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At least 613 records · Page 34

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↗

Sierra/SolidMechanics 5.0 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 5.0 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 conforming reproducing kernel (CRK) method, numerical fracture and failure modeling aids such as the extended finite element method (XFEM) and $\textit{J}$-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↗

Sierra/SolidMechanics 5.2 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 5.2 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 the conforming reproducing kernel (CRK) method, 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.

42 ENGINEERING↗

Initial framework for engineering-scale statistical creep-fatigue modeling

This report describes the integration of new solid and interface-cohesive mechanics systems into MOOSE. The purpose of these new systems is to support the ability of MOOSE to run full-field crystal plasticity finite element method simulations of key material processes in high temperature metallic materials. These simulations could be used to help accurately predict the performance of key high temperature structural materials in future advanced nuclear reactor components. Previous work implemented preliminary versions of many of these systems in MOOSE Apps. The current work reports on their integration into the main MOOSE tensor mechanics module along with associated improvements to the basic formulations and numerical implementations. Finally, the report provides an example of the full-field crystal plasticity simulations now possible in MOOSE, including examples of realistic geometries requiring millions of degrees of freedom to resolve the microstructural features and macroscale geometry.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Sierra/SolidMechanics 5.4 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 5.4 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 the conforming reproducing kernel (CRK) method, 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.

74 ATOMIC AND MOLECULAR PHYSICS↗

Sierra/SolidMechanics 5.6 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 5.6 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 the conforming reproducing kernel (CRK) method, 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↗

Sierra/SolidMechanics 5.8 In-Development Manual

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 5.8 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 the conforming reproducing kernel (CRK) method, 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.

42 ENGINEERING↗

Sierra/SolidMechanics 5.10 In-Development Manual

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 5.10 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 the conforming reproducing kernel (CRK) method, 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.

42 ENGINEERING↗

Sierra/SolidMechanics 5.16 Capabilities in Development Manual

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 5.16 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 the conforming reproducing kernel (CRK) method, 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↗

Assessment of Existing OpenStudio Measures: Reviews, Interviews, and Future Developments

OpenStudio Measure development is continuously in progress and greatly propelled by the collaborative efforts within the building energy modeling community. To ensure the widespread adoption and benefit of OpenStudio Measures, developers must understand the current status of Measure development and the needs of OpenStudio Measure users. The first step involves a comprehensive review of existing content to prevent redundancy and gain insights into how OpenStudio Measures are used in the building energy modeling community. This knowledge can then be integrated into the Measure development process, and the expertise of practitioners and OpenStudio Measure users can be leveraged to shape future Measures. Numerous OpenStudio Measures have been created and shared on the Building Component Library (BCL). The BCL is an open-source repository housing various OpenStudio-related resources, including building component blocks, descriptive metadata, and Measures describing modifications to building energy models. The OpenStudio Measures in BCL encompass a wide range of energy conservation Measures from basic lighting power reduction to complex HVAC model transformation. They also enable users to generate customized reports and facilitate the integration of energy simulation with other analytical processes. This report presents review of 272 currently available OpenStudio Measures in BCL. The OpenStudio Measures were reviewed by category and subcategory. These Measures are summarized by their functionalities and keywords. To gain insights into how OpenStudio Measures are used in building energy modeling community, interviews were conducted. A total of 12 interview responses were collected from 6 individuals in the industry and 6 individuals in academia. The knowledge acquired from reviewing the existing Measures and interview results will be integrated into the Measure development process, and the expertise of practitioners and OpenStudio Measure users will be leveraged to shape future Measures.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Enabling Power at Sea: Opportunities for Expanded Ocean Observations through Marine Renewable Energy Integration

The blue economy is a dynamic and rapidly growing movement that captures the interplay between economic, social, and ecological sustainability of the ocean and encompasses numerous maritime sectors and activities (e.g., commerce and trade; living resources; renewable energy; minerals, materials, and freshwater; and ocean health and data). The demand for ocean data to inform scientific, risk reduction, and national security needs is leading to a large increase in the number of deployed ocean observation and monitoring systems, most of which require increased power. Because ocean observation systems are often placed in remote locations, they primarily rely on energy storage (or in some cases in situ energy generation) to power instruments and equipment, which imposes limits on sampling rates, deployment times, and spatiotemporal resolution of data. The U.S. Department of Energy Water Power Technologies Office is exploring the potential for marine renewable energy (MRE) devices (largely wave and tidal energy converters) to provide power to support multiple blue economy opportunities. A portion of these opportunities focus on power at sea markets for providing power in off-grid and offshore locations to support a variety of ocean-based activities, including ocean observation and navigation, underwater vehicle charging, marine aquaculture, marine algae farming, and seawater mining. Initially, research has focused on better understanding how and where MRE can provide a consistent source of reliable power to extend ocean observing missions, including operation of autonomous underwater vehicles. Online surveys as well as phone and in-person interviews were conducted with experts in the field of ocean observing systems and observatories to gather end-user requirements, determine energy needs, identify opportunities for codevelopment, and pinpoint constraints for MRE to meet those needs. The surveys and interviews provided feedback on the potential for powering devices and vehicles using MRE, including identifying common themes and challenges that will inform foundational research and development steps needed to advance the integration of MRE with ocean observing systems. In most cases, additional power generation on the order of watts was identified as significantly beneficial to enhancing ocean observations capabilities.

16 TIDAL AND WAVE POWER↗

p -adic reconstruction of rational functions in multiloop amplitudes

Numerical reconstruction techniques are widely employed in the calculation of multiloop scattering amplitudes. In recent years, it has been observed that the rational functions in multiloop calculations greatly simplify under partial fractioning. In this article, we present a technique to reconstruct rational functions directly in partial-fractioned form, by evaluating the functions at special integer points chosen for their properties under a p -adic metric. As an application, we apply this technique to reconstruct the largest rational function in the integration-by-parts reduction of one of the rank-5 integrals appearing in two-loop five-point full-color massless amplitude calculations in quantum chromodynamics. The number of required numerical probes (per prime field) is found to be around 25 times smaller than in conventional techniques, and the obtained result is 130 times smaller. The reconstructed result displays signs of additional structure that could be used to further reduce its size and the number of required probes. Published by the American Physical Society 2024

Astronomy & Astrophysics↗

Numerical challenges for energy conservation in N -body simulations of collapsing self-interacting dark matter halos

Dark matter (DM) halos can be subject to gravothermal collapse if the DM is not collisionless, but engaged in strong self-interactions instead. When the scattering is able to efficiently transfer heat from the centre to the outskirts, the central region of the halo collapses and reaches densities much higher than those for collisionless DM. This phenomenon is potentially observable in studies of strong lensing. Current theoretical efforts are motivated by observations of surprisingly dense substructures. However, a comparison with observations requires accurate predictions. One method to obtain such predictions is to use N-body simulations. Collapsed halos are extreme systems that pose severe challenges when applying state-of-the-art codes to model self-interacting dark matter (SIDM). In this work, we investigate the root of such problems, with a focus on energy non-conservation. Moreover, we discuss possible strategies to avoid them. We ran N-body simulations, both with and without SIDM, of an isolated DM-only halo and we adjusted the numerical parameters to check the accuracy of the simulation. We find that not only the numerical scheme for SIDM can lead to energy non-conservation, but also the modelling of gravitational interaction and the time integration are problematic. The main issues we find are: (a) particles changing their time step in a non-time-reversible manner; (b) the asymmetry in the tree-based gravitational force evaluation; and (c) SIDM velocity kicks breaking the time symmetry. Tuning the parameters of the simulation to achieve a high level of accuracy allows us to conserve energy not only at early stages of the evolution, but also later on. However, the cost of the simulations becomes prohibitively large as a result. Some of the problems that make the simulations of the gravothermal collapse phase inaccurate can be overcome by choosing appropriate numerical schemes. However, other issues still pose a challenge. Our findings motivate further works on addressing the challenges in simulating strong DM self-interactions.

dark matter↗

Software For Advanced Large-scale Analysis Of Magnetic Confinement For Numerical Design, Engineering & Research (salamander)

As magnetic confinement fusion energy gains traction internationally to enable abundant energy production, designing components for fusion systems is a pressing challenge. During the planned lifetime of a fusion device, components evolve in extreme environments and must withstand large, repeated thermal loads and bombardment by 14 MeV neutrons, plasma ions, and neutral particles (deuterium, tritium, and helium), corrosive conditions, etc. All these physical processes take place simultaneously, interact in intricate ways, and impose important constraints that can affect performance. Experimental data is rare and costly to obtain, making design particularly challenging. Predictive computational frameworks must be an integral part of an accelerated and cost-effective design process by modeling fusion system performance in simulated environments. To better understand component degradation and operational impacts on their performance, the Software for Advanced Large-scale Analysis of MAgnetic confinement for Numerical Design, Engineering & Research (SALAMANDER) is designed as an open-source, fully integrated, multiphysics, multiscale, NQA-1 compliant framework facilitating 3D, high-fidelity fusion system modeling. To that end, SALAMANDER is a MOOSE-based framework, and therefore leverages MOOSE upstream libraries such as PETSc and libMesh to deliver sophisticated finite element, finite volume, and nonlinear solver technology for fusion energy simulations. SALAMANDER couples MOOSE physics module capabilities—such as thermal hydraulics, heat conduction, Navier-Stokes, and thermomechanics—with tritium transport via TMAP8, neutronics via Cardinal, and nascent particle-in-cell capabilities. Direct simulation Monte Carlo methods will be used to address neutral transport near the walls. By coupling all these physics in an integrated application, SALAMANDER will enable high-fidelity modeling of irradiation levels and plasma exposure conditions of plasma facing components and their impact on heat and tritium distributions, as well as the resulting mechanical constraints experienced by the plasma facing components and performance of blanket systems. Furthermore, SALAMANDER will be particularly suited for engineering studies thanks to the stochastic tool module readily available in MOOSE, allowing for extended uncertainty quantification and risk analysis studies. It is also able to use computer-aided design (CAD) meshes to model complex geometries, which is indispensable for fusion systems. SALAMANDER therefore supports design, safety, engineering, and research projects for magnetic confinement fusion systems

Simon, Pierre-Clement [Idaho National Laboratory (↗

Analysis of heat transfer and AuNPs-mediated photo-thermal inactivation of E. coli at varying laser powers using single-phase CFD modeling

In the wake of the COVID-19 pandemics, the demand for innovative and effective methods of bacterial inactivation has become a critical area of research, providing the impetus for this study. The purpose of this research is to analyze the AuNPs-mediated photothermal inactivation of E. coli. Gold nanoparticles irradiated by laser represent a promising technique for combating bacterial infection that combines high-tech and scientific progress. The intermediate aim of the work was to present the calibration of the model with respect to the gold nanorods experiment. The purpose of this work is to study the effect of initial concentration of E. coli bacteria, the design of the chamber and the laser power on heat transfer and inactivation of E. coli bacteria. Using the CFD simulation, the work combines three main concepts. 1. The conversion of laser light to heat has been described by a combination of three distinctive approximations: a- Discrete particle integration to take into account every nanoparticle within the system, b- Rayleigh-Drude approximation to determine the scattering and extinction coefficients and c- Lambert–Beer–Bourger law to describe the decrease in laser intensity across the AuNPs. 2. The contribution of the presence of E. coli bacteria to the thermal and fluid-dynamic fields in the microdevice was modeled by single-phase approach by determining the effective thermophysical properties of the water-bacteria mixture. 3. An approach based on a temperature threshold attained at which bacteria will be inactivated, has been used to predict bacterial response to temperature increases. The comparison of the thermal fields and temporal temperature changes obtained by the CFD simulation with those obtained experimentally confirms the accuracy of the light-heat conversion model derived from the aforementioned approximations. The results show a linear relationship between maximum temperature and variation in laser power over the range studied, which is in line with previous experimental results. It was also found that the temperature inside the microchamber can exceed 55 °C only when a laser power higher than 0.8 W is used, so bacterial inactivation begins. The experimental data allows to determinate the concentration of nanoparticles. This parameter is introduced into the mathematical model obtaining the same number of AuNPs. However, this assumption introduces a certain simplification, as in the mathematical model the distribution of nanoparticles is uniform. This work is directly connected to the use of gold nanoparticles for energy conversion, as well as the field of bacterial inactivation in microfluidic systems such as lab-on-a-chip. Presented mathematical and numerical models can be extended to the entire spectrum of wavelengths with particular use of white light in the inactivation of bacteria. This work represents a significant advancement in the field, as to the best of the authors’ knowledge, it is the first to employ a single-phase computational fluid dynamics (CFD) approach specifically combined with the thermal inactivation of bacteria. Moreover, this research pioneers the use of a numerical simulation to analyze the temperature threshold of photothermal inactivation of E. coli mediated by gold nanorods (AuNRs). The integration of these methodologies offers a new perspective on optimizing bacterial inactivation techniques, making this study a valuable contribution to both computational modeling and biomedical applications.

36 MATERIALS SCIENCE↗

Poster Abstract: Leveraging Large Language Models to Reveal Interpretable Cooling Behaviors from Smart Thermostat Data

Frequent heatwaves and hot summers increasingly challenge occupant comfort, health, and energy grid stability. Addressing these challenges requires a detailed understanding of household cooling behaviors, such as thermostat adjustments and adaptive responses to extreme conditions. Traditional analyses often rely on aggregated numerical metrics that overlook subtle but important household-specific variations. In this study, we introduce a generalizable methodology that integrates large language models (LLMs) with vision capabilities to enable scalable and detailed analysis of residential thermostat data. Using Ecobee's Donate Your Data (DYD) dataset—which provides five-minute records of indoor temperatures, thermostat setpoints, and HVAC runtimes—we focus on two U.S. cities with contrasting summer climates : Austin (TX) and Phoenix (AZ). Because raw time-series data are not well suited for direct LLM analysis, we transform them into visual representations, such as daily indoor temperature trajectories and weekly runtime histograms, to better capture behavioral variations. Leveraging LLMs' visual interpretation, we extract descriptive behavioral features, including temperature preferences, time-of-day cooling orientation, anticipatory versus reactive heatwave responses, and behavioral consistency. These semantic features support unsupervised clustering to identify distinct occupant archetypes at scale, revealing differences—such as morning-centric anticipatory coolers versus households that shift toward warmer setpoints during heatwaves—that can inform demand response, resilience planning, and health-aware interventions. By converting raw numerical data into interpretable behavioral patterns, this methodology enables scalable and practical analysis of occupant behavior, supporting actionable insights for comfort, resilience, and energy management.

Nihar, Kopal↗

PipeSight: A High-Performance Computing Platform for Pipeline Integrity Management

The Phase I feasibility study completed as part of this project has led to a number of innovative technologies being developed and has laid the foundation for a successful Phase II effort to commercialize a platform for managing the integrity of pipelines for the damage mechanisms of the new, hybrid-energy based economy. To ground the development efforts and direction of the project, an extensive market research and customer discovery effort was undertaken early in Phase I. Through this effort, a number of pipeline owners and operators were interviewed, and the following key findings were discovered about the pipeline industry: • Small pipeline operators do not have the central engineering groups necessary to perform their own independent analysis of inspection data, but instead rely on summarized tally sheets provided to them by inspection service providers. • The time it takes to go from an inspection to a completed engineering assessment, even for small segments of pipeline, can take anywhere from 30-120 days. During this delay, critical threats can (and have been known to) cause failures. • Uncertainty is often not accounted for in the assessment of pipeline integrity. The tally sheets provided by third-party service providers are almost always deterministic in nature, identifying threats that present a concern only to the current (not the future) integrity of the pipeline. • It is uncommon to apply the latest technologies to perform advanced assessments of damaged pipelines. There is a desire to use more advanced analysis capabilities to assess threats. Many pipeline operators indicated that they would often excavate a pipeline to perform an inspection and find that the damage was not as bad as they anticipated, thus using limited resources unnecessarily. Companies are not consistent in their use of inspection data to determine corrosion rates, and those that do only calculate deterministic corrosion rates. • The industry has prominently relied on time-based inspections but has recently started to transition to risk-based inspections. However, there appears to be no uniform guidance on how to do so while properly accounting for all sources of uncertainty. • Companies are not storing inspection data in a manner that allows for the ready determination of temporal trends. • Predictive maintenance principles and practices are beginning to be used by early adopters • Some pipelines are being re-purposed to transport different process fluids than they were designed for, e.g., H 2 and CO 2 rich process streams to serve the new hybrid-energy based economy, which are presenting new integrity concerns for the existing pipeline network that crisscrosses the United States. As a result of these discoveries, we were able to target the development efforts in Phase I to best serve the needs of the industry. In Phase I, we developed a way to correlate multiple large-scale scans of the pipeline to determine a probabilistic corrosion rate that accounts for all sources of error and uncertainty in the inspection process. This probabilistic corrosion rate can be used to predict the future thickness distribution of the pipe wall. We demonstrate how this analysis may be performed in an analytical fashion and has been implemented in such a manner that it can be readily distributed using GPU computing through integration of the Kokkos programming model. We also make a very novel extension of the analytical corrosion rate model to Bayesian Networks (an explainable AI technique) that can account for non-parametric distributions of corrosion rates. With the predictions made above for the probabilistic corrosion rate and corresponding future distribution of the pipe wall thickness, we can assess the integrity of the pipeline through the use of a probabilistic engineering assessment. We developed a novel screening data analysis approach that can rapidly identify ‘hotspots’ (local thin areas) where the integrity of the pipeline is a concern. Once more, we implemented this screening approach in C++ to leverage GPU computing via the Kokkos programming model. After the critical hotspots are identified, we developed a program that can automatically generate an advanced finite element model of the damaged regions. Since the number of damaged regions that require advanced analysis can number in the thousands, we integrated an open-source container-native workflow engine for orchestrating parallel jobs on the cloud. Initially, these advanced numerical models were only designed to account for loading due to internal pressure. However, in a slight pivot from the initial Phase I proposal, we developed a complete pipe stress analysis program (called Simflex) which can simulate the complete pipeline and its response to thermal expansion, pressure, thermal bowing, weight, wind, earthquake, support displacement, support friction and external forces. This pipe stress analysis program was written generically, to handle any piping system, but contains the features needed to model long pipelines (i.e., it incorporates a model for soil mechanics and can account for the nonlinear boundary conditions necessary to simulate long underground pipelines). This pipe stress analysis program can simulate any segment of the pipeline (simple or complex) under any set of conditions and loads, to determine the supplemental loads (axial forces and bending moments) at the location of damage. This enables the most accurate state of stress to be accounted for in the pipeline, which can prove critical when evaluating the integrity of a damaged region. In the process of developing the technologies to perform the integrity assessment of the pipeline, we also extended one of the industry standard approaches for performing the assessment of local thin areas that extend more in the circumferential direction than the longitudinal direction of the pipeline. This approach was presented to the API 579-1/AS ME FFS-1 steering committee in November 2021 for consideration in the next edition of the industry standard for Fitness-For-Service (expected to be released in 2023). To help pipeline operators make decisions with the results on any integrity assessment, we developed a new approach to the life-cycle management of pipelines which uses a Bayesian Decision Network. The network is designed to help pipeline operators plan and prioritize inspection activities and ultimately make smarter, more cost-effective decisions. The Bayesian approach accounts for all sources of uncertainty and carries them through to the final optimal decisions, providing a probabilistic framework for optimizing inspection intervals. The proof-of-concept networks developed in the feasibility study are complete, verified, and are focused on a subset of the pipeline. To expand this novel approach to the scale necessary for an entire network of pipelines in Phase II, we will leverage the DOE-funded Bengi solver for industrial-scale decision making with Bayesian Networks [22]. Once implemented, we will be able to provide the pipeline industry with a much-needed tool for optimal inspection planning using truly explainable artificial intelligence (XAI). To handle all of these advanced capabilities into a cloud-based platform, the architecture of the Equity Engineering Cloud (EEC) was extended to include Argo Workflows, a framework capable of distributing and managing a massive number of jobs that consume their own resources, such that thousands of serial finite element simulations can be run in parallel. As part of this substantial undertaking, we also integrated Argo Continuous Delivery (CD) into the EEC, to aid with the rapid prototyping and iterations that will be imperative to the success of the PipeSight platform’s Agile development process in Phase II. As part of the pipe stress analysis program, we also developed a custom visualizer that leverages the DOE-funded VTK visualization library. We added custom contouring capabilities and a means for interacting visually with both the inputs and outputs of the pipe stress analysis program. We also developed routines for automating the post-processing of the finite element simulations to determine if any failure criteria are met and to visualize the deformations, stresses and strains in ParaView using the exodus II file format (a subset of netCDF).

24 POWER TRANSMISSION AND DISTRIBUTION↗

Multirate linearly-implicit GARK schemes

Many complex applications require the solution of initial-value problems where some components change fast, while others vary slowly. Multirate schemes apply different step sizes to resolve different components of the system, according to their dynamics, in order to achieve increased computational efficiency. The stiff components of the system, fast or slow, are best discretized with implicit base methods in order to ensure numerical stability. To this end, linearly implicit methods are particularly attractive as they solve only linear systems of equations at each step. This paper develops the Multirate GARK-ROS/ROW (MR-GARK-ROS/ROW) framework for linearly-implicit multirate time integration. The order conditions theory considers both exact and approximative Jacobians. The effectiveness of implicit multirate methods depends on the coupling between the slow and fast computations; an array of efficient coupling strategies and the resulting numerical schemes are analyzed. Multirate infinitesimal step linearly-implicit methods, that allow arbitrarily small micro-steps and offer extreme computational flexibility, are constructed. The new unifying framework includes existing multirate Rosenbrock(-W) methods as particular cases, and opens the possibility to develop new classes of highly effective linearly implicit multirate integrators.

97 MATHEMATICS AND COMPUTING↗