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DOE OSTI2020

ConnectIt: a framework for static and incremental parallel graph connectivity algorithms

Connected components is a fundamental kernel in graph applications. The fastest existing multicore algorithms for solving graph connectivity are based on some form of edge sampling and/or linking and compressing trees. However, many combinations of these design choices have been left unexplored. In this paper, we design the ConnectIt framework, which provides different sampling strategies as well as various tree linking and compression schemes. ConnectIt enables us to obtain several hundred new variants of connectivity algorithms, most of which extend to computing spanning forest. In addition to static graphs, we also extend ConnectIt to support mixes of insertions and connectivity queries in the concurrent setting. We present an experimental evaluation of ConnectIt on a 72-core machine, which we believe is the most comprehensive evaluation of parallel connectivity algorithms to date. Compared to a collection of state-of-the-art static multicore algorithms, we obtain an average speedup of 12.4x (2.36x average speedup over the fastest existing implementation for each graph). Using ConnectIt, we are able to compute connectivity on the largest publicly-available graph (with over 3.5 billion vertices and 128 billion edges) in under 10 seconds using a 72-core machine, providing a 3.1x speedup over the fastest existing connectivity result for this graph, in any computational setting. For our incremental algorithms, we show that our algorithms can ingest graph updates at up to several billion edges per second. To guide the user in selecting the best variants in ConnectIt for different situations, we provide a detailed analysis of the different strategies. Finally, we show how the techniques in ConnectIt can be used to speed up two important graph applications: approximate minimum spanning forest and SCAN clustering.

Computer Science↗

DOE OSTI2021

Towards a Unified theory of Fractional and Nonlocal Vector Calculus

Nonlocal and fractional-order models capture effects that classical partial differential equations cannot describe; for this reason, they are suitable for a broad class of engineering and scientific applications that feature multiscale or anomalous behavior. This has driven a desire for a vector calculus that includes nonlocal and fractional gradient, divergence and Laplacian type operators, as well as tools such as Green’s identities, to model subsurface transport, turbulence, and conservation laws. In the literature, several independent definitions and theories of nonlocal and fractional vector calculus have been put forward. Some have been studied rigorously and in depth, while others have been introduced ad-hoc for specific applications. The goal of this work is to provide foundations for a unified vector calculus by (1) consolidating fractional vector calculus as a special case of nonlocal vector calculus, (2) relating unweighted and weighted Laplacian operators by introducing an equivalence kernel, and (3) proving a form of Green’s identity to unify the corresponding variational frameworks for the resulting nonlocal volume-constrained problems. Here, the proposed framework goes beyond the analysis of nonlocal equations by supporting new model discovery, establishing theory and interpretation for a broad class of operators, and providing useful analogues of standard tools from the classical vector calculus.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Nonlinear analog processing with anisotropic nonlinear films

Digital signal processing is the cornerstone of several modern-day technologies, yet in multiple applications it faces critical bottlenecks related to memory and speed constraints. Thanks to recent advances in metasurface design and fabrication, light-based analog computing has emerged as a viable option to partially replace or augment digital approaches. Several light-based analog computing functionalities have been demonstrated using patterned flat optical elements, with great opportunities for integration in compact nanophotonic systems. So far, however, the available operations have been restricted to the linear regime, limiting the impact of this technology to a compactification of Fourier optics systems. In this paper, we introduce nonlinear operations to the field of metasurface-based analog optical processing, demonstrating that nonlinear optical phenomena, combined with nonlocality in flat optics, can be leveraged to synthesize kernels beyond linear Fourier optics, paving the way to a broad range of new opportunities. As a practical demonstration, we report the experimental synthesis of a class of nonlinear operations that can be used to realize broadband, polarization-selective analog-domain edge detection.

analog image processing↗

DOE OSTI2020

Custom NEON AOP reflectance mosaics and maps of shade masks, canopy water content

This mosaic of visible to shortwave infrared (VSWIR) data was derived from the assignable asset NEON AOP radiance data that was collected by LBNL’s Watershed Function SFA during the summer of 2018 (DOI: 10.15485/1617204). This atmospheric correction was completed to take into account site-specific terrain variability in the 334 km2 survey area centered around Crested Butte, CO. The atmospheric correction was completed using ACORN atmospheric correction software executed on 200 x 200 pixel kernels rather than line by line in order to capture local flight altitude conditions. Manual cloud delineation removed any small shaded areas that occurred within the data collection areas. Mosaics were developed based on preference for days that were in close timing proximity to the coincident ground campaign and with mosaicing criteria that minimized the angle between the sun and the sensor to retrieve the most consistent reflectance (min_phase_refl_tiled). Finally, we generated shade masks based on the geometry between the sun angle at time of flight, the ground surface, and the sensor. Here we provide the orthomosaiced estimated reflectance data (min_phase_refl_tiled.tif), canopy water content (wtrl), estimated atmospheric water vapor (wtrv), the observational data (obs) for this particular mosaic, the estimated visibility (vis), shade masks derived from the digital surface elevation model (shade) and the digital terrain model (shade_tch) added to the canopy height model (DOI: 10.15485/1617203), and a wavelength metadata file. Each image file is provided as a GeoTiff with internal tiling and LZW compression. These data can also be found on Google Earth Engine for extraction, download, and analysis of smaller extents (Google Earth Engine data is linked in external link table).

2018 NEON and 2025 CHESS Campaigns↗

DOE OSTI2025

Dataset: "Widespread Drought-driven Declines in Streamflows and Water quality in the Upper Colorado River Basin (1998-2022)"

This data package contains the associated data and scripts for Nagamoto, E., Ombadi, M., Ciulla, F. et al. Widespread drought-driven declines in streamflows and water quality in the Upper Colorado River Basin during 1998-2022. Commun Earth Environ 7, 734 (2026). https://doi.org/10.1038/s43247-026-03890-5. This purpose of this study was to investigate the impact of the 21st century drought on water quantity and quality at catchments throughout the Upper Colorado River Basin (UCRB). We used stream flow, water temperature, specific conductance, air temperature, precipitation, and catchment attribute data for over 200 sites in the UCRB, collected from the National Water Information System using Basin3D (Varadharajan, 2023), GAGESII (Falcone, 2010), and the Google Earth Engine. We identified years of severe drought between 1998 and 2022 using the Standardized Precipitation Evaporation Index (SPEI), then calculated the relative change percentage of the stream flow, water temperature, and specific conductance from drought versus non-drought years. We used the attribute information from GAGESII to investigate what physical traits of catchments are associated streamflow vulnerability (greater relative change) or resilience to drought. We used land cover data from the National Land Cover Database (USGS, 2024) to assess any changes to physical attributes that may not be represented in the static attributes information in GAGESII. To increase data availability, we modeled stream temperature using methods from Willard, 2023. While the study period is water years 1998 to 2022, the raw water quantity and quality data extends to 1950 and the meteorological data extends to 1980. The data and code can be downloaded via the UCRB_drought.zip. Within the zip, the files are organized as follows: - INPUTS: Contains all input data used in UCRB_Drought_Workflow.ipynb - OUTPUTS: Contains all intermediate data created from UCRB_Drought_Workflow.ipynb as well as final products including the calculated Standardized Evapotranspiration Index (SPEI) - climatic_variables: The code used to collect meteorologic data from Google Earth Engine - feature_importance: The code used for the catchment attributes analysis - preprocessing: Code used in UCRB_Drought_Workflow_Preprocessing.ipynb - pyeto: Code used in UCRB_Drought_Workflow_Preprocessing.ipynb - calculations: Code used in UCRB_Drought_Workflow_Impacts.ipynb - plotting: Code used in UCRB_Drought_Workflow_Impacts.ipynb - README.md - UCRB_Drought_Workflow_Preprocessing.ipynb: The code used to prep raw data for the analysis - UCRB_Drought_Workflow_Impact.ipynb: The code which uses the prepped raw data for analysis, and plots all figures - requirements_ucrb-drought_v2.yml: The requirements file to create a virtual environment and Jupyter Lab kernel to run the code The INPUTS folder is organized into the following major directories and sub-directories. The "RDC_WT_SC_RAW" folder contains raw data for streamflow, water temperature, and specific conductance in a ".h5" file. The "NLCD_RAW" folder contains ".csv" files with annual land cover percentages for counties within the UCRB. The "MET_RAW" folder contains a ".csv" file with monthly meteorological data (air temperature and precipitation) for the sites in the UCRB which was obtained from code in the climatic_variables folder. The "GAGESII" folder contains ".csv" files with physical catchment attribute variables for catchments across the country. The "WT_LSTM_data" folder contains ".csv" files with calculated WT (Willard, 2023) and the associated RMSEs. The "Upper_Colorado_River_Basin_Boundary" folder contains geographic data including a shapefile for plotting in the UCRB_Drought_Workflow.ipynb. The "RESERVOIRS_RAW" folder contains ".csv" files for each reservoir in the UCRB with daily reservoir storage. There are also two files in the INPUTS folder that have combined reservoir storage data and reservoir metadata. The OUTPUTS folder is organized into the following major directories and sub-directories. The "RDC_WT_SC_data" folder contains a folder "Water_year" with the associated cleaned data, metadata, and data availability information in ".csv" files, a folder "Median_Relchange" with the relative change comparing drought to non-drought years in ".csv" files, and a folder "Peak95_Min5_Relchange" that has ".csv" files for the relative change in peak (95th %) and minimum (5th %) variables. The "NLCD_data" folder contains the difference in land cover from the beginning to end of the study period and the percentage of the county that is within UCRB bounds can be found in Nagamoto et al (2025)). The "MET_data" folder contains separated monthly air temperature and precipitation data and the calculated PET in ".csv" files. The "SPEI_data" folder contains ".csv" files with calculated SPEI values (one restricted to the study period and the other with information from the entire MET data period). The "Paper_Tables" folder contains two ".csv" files containing site information and data availability and information about the GAGESII trait aggregated categories. The base directory includes the file “flmd.csv” for a list and description of all files and the file “dd.csv” for data dictionaries. Scripts for preprocessing, analysis, and figure generation are located in the associated GitHub repository found at [https://github.com/iNAIADS/drought-impacts/tree/develop/UCRB-drought]. UPDATE 1: Title and code file updated to match submitted manuscript 10-15-2025. UPDATE 2: Code and data files updated to match revised manuscript 3-4-2026. UPDATE 3: Code and data files updated to match revised manuscript 6-7-2026. ** NOTE: DD and FLMD have not been updated yet. UPDATE 4: Added associated Manuscript information and DD and FLMD have been updated. To cite this code, please use the following BibTeX: @misc{nagamoto2025drought, author = {Emily Nagamoto and Fabio Ciulla and Mohammad Ombadi and Jared Willard and Rosemary Carroll and Charuleka Varadharajan}, title = {Dataset: "Widespread Drought-driven Declines in Streamflows and Water quality in the Upper Colorado River Basin (1998-2022)"}, year = {2025}, doi = {10.15485/2551894}, publisher = {ESS-DIVE Repository}, url = {https://data.ess-dive.lbl.gov/datasets/doi:10.15485/2551894} }

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Inference of Induced Fracture Geometries Using Fiber-Optic Distributed Strain Sensing in Hydraulic Fracture Test Site 2

Fiber-optic Distributed Strain Sensor observations in a vertical well allow rapid inference of the time evolution of nearby hydraulic fracture heights and their vertical aperture distributions during stimulation and depressurization. We describe a computationally efficient deconvolutional model based on an elastostatic kernel for fracture opening within an isotropic, homogeneous, linear elastic medium. Furthermore, an application of this model to observations from the Hydraulic Fracture Test Site 2 reveals that ultimate fracture heights are typically greater than those indicated by microseismic monitoring, and some hydraulic fractures continue their upward growth for several hours after high-pressure injections ceased.

58 GEOSCIENCES↗

DOE OSTI2020

Learning to Optimize Variational Quantum Circuits to Solve Combinatorial Problems

Quantum computing is a computational paradigm with the potential to outperform classical methods for a variety of problems. Proposed recently, the Quantum Approximate Optimization Algorithm (QAOA) is considered as one of the leading candidates for demonstrating quantum advantage in the near term. QAOA is a variational hybrid quantum-classical algorithm for approximately solving combinatorial optimization problems. The quality of the solution obtained by QAOA for a given problem instance depends on the performance of the classical optimizer used to optimize the variational parameters. In this paper, we formulate the problem of finding optimal QAOA parameters as a learning task in which the knowledge gained from solving training instances can be leveraged to find high-quality solutions for unseen test instances. To this end, we develop two machine-learning-based approaches. Our first approach adopts a reinforcement learning (RL) framework to learn a policy network to optimize QAOA circuits. Our second approach adopts a kernel density estimation (KDE) technique to learn a generative model of optimal QAOA parameters. In both approaches, the training procedure is performed on small-sized problem instances that can be simulated on a classical computer; yet the learned RL policy and the generative model can be used to efficiently solve larger problems. Furthermore, extensive simulations using the IBM Qiskit Aer quantum circuit simulator demonstrate that our proposed RL- and KDE-based approaches reduce the optimality gap by factors up to 30.15 when compared with other commonly used off-the-shelf optimizers.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

LaplaceInterpolation.jl: A Julia package for fast interpolation on a grid

We implement a linear-time algorithm for interpolation on a regular multidimensional grid in the Julia language. The algorithm is an approximate Laplace interpolation (Press, 1992) when no parameters are given; and when parameters m ∈ Z and ϵ > 0 are set, the interpolant approximates a Matérn kernel, of which radial basis functions and polyharmonic splines are a special case. We implement, in addition, Neumann, Dirichlet (trivial), and average boundary conditions with potentially different aspect ratios in the different dimensions. The interpolant functions in arbitrary dimensions.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

MLMOD: Machine Learning Methods for Data-Driven Modeling in LAMMPS

MLMOD is a software package for incorporating machine learning approaches and models into simulations of microscale mechanics and molecular dynamics in LAMMPS. Recent machine learning approaches provide promising data-driven approaches for learning representations for system behaviors from experimental data and high fidelity simulations. The package facilitates learning and using data-driven models for (i) dynamics of the system at larger spatial-temporal scales (ii) interactions between system components, (iii) features yielding coarser degrees of freedom, and (iv) features for new quantities of interest characterizing system behaviors. MLMOD provides hooks in LAMMPS for (i) modeling dynamics and time-step integration, (ii) modeling interactions, and (iii) computing quantities of interest characterizing system states. The package allows for use of machine learning methods with general model classes including Neural Networks, Gaussian Process Regression, Kernel Models, and other approaches. Here we discuss our prototype C++/Python package, aims, and example usage. For related papers, examples, updates, and additional information see https://github.com/atzberg/mlmod and http://atzberger.org/.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Optimization of Water-Alternating-CO2 Injection Field Operations Using a Machine-Learning-Assisted Workflow

Summary This paper will present a robust workflow to address multiobjective optimization (MOO) of carbon dioxide (CO2)-enhanced oil recovery (EOR)-sequestration projects with a large number of operational control parameters. Farnsworth unit (FWU) field, a mature oil reservoir undergoing CO2 alternating water injection (CO2-WAG) EOR, will be used as a field case to validate the proposed optimization protocol. The expected outcome of this work would be a repository of Pareto-optimal solutions of multiple objective functions, including oil recovery, carbon storage volume, and project economics. FWU’s numerical model is used to demonstrate the proposed optimization workflow. Because using MOO requires computationally intensive procedures, machine-learning-based proxies are introduced to substitute for the high-fidelity model, thus reducing the total computation overhead. The vector machine regression combined with the Gaussian kernel (Gaussian-SVR) is used to construct proxies. An iterative self-adjusting process prepares the training knowledge base to develop robust proxies and minimizes computational time. The proxies’ hyperparameters will be optimally designed using Bayesian optimization to achieve better generalization performance. Trained proxies will be coupled with multiobjective particle swarm Optimization (MOPSO) protocol to construct the Pareto-front solution repository. The outcomes of this workflow will be a repository containing Pareto-optimal solutions of multiple objectives considered in the CO2-WAG project. The proposed optimization workflow will be compared with another established methodology using a multilayer neural network (MLNN) to validate its feasibility in handling MOO with a large number of parameters to control. Optimization parameters used include operational variables that might be used to control the CO2-WAG process, such as the duration of the water/gas injection period, producer bottomhole pressure (BHP) control, and water injection rate of each well included in the numerical model. It is proved that the workflow coupling Gaussian-SVR proxies and the iterative self-adjusting protocol is more computationally efficient. The MOO process is made more rapid by squeezing the size of the required training knowledge base while maintaining the high accuracy of the optimized results. The outcomes of the optimization study show promising results in successfully establishing the solution repository considering multiple objective functions. Results are also verified by validating the Pareto fronts with simulation results using obtained optimized control parameters. The outcome from this work could provide field operators an opportunity to design a CO2-WAG project using as many inputs as possible from the reservoir models. The proposed work introduces a novel concept that couples Gaussian-SVR proxies with a self-adjusting protocol to increase the computational efficiency of the proposed workflow and to guarantee the high accuracy of the obtained optimized results. More importantly, the workflow can optimize a large number of control parameters used in a complex CO2-WAG process, which greatly extends its utility in solving large-scale MOO problems in various projects with similar desired outcomes.

Energy & Fuels↗

DOE OSTI2023

Solving 3d gravity with Virasoro TQFT

We propose a precise reformulation of 3d quantum gravity with negative cosmological constant in terms of a topological quantum field theory based on the quantization of the Teichmüller space of Riemann surfaces that we refer to as “Virasoro TQFT”. This TQFT is similar, but importantly not equivalent, to SL(2, \mathbb{R} ℝ ) Chern-Simons theory. This sharpens the folklore that 3d gravity is related to SL(2, \mathbb{R} ℝ ) Chern-Simons theory into a precise correspondence, and resolves some well-known issues with this lore at the quantum level. Our proposal is computationally very useful and provides a powerful tool for the further study of 3d gravity. In particular, we explain how together with standard TQFT surgery techniques this leads to a fully algorithmic procedure for the computation of the gravity partition function on a fixed topology exactly in the central charge. Mathematically, the relation leads to many nontrivial conjectures for hyperbolic 3-manifolds, Virasoro conformal blocks and crossing kernels.

Collier, Scott↗

DOE OSTI2020

Higher spin partition functions via the quasinormal mode method in de Sitter quantum gravity

In this note we compute the 1-loop partition function of spin- s s fields on Euclidean de Sitter space S^{2n+1} S 2 n + 1 using the quasinormal mode method. Instead of computing the quasinormal mode frequencies from scratch, we use the analytic continuation prescription L_{\text{AdS}}\to iL_{\text{dS}} L AdS → i L dS , appearing in the dS/CFT correspondence, and Wick rotate the normal mode frequencies of fields on thermal \text{AdS}_{2n+1} AdS 2 n + 1 into the quasinormal mode frequencies of fields on de Sitter space. We compare the quasinormal mode and heat kernel methods of calculating 1-loop determinants, finding exact agreement, and furthermore explicitly relate these methods via a sum over the conformal dimension. We discuss how the Wick rotation of normal modes on thermal \text{AdS}_{2n+1} AdS 2 n + 1 can be generalized to calculating 1-loop partition functions on the thermal spherical quotients S^{2n+1}/\mathbb{Z}_{p} S 2 n + 1 / ℤ p . We further show that the quasinormal mode frequencies encode the group theoretic structure of the spherical spacetimes in question, analogous to the analysis made for thermal AdS in [1-3] .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Exploring the unknown Lambda-neutron interaction

No published \Lambda Λ n scattering data exist. A relativistic heavy-ion experiment has suggested that a \Lambda Λ nn bound state was seen. However, several theoretical analyses have cast serious doubt on the bound-state assertion. Nevertheless, there could exist a three-body \Lambda Λ nn resonance. Such a resonance could be used to constrain the \Lambda Λ n interaction. We discuss \Lambda Λ nn calculations using nn and \Lambda Λ n pairwise interactions of rank-one, separable form that fit effective range parameters of the nn system and those hypothesized for the as yet unobserved \Lambda Λ n system based upon four different \Lambda Λ N potentials. The use of rank-one separable potentials allows one to analytically continue the \Lambda Λ nn Faddeev equations onto the second complex energy plane in search of resonance poles, by examining the eigenvalue spectrum of the kernel of the Faddeev equations. Although each of the potential models predicts a \Lambda Λ nn sub-threshold resonance pole, scaling of the \Lambda Λ n interaction by as little as \sim ∼ 5% does produce a physical resonance. This suggests that one may use photo-(electro-)production of the \Lambda Λ nn system from tritium as a tool to examine the strength of the \Lambda Λ n interaction.

Gibson, Benjamin↗

DOE OSTI2022

The photon content of the proton in the CT18 global analysis

Recently, two photon PDF sets based on implementations of the LUX ansatz into the CT18 global analysis were released. In CT18lux, the photon PDF is calculated directly using the LUX master formula for all scales, \mu μ . In an alternative realization, CT18qed, the photon PDF is initialized at the starting scale, \mu_0 μ 0 , using the LUX formulation and evolved to higher scales \mu(>\mu_0) μ ( > μ 0 ) with a combined QED+QCD kernel at \mathcal{O}(\alpha),~\mathcal{O}(\alpha\alpha_s) 𝒪 ( α ) , 𝒪 ( α α s ) and \mathcal{O}(\alpha^2) 𝒪 ( α 2 ) . In the small- x x region, the photon PDF uncertainty is mainly induced by the quark and gluon PDFs, through the perturbative DIS structure functions. In comparison, the large- x x photon uncertainty comes from various low-energy, nonperturbative contributions, including variations of the inelastic structure functions in the resonance and continuum regions, higher-twist and target-mass corrections, and elastic electromagnetic form factors of the proton. We take the production of doubly-charged Higgs pairs, (H^{++}H^{--}) ( H + + H − − ) , as an example of scenarios beyond the Standard Model to illustrate the phenomenological implications of these photon PDFs at the LHC.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Gluon pseudo-distributions at short distances

We present the results that are necessary in the ongoing lattice calculations of the gluon parton distribution functions (PDFs) within the pseudo-PDF approach. We identify the two-gluon correlator functions that contain the invariant amplitude determining the gluon PDF in the light-cone z^2 \to 0 z 2 → 0 limit, and perform one-loop calculations in the coordinate representation in an explicitly gauge-invariant form. Ultraviolet (UV) terms, which contain \ln (-z^2) ln ( − z 2 ) -dependence cancel in the reduced Ioffe-time distribution (ITD), and we obtain the matching relation between the reduced ITD and the light-cone ITD. Using a kernel form, we get a direct connection between lattice data for the reduced ITD and the normalized gluon PDF.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Bilevel Parameter Optimization for Nonlocal Image Denoising Models

We propose a bilevel optimization approach for the determination of parameters in nonlocal image denoising. We consider both spatial weights in front of the fidelity term, as well as weights within the kernel of the nonlocal operator. In both cases we investigate the differentiability of the solution operator in function spaces and derive a first order optimality system that characterizes local minima. For the numerical solution of the problems, we propose a second-order optimization algorithm in combination with a finite element discretization of the nonlocal denoising models and a computational strategy for the solution of the resulting dense linear systems. Several experiments are run in order to show the suitability of our approach.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Exascale Algorithms and Software for Lattice Field Theory in High Energy Physics: Searching Beyond the Standard Model

The Boston University component has focused on the algorithmic development of new Multigrid solver for the critical kernel for the Dirac propagators that dominated the both simulation require for lattice ensemble and the analysis of physical correlation functions. Progress on this has meet the above objects, even exceeding them a bit. The result is the beginning if multiscale lattice QCD applicable to future Exascale hardware and the development of the QUDA software for NVIDIA GPUs to give near optimal performance. As we approach exascale hardware and computation at that scale this provides the infrastructure for further advances.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Sierra/SolidMechanics 4.56 Capabilities In Development

This user's guide documents capabilities in Sierra/SolidMechanics which remain "in-development" and thus are not tested and hardened to the standards of capabilities listed in Sierra/SM 4.56 User's Guide. Capabilities documented herein are available in Sierra/SM for experimental use only until their official release. These capabilities include, but are not limited to, novel discretization approaches such as peridynamics and the reproducing kernel particle method (RKPM), numerical fracture and failure modeling aids such as the extended finite element method (XFEM) and J-integral, explicit time step control techniques, dynamic mesh rebalancing, as well as a variety of new material models and finite element formulations.

97 MATHEMATICS AND COMPUTING↗