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NASA NTRS1994

Man-machine Integration Design and Analysis System (MIDAS) Task Loading Model (TLM) experimental and software detailed design report

This is the experimental and software detailed design report for the prototype task loading model (TLM) developed as part of the man-machine integration design and analysis system (MIDAS), as implemented and tested in phase 6 of the Army-NASA Aircrew/Aircraft Integration (A3I) Program. The A3I program is an exploratory development effort to advance the capabilities and use of computational representations of human performance and behavior in the design, synthesis, and analysis of manned systems. The MIDAS TLM computationally models the demands designs impose on operators to aide engineers in the conceptual design of aircraft crewstations. This report describes TLM and the results of a series of experiments which were run this phase to test its capabilities as a predictive task demand modeling tool. Specifically, it includes discussions of: the inputs and outputs of TLM, the theories underlying it, the results of the test experiments, the use of the TLM as both stand alone tool and part of a complete human operator simulation, and a brief introduction to the TLM software design.

Staveland, Lowell↗

NASA NTRS2011

NASA Applications for Computational Electromagnetic Analysis

Computational Electromagnetic Software is used by NASA to analyze the compatibility of systems too large or too complex for testing. Recent advances in software packages and computer capabilities have made it possible to determine the effects of a transmitter inside a launch vehicle fairing, better analyze the environment threats, and perform on-orbit replacements with assured electromagnetic compatibility.

Lewis, Catherine C.↗

NASA NTRS2012

Fault Mitigation Schemes for Future Spaceflight Multicore Processors

Future planetary exploration missions demand significant advances in on-board computing capabilities over current avionics architectures based on a single-core processing element. The state-of-the-art multi-core processor provides much promise in meeting such challenges while introducing new fault tolerance problems when applied to space missions. Software-based schemes are being presented in this paper that can achieve system-level fault mitigation beyond that provided by radiation-hard-by-design (RHBD). For mission and time critical applications such as the Terrain Relative Navigation (TRN) for planetary or small body navigation, and landing, a range of fault tolerance methods can be adapted by the application. The software methods being investigated include Error Correction Code (ECC) for data packet routing between cores, virtual network routing, Triple Modular Redundancy (TMR), and Algorithm-Based Fault Tolerance (ABFT). A robust fault tolerance framework that provides fail-operational behavior under hard real-time constraints and graceful degradation will be demonstrated using TRN executing on a commercial Tilera(R) processor with simulated fault injections.

software based↗

NASA NTRSDate not supplied

ES2Vec: Earth Science Metadata Suggestions and Analogical Reasoning

As the volume of text-based Earth science research grows, it is increasingly possible to discover latent relationships in the literature. However, traditional methodologies are restricted by limited computational capabilities and intractable problem spaces. Advancements in natural language processing (NLP) have allowed us to use an extensive Earth science corpus to create a domain-specific word vector model, Es2Vec, which we have used to surface latent relationships between Earth science concepts and generate improved keyword tags. Earth science metadata keyword assignment is a challenging problem. Dataset curators select appropriate keywords from the Global Change Master Directory (GCMD) set of keywords. The keywords an are integral part of the search and discovery of these datasets. Hence, the selection of keywords is crucial to increasing the discoverability of datasets. Utilizing machine learning techniques, we provide users with automated keyword suggestions to complement manual selection. We trained a machine learning model that leverages the semantic embedding ability of Word2Vec models to process abstracts and suggest relevant keywords. A user interface tool we built to assist data curators in the assignment of such keywords is also described.

word vectors↗

DOE OSTI2021

TQEA: Temporal Quantum Error Analysis

For the last few years quantum computers have captured researchers’ interest in solving complicated problems in finance, chemistry, machine learning, and many other NP problems. Quantum computing benefits from parallel computation, entanglement, and calculation speedup compared to classical computing. Even though the operations and number of qubits in quantum computers are limited, previous research showed that using quantum computers can be beneficial. These benefits gained researchers’ interest to work on the improvement of quantum computers and overcome the limitations by building more advanced quantum computers with fault tolerance capability, more physical qubits, and better operational gates. In practice, Quantum applications would be translated into Quantum Circuits and each circuit can contain one or many entanglements (s), single qubits operations, and readouts. The importance of running Quantum applications with controlled errors or without errors is critical to the desired result from Quantum readout. In this paper, we study the characteristics of superconducting quantum machines along with the previously proposed methods of Quantum error detection/correction and in order to build a better error model we propose a temporal method for analyzing the the behavior of qubits errors (T1 and T2), frequency of operation, entanglement errors, and readout errors. In order to detect and predict the behavior of each machine, we use simple exponential smoothing analysis on heuristic calibration data. Finally, based on observation, we show that based on frequency, qubits, readout and single operation errors we can build a temporal based model to study and predict the outcome of runs on each Quantum machine.

Baheri, Betis↗

DOE OSTI2022

NREL Stratus - Enabling Workflows to Fuse Data Streams, Modeling, Simulation, and Machine Learning

Integrating cloud services into advanced computing facilities provides significant new capabilities over focusing solely on traditional high performance computing (HPC) workloads. This brings complementary capabilities as well as enabling new focused roles for HPC. They are especially potent for workflows that fuse data streams, modeling and simulation ('modsim') and machine learning. A key challenge to adopting a hybrid edge-cloud-HPC model is to align optimal capability, data, and user intent on the right resources for each step in a workflow.?The NREL Stratus service provides a basis for this: Stratus layers capabilities needed to make?cloud services accessible to a lab-based scientific community on commercial offerings, and; currently supports upwards of 200 projects ranging from IOT integration to traditional modeling and simulation. This provides a real-world inventory of scientific workflow elements. A growing knowledge base enables placing these elements appropriately between the edge, cloud, and traditional HPC. This paper outlines a vision via reference architecture and the application of that architecture in a typical workflow highlighting multiple components: sensor data intake, cleaning and transforming (edge/cloud suitable); generation of synthetic data through modsim, computationally heavy ML training and hyperparameter optimization (HPC suitable), and; inference and deployment (cloud ideal). Every step in such a workflow involves a cost-benefit analysis regarding the data movement, computational efficiency, availability, latency, and resource capabilities. The reference architecture and examples outlined allow for understanding new opportunities in the context of emerging workflows that combine IOT, cloud, and HPC to bolster scientific productivity.

AI↗

DOE OSTI2022

28 NREL Stratus - Enabling Workflows to Fuse Data Streams, Modeling, Simulation, and Machine Learning: Preprint

AI↗

DOE OSTI2022

Assessment and Improvement of Fission Product Transport Predictions of Particle Fuel in BISON

The U.S. Department of Energy’s Nuclear Energy Advanced Modeling and Simulation (NEAMS) program aims to develop predictive capabilities by applying computational methods to the analysis and design of advanced reactor and fuel cycle systems. This program has been providing engineering-scale support for the development of BISON, a high-fidelity and high-resolution fuel performance tool. This study was motivated by the need to incorporate more physics-based models in BISON in order to foster tri-structural isotropic (TRISO) applications. This document details the integration of new modeling capabilities in BISON, including (1) development of pyrolytic carbon (PyC) and silicon carbide (SiC) layer anisotropic thermal and mass transport capabilities, (2) verification of the mass diffusion solution in TRISO modeling, (3) calibration of fission product diffusivity using Advanced Gas Reactor (AGR) experiments, (4) improved fission product release modeling by developing compact diffusion modeling capabilities, and (5) documentation of accelerated failure analysis on the BISON website. Improvements made to the diffusion models and parameters were documented and validated against AGR-1 and -2 experiment data.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

NASA NTRS2007

Development and Assessment of a Novel Training Package for Basic Maneuvering Tasks on a Flight Simulator Using Self Instruction Methods and Above Real Time Training (ARTT)

One result of the relatively recent advances in computing technology has been the decreasing cost of computers and increasing computational power. This has allowed high fidelity airplane simulations to be run on personal computers (PC). Thus, simulators are now used routinely by pilots to substitute real flight hours for simulated flight hours for training for an aircraft type rating thereby reducing the cost of flight training. However, FAA regulations require that such substitution training must be supervised by Certified Flight Instructors (CFI). If the CFI presence could be reduced or eliminated for certain tasks this would mean a further cost savings to the pilot. This would require that the flight simulator have a certain level of 'intelligence' in order to provide feedback on pilot performance similar to that of a CFI. The 'intelligent' flight simulator would have at least the capability to use data gathered from the flight to create a measure for the performance of the student pilot. Also, to fully utilize the advances in computational power, the simulator would be capable of interacting with the student pilot using the best possible training interventions. This thesis reports on the two studies conducted at Tuskegee University investigating the effects of interventions on the learning of two flight maneuvers on a flight simulator and the robustness and accuracy of calculated performance indices as compared to CFI evaluations of performance. The intent of these studies is to take a step in the direction of creating an 'intelligent' flight simulator. The first study deals with the comparisons of novice pilot performance trained at different levels of above real-time to execute a level S-turn. The second study examined the effect of out-of-the-window (OTW) visual cues in the form of hoops on the performance of novice pilots learning to fly a landing approach on the flight simulator. The reliability/robustness of the computed performance metrics was assessed by comparing them with the evaluations of the landing approach maneuver by a number of CFIs.

Ali, Syed Firasat↗

NASA NTRS2007

An Evaluation of Training Interventions and Computed Scoring Techniques for Grading a Level Turn Task and a Straight In Landing Approach on a PC-Based Flight Simulator

One result of the relatively recent advances in computing technology has been the decreasing cost of computers and increasing computational power. This has allowed high fidelity airplane simulations to be run on personal computers (PC). Thus, simulators are now used routinely by pilots to substitute real flight hours for simulated flight hours for training for an aircraft type rating thereby reducing the cost of flight training. However, FAA regulations require that such substitution training must be supervised by Certified Flight Instructors (CFI). If the CFI presence could be reduced or eliminated for certain tasks this would mean a further cost savings to the pilot. This would require that the flight simulator have a certain level of 'intelligence' in order to provide feedback on pilot perfolmance similar to that of a CFI. The 'intelligent' flight sinlulator would have at least the capability to use data gathered from the flight to create a measure for the performance of the student pilot. Also, to fully utilize the advances in computational power, the sinlulator would be capable of interacting with the student pilot using the best possible training interventions. This thesis reposts on the two studies conducted at Tuskegee University investigating the effects of interventions on the learning of two flight maneuvers on a flight sinlulator and the robustness and accuracy of calculated perfornlance indices as compared to CFI evaluations of performance. The intent of these studies is to take a step in the direction of creating an 'intelligent' flight simulator. The first study deals with the comparisons of novice pilot performance trained at different levels of above real-time to execute a level S-turn. The second study examined the effect of out-of-the-window (OTW) visual cues in the form of hoops on the performance of novice pilots learning to fly a landing approach on the flight simulator. The reliability/robustness of the computed performance metrics was assessed by comparing them with the evaluations of the landing approach maneuver by a number of CFIs.

Heath, Bruce E.↗

DOE OSTI2023

Advanced Simulation and Computing: ASC FY24 Implementation Plan

The DOE National Nuclear Security Administration (NNSA) Stockpile Stewardship Program (SSP) is an integrated technical program for maintaining the safety, security, and reliability of the U.S. nuclear stockpile. The SSP incorporates nuclear test data, computational modeling and simulation, and experimental facilities to advance understanding of nuclear weapons. The suite of data analyzed comes from activities including previous nuclear tests, stockpile surveillance, experimental research, and development and engineering programs. This integrated national program requires the continued use of experimental facilities and the computational capabilities to support the SSP missions. These component parts, in addition to an appropriately scaled production capability, enable NNSA to support stockpile requirements. The ultimate goal of the SSP, and thus of the Advanced Simulation and Computing (ASC) program, is to ensure that the U.S. maintains a safe, secure, and effective strategic deterrent. The ASC program is a cornerstone of the SSP, providing simulation capabilities and computational resources to support the annual stockpile assessment and certification process, study advanced nuclear weapons design and manufacturing processes, analyze accident scenarios and weapons aging, and provide the tools to enable stockpile Life Extension Programs (LEPs) and the resolution of Significant Finding Investigations (SFIs). This work requires a balance of resources, including technical staff, hardware, simulation software, and computer science solutions. The ASC program focuses on increasing the predictive capabilities in a three-dimensional (3D) simulation environment while maintaining support to the SSP. The Program continues to improve its unique tools for understanding and solving progressively more difficult stockpile problems (sufficient resolution, dimensionality, and scientific details), and quantifying critical margins and uncertainties. Resolving each issue requires increasingly difficult analyses because the aging process has progressively moved the stockpile further from the original test base. While the focus remains on the U.S. nuclear weapons program, where possible, the Program also enables the use of high-performance computing (HPC) and simulation tools to address broader national security needs, such as foreign nuclear weapon assessments and nuclear counterterrorism. The 2022 Nuclear Posture Review (NPR) calls for NNSA to “deliver a modern, adaptive nuclear security enterprise based on an integrated strategy for risk management, production-based resilience, science and technology innovation, and workforce initiatives.” Furthermore, “NNSA will establish a Science and Technology Innovation Initiative to accelerate the integration of science and technology (S&T) throughout its activities.” Executing this strategy necessitates the continued emphasis on developing and sustaining high-quality scientific and engineering staff, as well as supporting computational and experimental capabilities. These components constitute the foundation of the nuclear weapons program. The continued success of the SSP and LEPs is predicated upon the ability to credibly certify the stockpile, without a return to underground nuclear tests (UGTs). Shortly after the nuclear test moratorium entered into force in 1992, the Accelerated Strategic Computing Initiative (ASCI) was established to provide an extensive simulation capability to underpin stockpile certification. While computing and simulation have always been essential to the success of the nuclear weapons program, the program goal of ASCI was to execute NNSA’s vision of using these tools in support of the stockpile stewardship mission. The ASCI program was essential to the successful demonstration of the SSP, providing critical nuclear weapons simulation and modeling capabilities. ASCI officially evolved into the ASC program in fiscal year (FY) 2005, but the mission remains essentially the same: provide the simulation and computational capabilities that underpin the ability to maintain a safe, secure, effective nuclear weapon stockpile, without returning to underground nuclear testing. The capabilities that the ASC program provides at the national laboratories play a vital role in the nuclear security enterprise and are necessary for fulfilling the stockpile stewardship and life extension requirements outlined for NNSA. The Program develops modern simulation tools that provide insights into stockpile aging issues, provide the computational and simulation tools that enable designers and analysts to certify the current stockpile and life-extended nuclear weapons, and inform the decision-making process when any modifications in nuclear warheads or the associated manufacturing processes are deemed necessary. Furthermore, ASC is enhancing the predictive simulation capabilities that are essential to evaluate weapons effects, design experiments, and ensure test readiness. The ASC program continues to improve its unique tools to solve stockpile problems— with a focus on sufficient resolution, dimensionality, and scientific detail—to enable Quantification of Margins and Uncertainties (QMU) and to resolve the increasingly difficult analyses needed for stockpile stewardship. The needs of the Stockpile Management and Production Modernization programs (formerly Directed Stockpile Work) also drive the requirements for simulation and computational resources. These requirements include planned LEPs, stockpile support activities, and mitigation efforts against the potential for technical surprise. All of the weapons within the current stockpile are in some stage of the life extension process. The simulation and computational capabilities are crucial for successful execution of these life extensions and for ensuring NNSA can certify these life-extended weapons without conducting a UGT.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Interface Problem Formulation Improvements with Application to Nuclear Fuel Performance Analysis

The U.S. Department of Energy’s Nuclear Energy Advanced Modeling and Simulation Program aims to develop predictive capabilities by applying computational methods to the analysis and design of advanced reactor and fuel cycle systems. This program has been providing engineering scale support for the development of BISON, a high-fidelity and high-resolution fuel performance tool. This report documents new developments and robustness improvements in mechanical and thermal (gap heat transfer) contact formulations. The improvements range from the migration of industrial level (“assessment”) nuclear fuel model setups to the usage of mortar formulations, the addition of frictional contact to one-dimensional layered representations of fuel and cladding components, and the addition of the Petrov-Galerkin approach to dual mortar, which improves performance on curved, relatively coarse meshes. In addition, the Lagrange-multiplier enforcement of mechanical mortar contact constraints has been extended to two additional types of enforcement: penalty and augmented Lagrange-Uzawa. We show that the latter approach yields the same interface results as dual mortar in the Multiphysics Object-Oriented Simulation Environment, with the advantage of not worsening the condition number of the system matrix—thereby enabling the use of some general implementations of iterative preconditioners, at the expense of additional system evaluations (i.e., augmentations).

42 ENGINEERING↗

DOE OSTI2023

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

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

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2020

The Multiphysics on Advanced Platforms Project

In 2015, the Lawrence Livermore National Laboratory started development of next-generation multiphysics simulation capabilities for the National Nuclear Security Administration under the Advanced Technologies Development and Mitigation (ATDM) element of the Advanced Simulation and Computing program in collaboration with the Exascale Computing Project (ECP). A key driver for this effort across the NNSA tri-lab was the emergence of advanced high performance computing (HPC) architectures based on heterogeneous compute capabilities, including GPU based systems, as part of the national drive toward exascale computing platforms at multiple Department of Energy (DOE) facilities. Developing a multiphysics code capable of meeting the various simulation needs of the NNSA as defined by the current generation of integrated codes (or ICs), initially developed as part of the Accelerated Strategic Computing Initiative (ASCI) program beginning in 1996, and able to scale to the current 100 petaflop class pre-exascale systems, as well the forthcoming exaflop class computers, is a daunting challenge. To accomplish this ambitious goal, LLNL has embraced two key themes: use of high-order numerical methods and a modular approach to code development. The LLNL next generation effort is organized under the Multi-Physics on Advanced Platforms Project (MAPP). A foundational component of MAPP is the Axom computer science (CS) toolkit which provides infrastructure for the development of modular, performance portable, multi-physics application codes. MARBL is a next-generation application code built on the Axom base to address the modeling needs of the high energy density physics (HEDP) community for simulating high-explosive, magnetic or laser driven experiments such as inertial confinement fusion (ICF), pulsed-power magneto-hydrodynamics (MHD), equation of state (EOS) and material strength studies as part of the NNSA’s stockpile stewardship program (SSP).

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

SIERRA Multimechanics Module: Aria User Manual - Version 4.56

Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process ows via the incompressible Navier-Stokes equations specialized to a low Reynolds number (Re < 1) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newtons method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic h-adaptivity and dynamic load balancing are some of Arias more advanced capabilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

SIERRA Multimechanics Module: Aria User Manual - Version 4.58

Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process flows via the incompressible Navier-Stokes equations specialized to a low Reynolds number ( %3C 1 ) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newtons method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic -adaptivity and dynamic load balancing are some of Arias more advanced capabilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

SIERRA Multimechanics Module: Aria User Manual (V.5.0)

Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process %1Cows via the incompressible Navier-Stokes equations specialized to a low Reynolds number (Re < 1) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newtons method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic h-adaptivity and dynamic load balancing are some of Arias more advanced capabilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

SIERRA Multimechanics Module: Aria Thermal Theory Manual (V.5.0)

Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process flows via the incompressible Navier-Stokes equations specialized to a low Reynolds number ( Re < 1) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newtons method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic -adaptivity and dynamic load balancing are some of Arias more advanced capabilities.

97 MATHEMATICS AND COMPUTING↗