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At least 451 records · Page 25

Final Report of the Project "From the finite element method to the virtual element method"

The Finite Element Method (FEM) is a powerful numerical tool that is being used in a large number of engineering applications. The FEM is constructed on triangular/tetrahedral and quadrilateral/hexahedral meshes. Extending the FEM to general polygonal/polyhedral meshes in straightforward way turns out to be extremely difficult and leads to very complex and computationally expensive schemes. The reason for this failure is that the construction of the basis functions on elements with a very general shape is a non-trivial and complex task. In this project we developed a new family of numerical methods, dubbed the Virtual Element Method (VEM) for the numerical approximation of partial differential equations (PDE) of elliptic type suitable to polygonal and polyhedral unstructured meshes. We successfully formulated, implemented and tested these methods and studied both theoretically and numerically their stability, robustness and accuracy for diffusion problems, convection-reaction-diffusion problems, the Stokes equations and the biharmonic equations.

97 MATHEMATICS AND COMPUTING↗

Design, analysis and numerical experiments for the virtual element p and hp approximations of elliptic eigenvalue problems

We discuss the p- and the hp-versions of the virtual element method for the approximation of the eigenvalues of elliptic operators with a potential term on polygonal meshes. An application of this model is provided by the Schr¨odinger equation with a pseudo-potential term. We present in details the analysis of the p-version of the method, proving the exponential convergence in the case of analytic eigenfunctions. The theoretical results are supplied with a wide set of experiments. We also show numerically that, in the case of eigenfunctions with finite Sobolev regularity, an exponential approximation of the eigenvalues in terms of the cubic root of the number of degrees of freedom can be obtained by employing hp-refinements. Importantly, the geometric flexibility of polygonal meshes is exploited in the construction of the hp-spaces.

97 MATHEMATICS AND COMPUTING↗

A Virtual Element Method for the Full MHD system

In this manuscript we present a novel discretization for the incompressible MHD system. Our approach follows the framework of the Virtual Element Method and offers two main advantages. The method can be implemented in unstructured meshes making it highly versatile and capable of handling a wide array of problems involving interfaces, free-boundaries or adaptive refinements on the mesh. The second advantage involves the divergence of the magnetic field, our approach guarantees that it remains solenoidal. We include a theoretical proof of the condition on the magnetic field as well as energy estimates and a well-posedness study. The latter sheds light as to the stability properties of the method.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Virtual Power Plants and Energy Justice

The Federal Energy Regulatory Commission's (FERC) Order 2222, issued in September 2020, removes barriers for distributed energy resources (DERs) to participate in wholesale energy markets by allowing DERs to aggregate and participate in wholesale markets as a single entity, known as a virtual power plant (VPP). VPPs can provide balancing, reliability, and resiliency grid services and can participate in capacity, energy and ancillary services markets. They can also increase customer energy access and lower electricity bills. This report focuses on VPP business models, including considerations of energy justice (EJ). Through an analysis of the VPP value chain, business models, programs, and pilots, several VPP applications are identified and grouped by their ability to have quantitatively measurable or monetized benefits. Benefits and barriers specific to underserved communities are outlined, and VPP programs with an intentional focus on underserved communities are compared to those without such a focus.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Virtual Resource Management Framework (CRADA Final Report)

There is a need for advanced and widespread business automation within the nuclear industry to drive down operational costs while sustaining or improving safe operations. While there are many business process automation platforms commercially available, the difficulty is that business processes typically rely on a mixture of resource types to accomplish the desired activities and there is no universal software framework virtualizing diverse resource types for the purpose of automation. In this context, we are referring to any capability, physical or intangible, that can be used by an organization to achieve its objectives as a resource. To deploy business automation broadly and enable integrated operations for nuclear (ION), a framework is needed to represent all resource types and their associated disparate data within a plant and to enable seamless flow of resource information to the technologies used for process automation and resource optimization.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Final Technical Report (FTR) - DE-EE0009084: Prefabricated Construction: Guidance, Technical Assistance, and Virtual Inspections

This final technical report summarizes research, case studies, and resources developed from 2020–2025 on prefabricated construction and remote virtual inspections. It documents key findings on benefits, challenges, and best practices, highlights examples from multiple states, and provides guidance to support wider adoption of these innovations in the construction sector.

99 GENERAL AND MISCELLANEOUS↗

Virtual Power Plants and Distributed Energy Resource Management Systems

Virtual Power Plants (VPPs) are aggregations of DERs that can balance electrical loads and provide utility-scale and utility-grade grid services like a traditional power plant. This presentation covers VPP definition, State-of-the-Art, Grid Architectures, Example VPP studies, VPP Standards, and VPP Roadmap.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Virtual Power Plant Architecture and Resilient Design

Virtual Power Plants (VPPs) represent a fundamental shift in electric grid operations, aggregating distributed energy resources (DERs) such as solar panels and battery storage to deliver utility-scale grid services traditionally provided by centralized power plants. This report examines the unique architectural, operational, and digital assurance considerations that distinguish VPPs from conventional utility infrastructure as they scale from pilot projects to mainstream deployment across the United States. While VPPs offer significant opportunities for grid modernization and enhanced flexibility, their distributed, multi-stakeholder architecture introduces distinct security challenges that differ fundamentally from traditional generation facilities. The analysis identifies risks in VPP operations, including device-level security gaps, platform vulnerabilities, and communication protocol weaknesses that create expanded attack surfaces compared to centralized power plants. Through examination of real-world incidents and emerging threat patterns, the report demonstrates how some VPPs' reliance on consumer-owned devices, public internet infrastructure, and complex vendor ecosystems require new approaches to digital assurance and operational security. The findings provide practical guidance for utilities, regulators, and aggregators to implement robust security frameworks and operational best practices essential for maintaining grid reliability as VPP deployment accelerates under the Federal Energy Regulatory Commission (FERC) Order 2222 and related regulatory initiatives.

24 - POWER TRANSMISSION AND DISTRIBUTION↗

Drugsniffer: An Open Source Workflow for Virtually Screening Billions of Molecules for Binding Affinity to Protein Targets

The SARS-CoV2 pandemic has highlighted the importance of efficient and effective methods for identification of therapeutic drugs, and in particular has laid bare the need for methods that allow exploration of the full diversity of synthesizable small molecules. While classical high-throughput screening methods may consider up to millions of molecules, virtual screening methods hold the promise of enabling appraisal of billions of candidate molecules, thus expanding the search space while concurrently reducing costs and speeding discovery. Here, we describe a new screening pipeline, called drugsniffer, that is capable of rapidly exploring drug candidates from a library of billions of molecules, and is designed to support distributed computation on cluster and cloud resources. As an example of performance, our pipeline required ~40,000 total compute hours to screen for potential drugs targeting three SARS-CoV2 proteins among a library of ~3.7 billion candidate molecules.

59 BASIC BIOLOGICAL SCIENCES↗

Realistic Noise Generation to Enhance Realism of Virtual Lidar Scans

Many real-world phenomena corrupt light detection and ranging (lidar) measurements, such as laser energy attenuation, variations in aerosol concentration and composition with height, and hard target returns. Accurate studies of lidar scans using virtual lidar methods should include some realistic model of these corrupting effects to generate more realistic simulations of lidar scans. We present a simple model that characterizes noise caused by energy attenuation and aerosol stratification. The model requires limited inputs and is developed for a Halo Photonics Streamline XR lidar but is readily generalizable for other lidar systems. A critical component of this model is a model of the standard deviation of measured wind speed as a function of the backscattered signal’s signal-to-noise ratio. We derive a general model for this behavior that can be adapted to different scan settings.

17 WIND ENERGY↗

Virtual element approximations of the time-fractional nonlinear convection-diffusion equation on polygonal meshes

We extend the Virtual Element Method to a two-dimensional unsteady nonlinear convection-diffusion equation characterized by a fractional-order derivative with respect to the time variable. Our methodology is based on three fundamental technical components: a fractional version of the Grunwald-Letnikov approximation, discrete maximal regularity, and the regularity theory associated with non-linearity. We prove the method's well-posedness, i.e., the approximate solution's existence and uniqueness to the time-fractional convection-diffusion equation with a Lipschitz nonlinear source term. The fully discrete scheme inherently maintains stability and consistency by leveraging the discrete maximal regularity and the energy projection operator. The convergence in the L 2 -norm and H 1 -norm to various mesh configurations is validated by numerical results, underlining the practical effectiveness of the proposed method.

97 MATHEMATICS AND COMPUTING↗

Virtual Control Systems Environment (VCSE)

Will Atkins, a Sandia National Laboratories computer engineer discusses cybersecurity research work for process control systems. Will explains his work on the Virtual Control Systems Environment project to develop a modeling and simulation framework of the U.S. electric grid in order to study and mitigate possible cyberattacks on infrastructure.

97 MATHEMATICS AND COMPUTING↗

Computer Assisted Virtual Environment - CAVE

Research at the Center for Advanced Energy Studies is taking on another dimension with a 3-D device known as a Computer Assisted Virtual Environment. The CAVE uses projection to display high-end computer graphics on three walls and the floor. By wearing 3-D glasses to create depth perception and holding a wand to move and rotate images, users can delve into data.

3D↗

Design and Performance Testing of a Linear Array of Position-Sensitive Virtual Frisch-Grid CdZnTe Detectors for Uranium Enrichment Measurements

Abstract— Arrays of position-sensitive virtual Frisch-grid CdZnTe (CZT) detectors with enhanced energy resolution have been proposed for spectroscopy and imaging of gamma-ray sources in different applications. The flexibility of the array design, which can employ CZT crystals with thicknesses up to several centimeters in the direction of electron drift, allows for integration into different kinds of field-portable instruments. These can include small hand-held devices, compact gamma cameras and large field-of-view imaging systems. In this work, we present results for a small linear array of such detectors optimized for the low-energy region, 50-400 keV gamma-rays, which is principally intended for incorporation into hand-held instruments. There are many potential application areas for such instruments, including uranium enrichment measurements, storage monitoring, dosimetry and other safeguards-related tasks that can benefit from compactness and isotope-identification capability. The array described here provides a relatively large area with a minimum number of readout channels, which potentially allows the developers to avoid using an ASIC-based electronic readout by substituting it with hybrid preamplifiers followed by digitizers. The array prototype consists of six (5x5.7x25 mm3) CZT detectors positioned in a line facing the source to achieve a maximum exposure area (~10 cm2). Each detector is furnished with 5 mm-wide charge-sensing pads placed near the anode. The pad signals are converted into X-Y coordinates for each interaction event, which are combined with the cathode signals (for determining the Z coordinates) to give 3D positional information for all interaction points. This information is used to correct the response non-uniformity caused by material inhomogeneity, which therefore allows the usage of standard-grade (unselected) CZT crystals, while achieving high-resolution spectroscopic performance for the instrument. In this presentation we describe the design of the array, the results from detailed laboratory tests, and preliminary results from measurements taken during a field test.

36 MATERIALS SCIENCE↗

A Reduced-Order Aggregated Model for Parallel Inverter Systems with Virtual Oscillator Control: Preprint

This paper introduces a reduced-order aggregated model for parallel-connected inverters controlled with virtual oscillator control (VOC). The premise of VOC is to modulate inverter dynamics to emulate those of nonlinear oscillators with the goal of realizing a stable ac microgrid in the absence of communication, synchronous generation, or a stiff grid. To obtain a reduced-order model for a system of parallel-connected inverters with VOC, we first formulate a set of scaling laws that describe how the controller and filter parameters of a given inverter depend on its voltage and power rating. Subsequently, we show that N parallel inverters which adhere to this scaling law can be modeled with the same structure and hence the same computational burden of the model of a single inverter. The proposed aggregate model is experimentally validated on a system of three parallel inverters with heterogeneous power ratings.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Stochastic Virtual Battery Modeling of Uncertain Electrical Loads using Variational Autoencoder

Effective utilization of flexible loads for grid services, while satisfying end-user preferences and constraints, requires an accurate estimation of the aggregated predictive flexibility offered by the electrical loads. Recently, there have been efforts to quantify the predictive flexibility of thermostatic loads (e.g. residential air-conditioners, electric water-heaters) using the notion of virtual battery (VB), whose state evolution is governed by a first order dynamics including self-dissipation rate, and power and energy capacities. Identifying the VB model parameters for a collection of thermostatic loads, however, is challenging primarily due to uncertainties and lack of information regarding the end-user behavior, underlying device models and parameters. In this paper, we propose a \textit{variational autoencoder}-based deep learning algorithm to identify the parameters of the VB model. Using available sensors and meters data, the proposed algorithm generates not only point estimates of the VB parameters, but also confidence intervals around those values. Effectiveness of the proposed frameworks is demonstrated on a collection of electric water-heater loads, whose operation is driven by uncertain water usage profiles.

virtual battery, deep learning algorithms↗