · Page 26

ArborX 2.0

ArborX library tackles a problem of efficiently finding geometric objects that are close in space. Variations of this problem, such as finding the nearest neighbors of a point, or finding all objects within a certain distance, are inherent components of applications in many fields. The data may be large so that solving the problem efficiently may require significant computational resources, such as multiple processors or accelerators such as general purpose GPUs. ArborX' main advantage in its ability to solve large problems efficiently utilizing a combination of distributed and on-node parallelism. ArborX can be run efficiently on a wide variety of hardware, including GPUs from different vendors, which distinguishes it from other available libraries which typically choose only few of these. The other advantage is that it supports both types of user problems: spatial problems (useful for intersections and finding objects within certain distance), and nearest neighbor problems. ArborX also supports flexible interface in its interaction with a user. Particularly, it allows a user to call user's own function on a positive match, a functionality not rarely available in other libraries. ArborX implements construction and traversal algorithms using efficient tree structures, such as bounding volume hierarchy (BVH). At its core, ArborX uses linear BVH for its low construction cost and sufficient quality. ArborX implements both spatial and nearest-neighbor traversal algorithms. ArborX also provides several clustering algorithms (minimum spanning tree, DBSCAN, HDBSCAN*), interpolation using minimum least squares and ray tracing. ArborX is written using C++, and is parallelized using the message passing interface (MPI) for the distributed communication, and the Kokkos library for on-node parallelism. This approach allows ArborX to be run on a wide variety of hardware, from common laptops and desktops to supercomputers while using the same codebase.

Prokopenko, Andrey [Oak Ridge National Laboratory ↗

Wide-angle effects for peculiar velocities

ABSTRACT The line-of-sight peculiar velocities of galaxies contribute to their observed redshifts, breaking the translational invariance of galaxy clustering down to a rotational invariance around the observer. This becomes important when the line-of-sight direction varies significantly across a survey, leading to what are known as ‘wide-angle’ effects in redshift-space distortions. Wide-angle effects will also be present in measurements of the momentum field, i.e. the galaxy density-weighted velocity field, in upcoming peculiar velocity surveys. In this work, we study how wide-angle effects modify the predicted correlation function and power spectrum for momentum statistics, both in autocorrelation and in cross-correlation with the density field. Using both linear theory and the Zel'dovich approximation, we find that deviations from the plane-parallel limit are large and could become important in data analysis for low-redshift surveys. We point out that even multipoles in the cross-correlation between density and momentum are non-zero regardless of the choice of line of sight, and therefore contain new cosmological information that could be exploited. We discuss configuration space, Fourier space, and spherical analyses; providing exact expressions in each case rather than relying on an expansion in small angles. We hope these expressions will be of use in the analysis of upcoming surveys for redshift-space distortions and peculiar velocities.

79 ASTRONOMY AND ASTROPHYSICS↗

Improved renormalization group computation of likelihood functions for cosmological data sets

Evaluation of likelihood functions for cosmological large scale structure data sets (including CMB, galaxy redshift surveys, etc.) naturally involves marginalization, i.e., integration, over an unknown underlying random signal field. Recently, I showed how a renormalization group method can be used to carry out this integration efficiently by first integrating out the smallest scale structure, i.e., localized structure on the scale of differences between nearby data cells, then combining adjacent cells in a coarse graining step, then repeating this process over and over until all scales have been integrated. Here I extend the formulation in several ways in order to reduce the prefactor on the method's linear scaling with data set size. The key improvement is showing how to integrate out the difference between specific adjacent cells before summing them in the coarse graining step, compared to the original formulation in which small-scale fluctuations were integrated more generally. I suggest some other improvements in details of the scheme, including showing how to perform the integration around a maximum likelihood estimate for the underlying random field. In the end, an accurate likelihood computation for a million-cell Gaussian test data set runs in two minutes on my laptop, with room for further optimization and straightforward parallelization.

79 ASTRONOMY AND ASTROPHYSICS↗

Towards Superior Software Portability with SHAD and HPX C++ Libraries

As hardware architectures and software stacks complexity grows, development productivity, performance and software portability, quickly evolve from desirable features to actual needs. SHAD, the Scalable High-performance Algorithms and Data-structures C++ library is designed to mitigate these issues: it provides general purpose building blocks as well as high-level custom utilities, and offers a shared-memory programming abstraction which facilitates the programming of complex systems, scaling up to High Performance Computing clusters. SHAD’s portability is achieved through an abstract runtime interface, which decouples the upper layers of the library and hides the low level details of the underlying architecture. This layer enables SHAD to interface with different runtime/threading systems, e.g. Intel TBB and Global Memory and Threading (GMT). However, current backends targeting distributed systems, rely on a centralized controller which may possibly limit scalability up to hundreds of nodes and creates a network hot spot due to all to one communication for synchronization, and possibly resulting in degraded performance at high process counts. In this research, we explore HPX, the C++ standard library for parallelism and concurrency, as an additional backend in support of the SHAD library, and present the methodologies in support of local and remote task executions in SHAD with respect to HPX. Finally, we evaluate the proposed system by comparing against existing backends of SHAD and analyzing their performance on C++ Standard Template Library algorithms.

Wu, Nanmiao↗

Understanding Lustre Internals. Second Edition

The Lustre file system has become a preferred storage resource for systems on the Top500 list, and it is often the file system of choice for small- to medium-sized HPC systems that require parallel shared access to data. Several resources exist to help users deploy and configure Lustre, but the same cannot be said for resources that explain the inner workings of the Lustre source code. A previous ORNL technical report entitled "Understanding Lustre Filesystem Internals" (ORNL/TM-2009/117) provided an excellent summary of Lustre subsystem operations. However, that report is over a decade old and is based on Lustre version 1.6. Since that report was published, Lustre has evolved significantly. Several subsystems underwent significant code changes and many new features have been added to the file system, bringing the current Lustre version up to 2.15.This report aims to document and explain the internal workings of the latest version of the Lustre file system. It will provide more complete and up-to-date information than the previous technical report and should serve as a foundational document for anyone interested in Lustre software development. Key data structures will be described along with the APIs used for interaction among the various Lustre subsystems. Although the Lustre software is constantly being developed, the details in this document should remain relevant for the forseeable future.

97 MATHEMATICS AND COMPUTING↗

Characterization of the ePix100a and the FastCCD Semiconductor Detectors for the European XFEL

Here, the European X-ray Free Electron Laser (EuXFEL) is a research facility providing spatially coherent X-ray flashes in the energy range from 0 . 25 keV to 25 keV of unprecedented brilliance and with unique time structure: X-ray pulses with a 4 . 5 MHz repetition rate arranged in trains with 2700 pulses every 100 ms. The facility operates three photon beamlines called SASE 1, SASE 2 and SASE 3. Each of the beamlines is hosting two scientific experiments. The SASE 1 beamline started its user operation in September 2017, followed by successful first lasing at the SASE 2 beamline in May 2018. Early user experiments are planned to start in 2019 at this beamline, while early user experiments for the SASE 3 beamline are scheduled for the end of 2018. The quality of the experimental data will gain substantial benefits from an accurate characterization and calibration of the X-ray detectors. Supplementing high repetition rate detectors at MHz speeds, slower detectors such as the ePix100a and the FastCCD will be operated at the train repetition rate of 10 Hz. These 2D silicon pixelized detectors use fast parallel column-wise readout implemented as a CCD or as a hybrid pixel detector. In the following, characterization and analysis approaches for the FastCCD and the ePix100a detectors are discussed and the performance of the detectors is evaluated using appropriate state-of-the-art analysis techniques.

47 OTHER INSTRUMENTATION↗

Massively Parallel Bayesian Model Calibration and Uncertainty Quantification with Applications to Nuclear Fuels and Materials

The U.S. Department of Energy (DOE)’s Nuclear Energy Advanced Modeling and Simulation (NEAMS) program aims to develop predictive capabilities by applying computational methods to the analysis and design of advanced reactor and fuel cycle systems. This program has been providing engineering-scale support for the development of BISON, a high-fidelity and high-resolution fuel performance tool. Fuel behavior in a nuclear reactor is governed by a complex network of mechanisms interacting with various other physics aspects in the reactor system. Any model developed to represent the fuel behavior will likely be idealized resulting in uncertainties in their predictions compared to the observed data. As such, this report was motivated by the need to identify the sources of uncertainties and quantify and propagate them through the fuel model outputs. Such quantification of uncertainties will establish a level of model trustworthiness, identify approaches to improve the model trustworthiness, and even guide optimal experiment design for maximal information gain. To accomplish the uncertainty quantification for computational models, this report has relied on the Bayesian framework which provides probabilistic treatment of models their inputs and outputs. The current state-of-the-art on performing Bayesian Uncertainty Quantification (UQ) for nuclear engineering models using High Performance Computing (HPC) resources have been reviewed. Implementation of capabilities for massively parallel Bayesian UQ in Multiphysics Object-Oriented Simulation Environment (MOOSE) is discussed. Several verification cases are discussed to verify the accuracy of the quantified uncertainties using the developed computational capabilities in MOOSE. Then, the problem of quantifying the uncertainties in TRI-Structural isOtropic (TRISO) fuel silver release is addressed. For the first time, the uncertainties arising from the TRISO Fission Gas Release (FGR) model due to model inadequacy and experimental noise are quantified. Also, the Bayesian capabilities are applied to the calibration of the MATPRO creep model, a widely used model in several fuel assessment cases. The impact of the prediction uncertainties in the MATPRO model on the fuel cladding behavior as part of the TRIBULATION assessment case (which is an integral effects case) is investigated. This report concludes with a discussion on the future work for the UQ for computational models.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Control And Optimization Modular Modeling Application For Nuclear Deployment

The purpose of the COMMAND code is to provide a flexible, scalable tool for use in developing, integrating, and testing the technologies necessary for achieving autonomous operations of advanced nuclear reactors. The code enables users to efficiently implement custom simulations and experiments by combining key methods from different software modules. These modules are focused on: modeling and simulation tools, such as nuclear simulation tools used for high-fidelity modeling (e.g., Reactor Excursion and Leak Analysis Program [RELAP5-3D] and Monte Carlo N-Particle [MCNP]); machine learning and optimization tools (e.g., anomaly detection and data-driven modeling techniques); advanced control in its digital, high-performance, and supervisory control forms (e.g., proportional integral derivative (PID) control and model predictive control (MPC); and integration with hardware through industrial communication protocols. To ensure flexibility and scalability, COMMAND was designed to be both modular—the software “pieces” all inherit from generic building blocks and can be combined and connected to create complicated simulations—and high performing—designed for parallel processing, enabling simulations and experiments to take advantage of multi-core computers, servers, and nodes. The code is written in the Python programming language due to the language's popularity, active community, and open-source and cross-platform nature. Maintaining consistency with other simulation tools used within the nuclear energy community, users implement simulations and experiments through text input files, which define components, parameters, connections, etc., through lines of text. Given that COMMAND is written in Python, these input files are native Python scripts, and so use the standard Python structure and formatting. This also enables users to take advantage of Python's extensive package library to develop custom capabilities for their specific use cases.

Faber, Jacob [Idaho National Laboratory (INL), Ida↗

An Overview of Non-LWR Vessel Cooling Systems for Passive Decay Heat Removal (Technical Letter Final Report)

The following report provides a technical review of various reactor vessel cooling system (VCS) concepts under consideration for decay heat removal (DHR) in non-light water advanced reactor designs. This review focuses on ex-vessel designs, including the Reactor Cavity Cooling System (RCCS), the Reactor Vessel Auxiliary Cooling System (RVACS), and hybrid iterations, using both air and water cooling to achieve their heat removal function. Based on a literature review of publicly available sources published between 1979 and 2021, a technical summary is presented detailing existing and planned VCS design options, their applicability to specific reactor type, and review of authored research and development studies. Following an assessment of the availability of data and modeling tools, an evaluation was performed analyzing their likely performance during normal, degraded, and accident conditions, including reliability, stability, and longevity. With renewed consideration of air-based DHR systems by some US vendors, there is a need to fully understand the complexities inherent to natural circulation systems, and more importantly, how they may influence safety-related heat removal functions and system performance. For DHR systems that rely on air-based mode of cooling, this entails quantification of the impacts of low flow conditions during start-up, relative elevations of inlet and outlet ducts for below-grade installations, effects of the use of multiple parallel chimneys for redundancy, and impact of weather conditions at the plant site. For systems relying on water-based mode cooling, reliance on limited coolant inventory in an event of pipe break or extended duration accident scenarios, sensitivities related to stability of boiling flow and heat transfer conditions, and quantification of full-scale structural vibrations on balance of plant structures are among the complicating factors.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Creation of large temperature anisotropies in a laboratory plasma

Ion temperature anisotropy in an expanding magnetized plasma is investigated using laser induced fluorescence. Parallel and perpendicular ion velocity distribution functions (IVDFs) were measured simultaneously with high spatial resolution in the expanding plasma. Large ion temperature anisotropies (T ⊥i /T ∥i ~ 10) are observed in a conical region at the periphery of the expanding plasma plume. A simple 2D Boris stepper model that incorporates the measured electric field structure is able to reproduce the gross features of the measured perpendicular IVDFs. Here, a Nyquist stability analysis of the measured IVDFs suggests that multiple instabilities with k ⊥ρi ~ 1 and k ||ρi ~ 0.2 are likely to be excited in these plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Insights on the dissolution of water in an albite melt at high pressures and temperatures from a direct structural analysis

The water dissolution mechanism in silicate melts under high pressures is not well understood. Here we present the first direct structure investigation of a water-saturated albite melt to monitor the interactions between water and the network structure of silicate melt at the molecular level. In situ high-energy X-ray diffraction was carried out on the NaAlSi 3 O 8 -H 2 O system at 800 °C and 300 MPa, at the Advanced Photon Source synchrotron facility. The analysis of the X-ray diffraction data was augmented with classical Molecular Dynamics simulations of a hydrous albite melt, incorporating accurate water-based interactions. The results show that metal–oxygen bond breaking at the bridging sites occurs overwhelmingly at the Si site upon reaction with H 2 O, with subsequent Si–OH bond formation and negligible Al–OH formation. Furthermore, we see no evidence for the dissociation of the Al 3+ ion from the network structure upon breaking of the Si–O bond in the hydrous albite melt. The results also indicate that the Na + ion is an active participant in the modifications of the silicate network structure of the albite melt upon water dissolution at high P–T conditions. We do not find evidence for the Na + ion dissociating from the network structure upon depolymerization and subsequent formation of NaOH complexes. Instead, our results show that the Na + ion persists as a structure modifier with a shift away from Na–BO bonding to an increase in the extent of Na-NBO bonding, in parallel with pronounced depolymerization of the network. Our MD simulations show that the Si–O and Al–O bond lengths are expanded by about 6% in the hydrous albite melt compared to those of the dry melt at high P–T conditions. The changes in the network silicate structure of a hydrous albite melt at high pressure and temperature, as revealed in this study, must be considered in the advancement of water dissolution models of hydrous granitic (or alkali aluminosilicate) melts.

36 MATERIALS SCIENCE↗

Optical neural engine for solving scientific partial differential equations

Abstract Solving partial differential equations (PDEs) is the cornerstone of scientific research and development. Data-driven machine learning (ML) approaches are emerging to accelerate time-consuming and computation-intensive numerical simulations of PDEs. Although optical systems offer high-throughput and energy-efficient ML hardware, their demonstration for solving PDEs is limited. Here, we present an optical neural engine (ONE) architecture combining diffractive optical neural networks for Fourier space processing and optical crossbar structures for real space processing to solve time-dependent and time-independent PDEs in diverse disciplines, including Darcy flow equation, the magnetostatic Poisson’s equation in demagnetization, the Navier-Stokes equation in incompressible fluid, Maxwell’s equations in nanophotonic metasurfaces, and coupled PDEs in a multiphysics system. We numerically and experimentally demonstrate the capability of the ONE architecture, which not only leverages the advantages of high-performance dual-space processing for outperforming traditional PDE solvers and being comparable with state-of-the-art ML models but also can be implemented using optical computing hardware with unique features of low-energy and highly parallel constant-time processing irrespective of model scales and real-time reconfigurability for tackling multiple tasks with the same architecture. The demonstrated architecture offers a versatile and powerful platform for large-scale scientific and engineering computations.

Tang, Yingheng (ORCID:0009000153622546)↗

Data-Driven Optimization of the Processing Window for 316H Components Fabricated Using Laser Powder Bed Fusion

The Advanced Materials and Manufacturing Technologies Program is focused on accelerating the development and deployment of advanced materials and components fabricated via additive manufacturing with a specific focus on laser powder bed fusion (LPBF). As an initial case study, the program has selected 316H stainless steel (SS) as an initial material around which to develop a code case development strategy. This strategy involves two parallel approaches: (1) an equivalency approach whereby round-robin testing across multiple collaborating laboratories demonstrates repeatability in processing and direct comparisons with conventional wrought 316H material and (2) a revolutionary approach to code qualification combining in situ data collection and high-fidelity modeling to capture, predict, and bound the performance of LPBF 316HSS components. As part of this campaign, this work package has initiated an extensive process optimization campaign across three laboratories, each printing variations of LPBF 316HSS using three different LPBF units (Concept Laser, EOS, and Renishaw). In FY23, ORNL has focused on unique experimental designs spanning wide ranges in energy inputs and turning knobs such as scan speed, laser power, hatch spacing, layer thickness, spot size, scan rotation, and more. On the Concept Laser M2, 72 different combinations of processing variables were investigated with duplicate samples and different powder compositions. In total, 252 samples were printed with combined in situ sensing data. A parallel design of experiments was conducted on the Renishaw AM400 with an additional 390 printed specimens for analysis. All 642 miniature specimens, each with unique features included in each print to capture geometry-related heterogeneity, were subjected to high-throughput x-ray computed tomography (XCT) analysis to enable the downselection of specific processing parameters of interest. Then, using electrical discharge machining (EDM), miniature tensile specimens were extracted for mechanical testing and microscopy investigations. From the analysis performed in FY23, it was found that powder composition drastically affects the resulting microstructure and mechanical performance of 316SS. Specifically, changing from 316L to 316HSS powder results in a wide range of grain sizes with varying degrees of preferred grain orientation, which increases as a function of energy density. It was also found that due to stored heat in thin fin–type features, large microstructural differences can be seen within one part printed with one set of processing parameters. These variations in microstructure features, including grain size, the nanoscale dislocation structure, and grain texture, will all affect the irradiation performance and high-temperature mechanical performance of LPBF 316HSS parts. Two sets of concept laser processing parameters, spanning both refined and columnar grain structures, were scaled to print larger 316H builds for campaign testing (high-temperature creep and irradiation). In addition, at least two optimized processing parameter sets were identified for the Renishaw AM400 for round-robin testing in FY24 with Argonne National Laboratory. Future work includes printing samples using identical parameters identified by partner institutions, providing material for corrosion and high-temperature mechanical testing, and continuing evaluations of heterogeneity in larger printed parts.

36 MATERIALS SCIENCE↗

Data-Driven Optimization of the Processing Window for 316H Components Fabricated Using Laser Powder Bed Fusion

The Advanced Materials and Manufacturing Technologies Program is focused on accelerating the development and deployment of advanced materials and components fabricated via additive manufacturing with a specific focus on laser powder bed fusion (LPBF). As an initial case study, the program has selected 316H stainless steel (SS) as an initial material around which to develop a code case development strategy. This strategy involves two parallel approaches: (1) an equivalency approach whereby round-robin testing across multiple collaborating laboratories demonstrates repeatability in processing and direct comparisons with conventional wrought 316H material and (2) a revolutionary approach to code qualification combining in situ data collection and high-fidelity modeling to capture, predict, and bound the performance of LPBF 316HSS components. As part of this campaign, this work package has initiated an extensive process optimization campaign across three laboratories, each printing variations of LPBF 316HSS using three different LPBF units (Concept Laser, EOS, and Renishaw). In FY23, ORNL has focused on unique experimental designs spanning wide ranges in energy inputs and turning knobs such as scan speed, laser power, hatch spacing, layer thickness, spot size, scan rotation, and more. On the Concept Laser M2, 72 different combinations of processing variables were investigated with duplicate samples and different powder compositions. In total, 252 samples were printed with combined in situ sensing data. A parallel design of experiments was conducted on the Renishaw AM400 with an additional 390 printed specimens for analysis. All 642 miniature specimens, each with unique features included in each print to capture geometry-related heterogeneity, were subjected to high-throughput x-ray computed tomography (XCT) analysis to enable the downselection of specific processing parameters of interest. Then, using electrical discharge machining (EDM), miniature tensile specimens were extracted for mechanical testing and microscopy investigations. From the analysis performed in FY23, it was found that powder composition drastically affects the resulting microstructure and mechanical performance of 316SS. Specifically, changing from 316L to 316HSS powder results in a wide range of grain sizes with varying degrees of preferred grain orientation, which increases as a function of energy density. It was also found that due to stored heat in thin fin–type features, large microstructural differences can be seen within one part printed with one set of processing parameters. These variations in microstructure features, including grain size, the nanoscale dislocation structure, and grain texture, will all affect the irradiation performance and high-temperature mechanical performance of LPBF 316HSS parts. Two sets of concept laser processing parameters, spanning both refined and columnar grain structures, were scaled to print larger 316H builds for campaign testing (high-temperature creep and irradiation). In addition, at least two optimized processing parameter sets were identified for the Renishaw AM400 for round-robin testing in FY24 with Argonne National Laboratory. Future work includes printing samples using identical parameters identified by partner institutions, providing material for corrosion and high-temperature mechanical testing, and continuing evaluations of heterogeneity in larger printed parts.

36 MATERIALS SCIENCE↗

Genome-scale analysis of regulatory protein acetylation enzymes from photosynthetic eukaryotes

Background: Reversible protein acetylation occurring on Lys-Ne has emerged as a key regulatory post-translational modification in eukaryotes. It is mediated by two groups of enzymes: lysine acetyltransferases (KATs) and lysine deacetylases (KDACs) that catalyze the addition and removal of acetyl groups from target proteins. Estimates indicate that protein acetylation is second to protein phosphorylation in abundance, with thousands of acetylated sites now identified in different subcellular compartments. Considering the important regulatory role of protein phosphorylation, elucidating the diversity of KATs and KDACs across photosynthetic eukaryotes is essential in furthering our understanding of the impact of reversible protein acetylation on plant cell processes. Results: We report a genome-scale analysis of lysine acetyltransferase (KAT)- and lysine deacetylase (KDAC)-families from 53 photosynthetic eukaryotes. KAT and KDAC orthologs were identified in sequenced genomes ranging from glaucophytes and algae to land plants and then analyzed for evolutionary relationships. Based on consensus molecular phylogenetic and subcellular localization data we found new sub-classes of enzymes in established KAT- and KDAC-families. Specifically, we identified a non-photosynthetic origin of the HD-tuin family KDACs, a new monocot-specific Class I HDA-family sub-class, and a phylogenetically distinct Class II algal/heterokont sub-class which maintains an ankyrin domain not conserved in land plant Class II KDACs. Protein structure analysis showed that HDA- and SRT-KDACs exist as bare catalytic subunits with highly conserved median protein length, while all KATs maintained auxiliary domains, with CBP- and TAFII250-KATs displaying protein domain gain and loss over the course of photosynthetic eukaryote evolution in addition to variable protein length. Lastly, promoter element enrichment analyses across species revealed conserved cis-regulatory sequences that support KAT and KDAC involvement in the regulation of plant development, cold/drought stress response, as well as cellular processes such as the circadian clock. Conclusions: Our results reveal new evolutionary, structural, and biological insights into the KAT- and KDAC-families of photosynthetic eukaryotes, including evolutionary parallels to protein kinases and protein phosphatases. Further, we provide a comprehensive annotation framework through our extensive phylogenetic analysis, from which future research investigating aspects of protein acetylation in plants can use to position new findings in a broader context.

59 BASIC BIOLOGICAL SCIENCES↗

Decentralized Schemes with Overlap for Solving Graph-Structured Optimization Problems

We present a new algorithmic paradigm for the decentralized solution of graph-structured optimization problems that arise in the estimation and control of network systems. A key and novel design concept of the proposed approach is that it uses overlapping subdomains to promote and accelerate convergence. We show that the algorithm converges if the size of the overlap is sufficiently large and that the convergence rate improves exponentially with the size of the overlap. The proposed approach provides a bridge between fully decentralized and centralized architectures and is flexible in that it enables the implementation of asynchronous schemes, handling of constraints, and balancing of computing, communication, and data privacy needs. The proposed scheme is tested in an estimation problem for a 9241-node power network and we show that it outperforms the alternating direction method of multipliers.

asynchronous↗

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↗