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DOE OSTI2021

Twistor Actions for Integrable Systems

Many integrable systems can be reformulated as holomorphic vector bundles on twistor space. This is a powerful organizing principle in the theory of integrable systems. One shortcoming is that it is formulated at the level of the equations of motion. From this perspective, it is mysterious that integrable systems have Lagrangians. In this paper, we study a Chern-Simons action on twistor space and use it to derive the Lagrangians of some integrable sigma models. Our focus is on examples that come from dimensionally reduced gravity and supergravity. The dimensional reduction of general relativity to two spacetime dimensions is an integrable coset sigma model coupled to a dilaton and 2d gravity. The dimensional reduction of supergravity to two spacetime dimensions is an integrable coset sigma model coupled to matter fermions, a dilaton, and 2d supergravity. We derive Lax operators and Lagrangians for these 2d integrable systems using the Chern-Simons theory on twistor space. In the supergravity example, we use an extended setup in which twistor Chern-Simons theory is coupled to a pair of matter fermions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Nyström type exponential integrators for strongly magnetized charged particle dynamics

Solving for charged particle motion in electromagnetic fields (i.e. the particle pushing problem) is a computationally intensive component of particle-in-cell (PIC) methods for plasma physics simulations. This task is especially challenging when the plasma is strongly magnetized due numerical stiffness arising from the wide range of time scales between highly oscillatory gyromotion and long term macroscopic behavior. A promising approach to solve these problems is by a class of methods known as exponential integrators that can solve linear problems exactly and are A-stable. This work extends the standard exponential integration framework to derive Nyström-type exponential integrators that integrates the Newtonian equations of motion as a second-order differential equation directly. In particular, we derive second-order and third-order Nyström-type exponential integrators for strongly magnetized particle pushing problems. Numerical experiments show that the Nyström-type exponential integrators exhibit significant improvement in computation speed over the standard exponential integrators.

general physics↗

DOE OSTI2025

PDB-IHM: A System for Deposition, Curation, Validation, and Dissemination of Integrative Structures

Structures of many large biomolecular assemblies are now being determined using integrative approaches. In these approaches, information derived from multiple experimental and computational methods is combined to compute three-dimensional structures of multi-protein complexes and other macromolecular machines. A standalone prototype data resource for integrative structures called PDB-Dev was built, based on recommendations of the Integrative and Hybrid Methods (IHM) Task Force of the Worldwide Protein Data Bank (wwPDB). This effort included developing data standards and software tools for collecting, curating, validating, visualizing, archiving, and disseminating integrative structures that span diverse spatiotemporal scales and conformational states. Mechanisms have been created to validate integrative structures based on the experimental data underpinning them. Building upon this foundational framework, PDB-Dev has been further expanded to handle large dynamic macromolecular systems and integrative structures that combine, for example, experimental restraints with atomic coordinates computed by machine learning algorithms. Data standards and supporting tools have also been extended to capture information about biomolecular dynamics, such as conformational transitions and related kinetic data derived from biophysical methods. Recently, PDB-Dev was unified with the PDB archive and rebranded as PDB-IHM (pdb-ihm.org), further promoting FAIR (Findable, Accessible, Interoperable, and Reusable) principles of data stewardship for integrative structural biology.

IHMCIF↗

DOE OSTI2022

Integrated control of individual plasma scalars with simultaneous neoclassical tearing-mode suppression

A novel integrated-control architecture has been tested in nonlinear, one-dimensional simulations using the control-oriented transport simulator (COTSIM©) and in DIII-D experiments. Integrated architectures that can perform continuous-mission control while also handling off-normal events will be vital in future reactor-grade tokamaks. Continuous-mission controllers for individual magnetic and kinetic scalars (thermal stored-energy (W), volume-average toroidal rotation (Ω Φ ), and safety factor profile (q) at different spatial locations) have been integrated in this work with event-triggered neoclassical tearing-mode (NTM) suppression controllers by combining them into an architecture augmented by a supervisory and exception handling (S&EH) system and an actuator management (AM) system. Here, the AM system, which enables the integration of competing controllers, solves in real time a nonlinear optimization problem that takes into account the high-level control priorities dictated by the S&EH system. The resulting architecture offers a high level of integration and some of the functionalities that will be required to fulfill the advanced-control requirements anticipated for ITER. Initial simulations using COTSIM suggest that the plasma performance and its MHD stability may be improved under integrated feedback control. In addition, the integrated-control architecture has been implemented in the DIII-D plasma control system and tested experimentally for the first time ever in DIII-D in a high-q min scenario, which is a candidate for steady-state operation in ITER.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2016

Thermal Design and Characterization of Heterogeneously Integrated InGaP/GaAs HBTs

Flip-chip heterogeneously integrated n-p-n InGaP/GaAs heterojunction bipolar transistors (HBTs) with integrated thermal management on wide-bandgap AlN substrates followed by GaAs substrate removal are demonstrated. Without thermal management, substrate removal after integration significantly aggravates self-heating effects, causing poor I–V characteristics due to excessive device self-heating. An electrothermal codesign scheme is demonstrated that involves simulation (design), thermal characterization, fabrication, and evaluation. Thermoreflectance thermal imaging, electrical-temperature sensitive parameter-based thermometry, and infrared thermography were utilized to assess the junction temperature rise in HBTs under diverse configurations. In order to reduce the thermal resistance of integrated devices, passive cooling schemes assisted by structural modification, i.e., positioning indium bump heat sinks between the devices and the carrier, were employed. By implementing thermal heat sinks in close proximity to the active region of flip-chip integrated HBTs, the junction-to-baseplate thermal resistance was reduced over a factor of two, as revealed by junction temperature measurements and improvement of electrical performance. In conclusion, the suggested heterogeneous integration method accounts for not only electrical but also thermal requirements providing insight into realization of advanced and robust III–V/Si heterogeneously integrated electronics.

36 MATERIALS SCIENCE↗

DOE OSTI2016

Resonance Parameter Adjustment Based on Integral Experiments

Our project seeks to allow coupling of differential and integral data evaluation in a continuous-energy framework and to use the generalized linear least-squares (GLLS) methodology in the TSURFER module of the SCALE code package to update the parameters of a resolved resonance region evaluation. We recognize that the GLLS methodology in TSURFER is identical to the mathematical description of a Bayesian update in SAMMY, the SAMINT code was created to use the mathematical machinery of SAMMY to update resolved resonance parameters based on integral data. Traditionally, SAMMY used differential experimental data to adjust nuclear data parameters. Integral experimental data, such as in the International Criticality Safety Benchmark Experiments Project, remain a tool for validation of completed nuclear data evaluations. SAMINT extracts information from integral benchmarks to aid the nuclear data evaluation process. Later, integral data can be used to resolve any remaining ambiguity between differential data sets, highlight troublesome energy regions, determine key nuclear data parameters for integral benchmark calculations, and improve the nuclear data covariance matrix evaluation. Moreover, SAMINT is not intended to bias nuclear data toward specific integral experiments but should be used to supplement the evaluation of differential experimental data. Using GLLS ensures proper weight is given to the differential data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2013

Review of Variable Generation Integration Charges

The growth of wind and solar generation in the United States, and the expectation of continued growth of these technologies, dictates that the future power system will be operated in a somewhat different manner because of increased variability and uncertainty. A small number of balancing authorities have attempted to determine an 'integration cost' to account for these changes to their current operating practices. Some balancing authorities directly charge wind and solar generators for integration charges, whereas others add integration charges to projected costs of wind and solar in integrated resource plans or in competitive solicitations for generation. This report reviews the balancing authorities that have calculated variable generation integration charges and broadly compares and contrasts the methodologies they used to determine their specific integration charges. The report also profiles each balancing authority and how they derived wind and solar integration charges.

14 SOLAR ENERGY↗

DOE OSTI2014

Integrated Nuclear-Renewable Energy Systems: Foundational Workshop Report

The U.S. Department of Energy (DOE) recognizes the need to transform the energy infrastructure of the U.S. and elsewhere to systems that can drastically reduce environmental impacts in an efficient and economically viable manner while utilizing both hydrocarbon resources and clean energy generation sources. Thus, DOE is supporting research and development that could lead to more efficient utilization of clean energy generation sources, including renewable and nuclear options. A concept being advanced by the DOE Offices of Nuclear Energy (NE) and Energy Efficiency and Renewable Energy (EERE) is tighter coupling of nuclear and renewable energy sources in a manner that produces new energy currency for the combined electricity grid, industrial manufacturing, and the transportation energy sectors. This integration concept has been referred to as a “hybrid system” that is capable of providing the right type of energy, at the right time, in the right place. At the direction of DOE-NE and DOE-EERE leadership, project leads at Idaho National Laboratory (INL), National Renewable Energy Laboratory (NREL) and Massachusetts Institute of Technology (MIT) have identified and engaged stakeholders in discussing integrated energy systems that would optimize renewable and nuclear energy integration on a region-by-region basis. Subsequent work will entail conduct of technical, economic, environmental and socio-political evaluations of the leading integrated system options based on a set of criteria established with stakeholder input. The Foundational Workshop for Integrated Nuclear – Renewable Energy Systems was organized around the following objectives: 1. Identify and refine priority region-specific opportunities for integrated nuclear-renewable energy systems in the U.S.; 2. Select Figures of Merit (FOM) to rank and prioritize candidate systems; 3. Discuss enabling technology development needs; 4. Identify analysis requirements, capabilities and gaps to estimate FOM for integrated system options; 5. Identify experimental needs to develop and demonstrate nuclear-renewable energy systems.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

Technical and Economic Assessment and Gap Analysis of Advanced Nuclear Reactor Integration with a Reference Oil Refinery

Efforts to identify the most-economic methods to decarbonize several sectors of the U.S. economy are underway. Industrial processes such as crude-oil refining rely heavily on energy-dense and easily stored and transported fossil fuels for powering their operations. Refineries use large amounts of energy, primarily derived from fossil sources to separate crude-oil components, break down heavier hydrocarbons into lighter compounds, remove impurities, reform hydrocarbon molecules, and generate steam and electricity for pumps and compressors and other various auxiliary systems. Crude-oil refining operations such as distillation, cracking, desulfurization, reforming, utilities systems and some offsite facilities collectively account for most of the energy consumption. Other operations such as hydrocracking or hydrotreating also require hydrogen for developing hydrogenation reactions which involve substantial heating to keep the reactors at high-temperature and pressure levels. All heat and energy demands are typically provided by natural gas (NG), oil, or other fuels, which makes refinery industry one of the most-difficult sectors to decarbonize. Nuclear power is a viable and energy-dense source of clean electricity, heat, and hydrogen to provide the large, sustainable energy supply that the refining industry demands. The U.S. Department of Energy’s (DOE’s) Integrated Energy Systems (IES) program is working to perform research and development, design, economic siting, and risk analysis. This state-of-the-art work will enable the first on-site demonstrations and commercial deployments of advanced small modular nuclear reactors (SMNRs) integrated with industries such as chemical production, refining, iron and steel making, and more. IES seeks to demonstrate the ability of advanced nuclear reactors to meet the heat and power demands of these industries while reducing carbon emissions in a sustainable and cost-competitive way. The primary objective of this research effort is to analyze industrial-scale SMNR integration intended to decarbonize refining facilities. The foreseen outcome is the provision of reliable, cost-competitive, and sustainable clean energy, alongside a reduction of carbon emissions. Specifically, the focus of this work lies on meeting the reference facilities’ heat and electricity demands with nuclear power while also supplying clean hydrogen via integrated high-temperature steam electrolysis (HTSE). This report presents a comprehensive technical and economic assessment of the integration of advanced nuclear reactors into a reference refinery, leveraging financial incentives from the Inflation Reduction Act (IRA). The evaluation aims to explore the potential economic benefits and challenges associated with incorporating advanced nuclear reactors into refinery operations, particularly in terms of energy efficiency, economic implications and environmental impact. By examining both the technical feasibility and economic viability, this analysis seeks to identify existing gaps and propose solutions for successful nuclear integration implementation. The findings are intended to provide valuable insights for stakeholders considering the adoption of advanced nuclear reactors in the refining sector. A refinery reference-plant was developed, using an open-source refinery model, Petroleum Refinery Lifecycle Inventory Model (PRELIM) and expert assessment, as a base case for comparison with various nuclear integration options. The capacity of 100 kbd/day (KBD) of heavy crude-oil feed was selected to represent a general coking-type refinery with deep conversion capabilities (incorporating heavy-oil upgrading with FCC, coking, and associated hydrotreating process units), using a heavy crude-oil feed, which represents about 70% of U.S. refineries configurations. A summary of all cases considered in this study is shown in Table 1.

13 HYDRO ENERGY↗

DOE OSTI2020

Integrated Transmission-and-Distribution System Modeling of Power Systems: State-of-the-Art and Future Research Directions

Integrated transmission-and-distribution (T&D) modeling is a new and developing method for simulating power systems. Interest in integrated T&D modeling is driven by the changes taking place in power systems worldwide that are resulting in more decentralized power systems with increasingly high levels of distributed energy resources. Additionally, the increasing role of the hitherto passive energy consumer in the management and operation of power systems requires more capable and detailed integrated T&D modeling to understand the interactions between T&D systems. Although integrated T&D modeling has not yet found widespread commercial application, its potential for changing the decades-old power system modeling approaches has led to several research efforts in the last few years that tried to (i) develop algorithms and software for steady-state and dynamic modeling of power systems and (ii) demonstrate the advantages of this modeling approach compared with traditional, separated T&D system modeling. In this paper, we provide a review of integrated T&D modeling research efforts and the methods employed for steady-state and dynamic modeling of power systems. We also discuss our current research in integrated T&D modeling and the potential directions for future research. This paper should be useful for power systems researchers and industry members because it will provide them with a critical summary of current research efforts and the potential topics where research efforts are needed to further advance and demonstrate the utility of integrated T&D modeling.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS2014

Reflections on Centaur Upper Stage Integration by the NASA Lewis (Glenn) Research Center

The NASA Glenn (then Lewis) Research Center (GRC) led several expendable launch vehicle (ELV) projects from 1963 to 1998, most notably the Centaur upper stage. These major, comprehensive projects included system management, system development, integration (both payload and stage), and launch operations. The integration role that GRC pioneered was truly unique and highly successful. Its philosophy, scope, and content were not just invaluable to the missions and vehicles it supported, but also had significant Agencywide benefits. An overview of the NASA Lewis Research Center (now the NASA Glenn Research Center) philosophy on ELV integration is provided, focusing on Atlas/Centaur, Titan/Centaur, and Shuttle/Centaur vehicles and programs. The necessity of having a stable, highly technically competent in-house staff is discussed. Significant depth of technical penetration of contractor work is another critical component. Functioning as a cohesive team was more than a concept: GRC senior management, NASA Headquarters, contractors, payload users, and all staff worked together. The scope, content, and history of launch vehicle integration at GRC are broadly discussed. Payload integration is compared to stage development integration in terms of engineering and organization. Finally, the transition from buying launch vehicles to buying launch services is discussed, and thoughts on future possibilities of employing the successful GRC experience in integrating ELV systems like Centaur are explored.

Launch Vehicle↗

NASA NTRS2018

An Integrated Platform for Mission Performance: Goddard Space Flight Center's Meta Information System

Successful management of NASA Goddard Space Flight Centers portfolio of mission projects (i.e. spacecraft, spacecraft instruments / subsystems, and ground systems) depends upon numerous processes, data and information resources coming together throughout the life-cycle of the projects to enable sound decision-making, risk reduction, conformance with requirements and continual improvement. In the summer of 2012, GSFC SMA management recognized that the set of legacy data systems used to support the SMA mission and responsibilities at GSFC were not effective, integrated nor on par with best practices. Accordingly, GSFC SMA management launched a project to transform the GSFC electronic management system to create and deploy an integrated, state-of-the-market information system for process performance, data management and analytics that is currently operating in support of GSFC overall mission performance. The information system, known as Meta, provides controlled, process-based applications, integrated data management, and analytics for a robust set of integrated applications. Since the inception of the project, a lean, award-winning SMA project team has thus far designed, configured and managed the system to serve as an integrated platform for 18 applications that support key processes for GSFC and the Science Mission Directorate at NASA headquarters, such as internal Management System assessments, Supplier Assessments, Supplier Research & Analysis, Problem Reporting for in-house mission projects, On-orbit Anomaly Reporting for GSFC-operated spacecraft, GSFC Project Life-Cycle Reviews, Risk Management and Reporting, and SMA Project Team Reporting. The system has experienced steady growth in utilization with 1,917 users (NASA employees and support contractor personnel) and 44 gigabytes of data and related files managed by the system as of the end of April 2018. Overall, Meta has achieved increasing levels of process management and real-time data / information integration to enable improved process performance, richer analytics and informed decision-making. This paper will present and examine the need, goals, approach and design driving the management and operation of the Meta information system and its ongoing growth as an integrated platform for advancing NASA mission performance.

Integration↗

DOE OSTI2016

Modeling the Value of Integrated Canadian and U.S. Power Sector Expansion

The United States and Canada power systems are not isolated. Cross-border transmission and coordination of system operation create an interconnected power system, which results in combined imports and exports of electricity of greater than 70 TWh per year [1]. Currently, over 5 GW of new international transmission lines are in various stages of permitting and development. These lines may enable greater integration and coordination of the U.S. and Canada systems, which can in turn reduce challenges associated with integration of high penetrations of variable renewables. Furthermore, low-cost Canadian resources, such as wind and hydro, could contribute to compliance with the EPA's recently released Clean Power Plan. Improving integration and coordination internationally will reduce the costs of accessing these resources. This analysis work build on previous work by Ibanez and Zinaman [2]. In this work we seek to better understand the value of additional interconnection between the U.S. and Canadian power systems. Specifically, we quantify the value of additional interconnection and coordination within the Canadian-US integrated power system under scenarios in which large reductions (>80%) in power sector CO2 emissions are achieved. We explore how the ability to add additional cross-border transmission impacts capacity investment, the generation mix, system costs, and the ability of the system to integrate variable renewable energy into the power system. This analysis uses the Regional Energy Deployment System (ReEDS) capacity expansion model [3], [4] to quantify the value of the integrated power system expansion of the United States and Canada. ReEDS is an optimization model that assesses the deployment and operation (including transmission) of the electricity sector of the contiguous United States and Canadian provinces from 2016 through 2050. It has the ability to model the integration of renewable energy technologies into the grid. ReEDS captures renewable energy resources through the use of 356 individual resource regions and 134 balancing areas across the U.S. and is able to handle renewable energy issues such as variability in wind and solar output, transmission costs and constraints, and ancillary services requirements.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2016

Evaluating marginal likelihood with thermodynamic integration method and comparison with several other numerical methods

Evaluating marginal likelihood is the most critical and computationally expensive task, when conducting Bayesian model averaging to quantify parametric and model uncertainties. The evaluation is commonly done by using Laplace approximations to evaluate semianalytical expressions of the marginal likelihood or by using Monte Carlo (MC) methods to evaluate arithmetic or harmonic mean of a joint likelihood function. This study introduces a new MC method, i.e., thermodynamic integration, which has not been attempted in environmental modeling. Instead of using samples only from prior parameter space (as in arithmetic mean evaluation) or posterior parameter space (as in harmonic mean evaluation), the thermodynamic integration method uses samples generated gradually from the prior to posterior parameter space. This is done through a path sampling that conducts Markov chain Monte Carlo simulation with different power coefficient values applied to the joint likelihood function. The thermodynamic integration method is evaluated using three analytical functions by comparing the method with two variants of the Laplace approximation method and three MC methods, including the nested sampling method that is recently introduced into environmental modeling. The thermodynamic integration method outperforms the other methods in terms of their accuracy, convergence, and consistency. The thermodynamic integration method is also applied to a synthetic case of groundwater modeling with four alternative models. The application shows that model probabilities obtained using the thermodynamic integration method improves predictive performance of Bayesian model averaging. As a result, the thermodynamic integration method is mathematically rigorous, and its MC implementation is computationally general for a wide range of environmental problems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Introducing “ The Integrator ”: A novel technique to monitor environmental flow systems

Abstract We introduce “ The Integrator ,” a novel technique to quantify transport and reaction metrics commonly used to characterize flow systems. This development consists of two products: (1) The Integrator sampling device and (2) its supporting mathematical framework, which is compatible with semi‐continuous sensor data. The use of The Integrator device simplifies the logistics of sample collection and greatly reduces the number of samples needed, making it ideal to characterize systems that are: (1) difficult to access, (2) large and thus intractable or highly heterogeneous, and (3) highly instrumented otherwise but where a more holistic, mechanistic understanding may be gained by monitoring one or more currently untracked elements. We tested and validated The Integrator technique using experimental data collected from a heart rate monitor (high‐quality, high‐frequency data in response to known excitation events) and solute tracer experiments conducted in two contrasting (fourth and seventh order) rivers. In the Supporting Information , we provide details concerning the design of The Integrator device used in our field case studies and provide insight into potential improvements. Despite our case studies focus on the analysis of conservative and reactive transport of solutes in rivers, the principles behind The Integrator technique can be used to monitor water quality in hyporheic zones, aquifers, wetlands, swamps, karsts, oceans, wastewater treatment plants, pipe networks, and air quality. Furthermore, special arrangements of Integrator devices can be used to gather data at spatial and temporal resolutions that are currently unattainable due to high transportation and/or personnel costs.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Decomposition of Feynman integrals by multivariate intersection numbers

We present a detailed description of the recent idea for a direct decomposition of Feynman integrals onto a basis of master integrals by projections, as well as a direct derivation of the differential equations satisfied by the master integrals, employing multivariate intersection numbers. We discuss a recursive algorithm for the computation of multivariate intersection numbers, and provide three different approaches for a direct decomposition of Feynman integrals, which we dub the straight decomposition, the bottom-up decomposition, and the top-down decomposition. These algorithms exploit the unitarity structure of Feynman integrals by computing intersection numbers supported on cuts, in various orders, thus showing the synthesis of the intersection-theory concepts with unitarity-based methods and integrand decomposition. We perform explicit computations to exemplify all of these approaches applied to Feynman integrals, paving a way towards potential applications to generic multi-loop integrals.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Amplitudes, supersymmetric black hole scattering at $\mathcal{O}\left({G}^5\right)$, and loop integration

We compute the potential-graviton contribution to the scattering amplitude, the radial action, and the scattering angle of two extremal black holes in $\mathcal{N}$ = 8 supergravity at the fifth post-Minkowskian order and to next-to-leading order in a large mass expansion (first self-force order). Properties of classical unitarity cuts allow us to focus on the integration-by-parts reduction of planar integrals, while nonplanar integrals at this order are obtained from the planar ones by straightforward manipulations. We present the solution to the differential equations for all master integrals necessary to evaluate the classical scattering amplitudes of massive scalar particles at this order in all gravitational theories, in particular in $\mathcal{N}$ = 8 supergravity, and in general relativity. Despite the appearance of higher-weight generalized polylogarithms and elliptic functions in the solution to the differential equation for master integrals, the final supergravity answer is remarkably simple and contains only (harmonic) polylogarithmic functions up to weight 2. The systematic analysis of elliptic integrals discussed here, as well as the particular organization of boundary integrals in $\mathcal{N}$ = 8 observables are independent of supersymmetry and may have wider applications, including to aspects of collider physics.

Black Holes↗

DOE OSTI2021

Scaled boundary cubature scheme for numerical integration over planar regions with affine and curved boundaries

This paper introduces the scaled boundary cubature (SBC) scheme for accurate and efficient integration of functions over polygons and two-dimensional regions bounded by parametric curves. Over two-dimensional domains, the SBC method reduces integration over a region bounded by m curves to integration over m regions (referred to as curved triangular regions), where each region is bounded by two line segments and a curve. With proper (counterclockwise) orientation of the boundary curves, the scheme is applicable to convex and nonconvex domains. Additionally, for star-convex domains, a tensor-product cubature rule with positive weights and integration points in the interior of the domain is obtained. If the integrand is homogeneous, we show that this new method reduces to the homogeneous numerical integration scheme; however, the SBC scheme is more versatile since it is equally applicable to both homogeneous and non-homogeneous functions. This paper also introduces several methods for smoothing integrands with point singularities and near-singularities. When these methods are used, highly efficient integration of weakly singular functions is realized. Finally, the SBC method is applied to a number of benchmark problems, which reveal its broad applicability and superior performance (in terms of time to generate a rule and accuracy per cubature point) when compared to existing methods for integration.

42 ENGINEERING↗