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NASA NTRSDate not supplied

Introduction to Quantum Computing

Quantum computing offers the potential to revolutionize high-performance computing by providing a means to solve certain computational problems asymptotically faster than any classical computer. Quantum computing has advanced recently from merely a theoretical possibility to engineered reality, including commercial entities offering early prototype quantum processors, both special-purpose quantum annealers and general-purpose gate-model processors. The media have been showcasing each new development and implicitly conveying the message that quantum-computing ubiquity is nigh. Here, we will respond to this hype and provide an overview of the exciting but still early state of the field. In this tutorial, we introduce participants to the computational models that give quantum computing its immense computational power. We examine the thought processes that programmers need to map problems to quantum computers. And we discuss hardware and algorithmic challenges that must be overcome before quantum computing becomes a component of every software developer's repertoire. (Update of 2022 slides)

Quantum computing↗
DOE OSTI2025

OLCF’s Advanced Computing Ecosystem (ACE): FY25 Update for Ongoing Efforts

The advent of widespread use of artificial intelligence (AI) and machine learning (ML) models in science, coupled with fast data production rates of scientific instruments strain the traditional batch-oriented high-performance computing (HPC) environment. As scientific exploration continues to require more data and faster processing and analysis, new emerging technologies and capabilities to enable cross-facility and time-sensitive workflows are required for seamless integration of HPC and experimental facilities. The Advanced Computing Ecosystem (ACE) is a strategic initiative within the Oak Ridge Leadership Computing Facility (OLCF) established in 2024 to support the development of cutting-edge technologies to advance computational research and infrastructure at OLCF and across the Department of Energy (DOE). Several DOE initiatives are spearheading the evolution of the scientific landscape by blurring facility boundaries and connecting the user facilities to advance scientific capabilities and ensure energy dominance. The DOE Integrated Research Infrastructure (IRI) program is one example that is laying a foundation to support complex cross-facility workflows. The IRI program aims to integrate diverse computational resources, data infrastructures, and scientific instruments to facilitate collaboration and accelerate scientific discovery. The Interconnected Science Ecosystem (INTERSECT) initiative at Oak Ridge National Laboratory (ORNL) is another example that aims to revolutionize scientific research through AI-driven, interconnected autonomous laboratories and research facilities. Finally, the American Science Cloud (AmSC), recently announced in the “One Big Beautiful Bill”, aims to leverage prior infrastructure efforts of the IRI and automation and AI efforts of INTERSECT (and others) to build a federated, AI-augmented AmSC platform to unify the DOE’s computing, experimental, and data resources to catalyze scientific innovation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Roadmap for unconventional computing with nanotechnology

Abstract In the ‘Beyond Moore’s Law’ era, with increasing edge intelligence, domain-specific computing embracing unconventional approaches will become increasingly prevalent. At the same time, adopting a variety of nanotechnologies will offer benefits in energy cost, computational speed, reduced footprint, cyber resilience, and processing power. The time is ripe for a roadmap for unconventional computing with nanotechnologies to guide future research, and this collection aims to fill that need. The authors provide a comprehensive roadmap for neuromorphic computing using electron spins, memristive devices, two-dimensional nanomaterials, nanomagnets, and various dynamical systems. They also address other paradigms such as Ising machines, Bayesian inference engines, probabilistic computing with p-bits, processing in memory, quantum memories and algorithms, computing with skyrmions and spin waves, and brain-inspired computing for incremental learning and problem-solving in severely resource-constrained environments. These approaches have advantages over traditional Boolean computing based on von Neumann architecture. As the computational requirements for artificial intelligence grow 50 times faster than Moore’s Law for electronics, more unconventional approaches to computing and signal processing will appear on the horizon, and this roadmap will help identify future needs and challenges. In a very fertile field, experts in the field aim to present some of the dominant and most promising technologies for unconventional computing that will be around for some time to come. Within a holistic approach, the goal is to provide pathways for solidifying the field and guiding future impactful discoveries.

Finocchio, Giovanni (ORCID:0000000210433876)↗
DOE OSTI2025

ChemComp: A Compilation Framework for Computing with Chemical Reaction Networks

The acceleration of scientific computation, data analytics, and artificial intelligence is driving a surge in computational requirements. Yet, state-of-the-art high-performance computing systems are approaching physical limitations that impede further significant improvements in energy efficiency. As we move towards post-exascale computing systems, innovative approaches are necessary to overcome this barrier in power consumption. Novel analog and hybrid digital-analog architectures hold promise for enhancing energy efficiency by several orders of magnitude. Biochemical computation stands out among the various solutions being explored due to its potential to enable new classes of devices with immense computational capabilities. These devices can capitalize on the inherent efficacy of biological cells in solving optimization problems and are scalable through increasing reaction system size or vessel capacity, potentially satisfying scientific computing's high-performance requirements. Nonetheless, several theoretical and practical limitations persist, including problem formulation and mapping to chemical reaction networks (CRNs) and implementation of actual CRN devices. In this paper, we propose a framework for biochemical computation using systems chemistry. We present the initial components of our approach: an abstract chemical reaction dialect implemented as a multi-level intermediate representation (MLIR) compiler extension and a pathway to represent mathematical problems with CRNs. To showcase the potential of this approach, we emulate a simplified chemical reservoir device. This work lays the groundwork for leveraging chemistry's computing potential in creating energy-efficient, high-performance computing systems tailored to contemporary computational needs.

artificial intelligence↗
NASA NTRS1982

Development of a locally mass flux conservative computer code for calculating 3-D viscous flow in turbomachines

The VANS successive approximation numerical method was extended to the computation of three dimensional, viscous, transonic flows in turbomachines. A cross-sectional computer code, which conserves mass flux at each point of the cross-sectional surface of computation was developed. In the VANS numerical method, the cross-sectional computation follows a blade-to-blade calculation. Numerical calculations were made for an axial annular turbine cascade and a transonic, centrifugal impeller with splitter vanes. The subsonic turbine cascade computation was generated in blade-to-blade surface to evaluate the accuracy of the blade-to-blade mode of marching. Calculated blade pressures at the hub, mid, and tip radii of the cascade agreed with corresponding measurements. The transonic impeller computation was conducted to test the newly developed locally mass flux conservative cross-sectional computer code. Both blade-to-blade and cross sectional modes of calculation were implemented for this problem. A triplet point shock structure was computed in the inducer region of the impeller. In addition, time-averaged shroud static pressures generally agreed with measured shroud pressures. It is concluded that the blade-to-blade computation produces a useful engineering flow field in regions of subsonic relative flow; and cross-sectional computation, with a locally mass flux conservative continuity equation, is required to compute the shock waves in regions of supersonic relative flow.

Walitt, L.↗
NASA NTRS1992

Multidisciplinary computational aerosciences

As the challenges of single disciplinary computational physics are met, such as computational fluid dynamics, computational structural mechanics, computational propulsion, computational aeroacoustics, computational electromagnetics, etc., scientists have begun investigating the combination of these single disciplines into what is being called multidisciplinary computational aerosciences (MCAS). The combination of several disciplines not only offers simulation realism but also formidable computational challenges. The solution of such problems will require computers orders of magnitude larger than those currently available. Such computer power can only be supplied by massively parallel machines because of the current speed-of-light limitation of conventional serial systems. Even with such machines, MCAS problems will require hundreds of hours for their solution. To efficiently utilize such a machine, research is required in three areas that include parallel architectures, systems software, and applications software. The main emphasis of this paper is the applications software element. Examples that demonstrate application software for multidisciplinary problems currently being solved at NASA Ames Research Center are presented. Pacing items for MCAS are discussed such as solution methodology, physical modeling, computer power, and multidisciplinary validation experiments.

Kutler, Paul↗
NASA NTRS1994

Fuzzy logic, neural networks, and soft computing

The past few years have witnessed a rapid growth of interest in a cluster of modes of modeling and computation which may be described collectively as soft computing. The distinguishing characteristic of soft computing is that its primary aims are to achieve tractability, robustness, low cost, and high MIQ (machine intelligence quotient) through an exploitation of the tolerance for imprecision and uncertainty. Thus, in soft computing what is usually sought is an approximate solution to a precisely formulated problem or, more typically, an approximate solution to an imprecisely formulated problem. A simple case in point is the problem of parking a car. Generally, humans can park a car rather easily because the final position of the car is not specified exactly. If it were specified to within, say, a few millimeters and a fraction of a degree, it would take hours or days of maneuvering and precise measurements of distance and angular position to solve the problem. What this simple example points to is the fact that, in general, high precision carries a high cost. The challenge, then, is to exploit the tolerance for imprecision by devising methods of computation which lead to an acceptable solution at low cost. By its nature, soft computing is much closer to human reasoning than the traditional modes of computation. At this juncture, the major components of soft computing are fuzzy logic (FL), neural network theory (NN), and probabilistic reasoning techniques (PR), including genetic algorithms, chaos theory, and part of learning theory. Increasingly, these techniques are used in combination to achieve significant improvement in performance and adaptability. Among the important application areas for soft computing are control systems, expert systems, data compression techniques, image processing, and decision support systems. It may be argued that it is soft computing, rather than the traditional hard computing, that should be viewed as the foundation for artificial intelligence. In the years ahead, this may well become a widely held position.

Zadeh, Lofti A.↗
NASA NTRS1994

Infinite possibilities: Computational structures technology

Computational Fluid Dynamics (or CFD) methods are very familiar to the research community. Even the general public has had some exposure to CFD images, primarily through the news media. However, very little attention has been paid to CST--Computational Structures Technology. Yet, no important design can be completed without it. During the first half of this century, researchers only dreamed of designing and building structures on a computer. Today their dreams have become practical realities as computational methods are used in all phases of design, fabrication and testing of engineering systems. Increasingly complex structures can now be built in even shorter periods of time. Over the past four decades, computer technology has been developing, and early finite element methods have grown from small in-house programs to numerous commercial software programs. When coupled with advanced computing systems, they help engineers make dramatic leaps in designing and testing concepts. The goals of CST include: predicting how a structure will behave under actual operating conditions; designing and complementing other experiments conducted on a structure; investigating microstructural damage or chaotic, unpredictable behavior; helping material developers in improving material systems; and being a useful tool in design systems optimization and sensitivity techniques. Applying CST to a structure problem requires five steps: (1) observe the specific problem; (2) develop a computational model for numerical simulation; (3) develop and assemble software and hardware for running the codes; (4) post-process and interpret the results; and (5) use the model to analyze and design the actual structure. Researchers in both industry and academia continue to make significant contributions to advance this technology with improvements in software, collaborative computing environments and supercomputing systems. As these environments and systems evolve, computational structures technology will evolve. By using CST in the design and operation of future structures systems, engineers will have a better understanding of how a system responds and lasts, more cost-effective methods of designing and testing models, and improved productivity. For informational and educational purposes, a videotape is being produced using both static and dynamic images from research institutions, software and hardware companies, private individuals, and historical photographs and drawings. The extensive number of CST resources indicates its widespread use. Applications run the gamut from simpler university-simulated problems to those requiring solutions on supercomputers. In some cases, an image or an animation will be mapped onto the actual structure to show the relevance of the computer model to the structure. Transferring the digital files to videotape presents a number of problems related to maintaining the quality of the original image, while still producing a broadcast quality videotape. Since researchers normally do not create a computer image using traditional composition theories or video production requirements, often the image loses some of its original digital quality and impact when transferred to videotape. Although many CST images are currently available, those that are edited into the final project must meet two important criteria: they must complement the narration, and they must be broadcast quality when recorded on videotape.

Beam, Sherilee F.↗
NASA NTRS1994

Interactive visualization of Earth and Space Science computations

Computers have become essential tools for scientists simulating and observing nature. Simulations are formulated as mathematical models but are implemented as computer algorithms to simulate complex events. Observations are also analyzed and understood in terms of mathematical models, but the number of these observations usually dictates that we automate analyses with computer algorithms. In spite of their essential role, computers are also barriers to scientific understanding. Unlike hand calculations, automated computations are invisible and, because of the enormous numbers of individual operations in automated computations, the relation between an algorithm's input and output is often not intuitive. This problem is illustrated by the behavior of meteorologists responsible for forecasting weather. Even in this age of computers, many meteorologists manually plot weather observations on maps, then draw isolines of temperature, pressure, and other fields by hand (special pads of maps are printed for just this purpose). Similarly, radiologists use computers to collect medical data but are notoriously reluctant to apply image-processing algorithms to that data. To these scientists with life-and-death responsibilities, computer algorithms are black boxes that increase rather than reduce risk. The barrier between scientists and their computations can be bridged by techniques that make the internal workings of algorithms visible and that allow scientists to experiment with their computations. Here we describe two interactive systems developed at the University of Wisconsin-Madison Space Science and Engineering Center (SSEC) that provide these capabilities to Earth and space scientists.

Hibbard, William L.↗
NASA NTRS2000

Information Power Grid: Distributed High-Performance Computing and Large-Scale Data Management for Science and Engineering

We use the term "Grid" to refer to distributed, high performance computing and data handling infrastructure that incorporates geographically and organizationally dispersed, heterogeneous resources that are persistent and supported. This infrastructure includes: (1) Tools for constructing collaborative, application oriented Problem Solving Environments / Frameworks (the primary user interfaces for Grids); (2) Programming environments, tools, and services providing various approaches for building applications that use aggregated computing and storage resources, and federated data sources; (3) Comprehensive and consistent set of location independent tools and services for accessing and managing dynamic collections of widely distributed resources: heterogeneous computing systems, storage systems, real-time data sources and instruments, human collaborators, and communications systems; (4) Operational infrastructure including management tools for distributed systems and distributed resources, user services, accounting and auditing, strong and location independent user authentication and authorization, and overall system security services The vision for NASA's Information Power Grid - a computing and data Grid - is that it will provide significant new capabilities to scientists and engineers by facilitating routine construction of information based problem solving environments / frameworks. Such Grids will knit together widely distributed computing, data, instrument, and human resources into just-in-time systems that can address complex and large-scale computing and data analysis problems. Examples of these problems include: (1) Coupled, multidisciplinary simulations too large for single systems (e.g., multi-component NPSS turbomachine simulation); (2) Use of widely distributed, federated data archives (e.g., simultaneous access to metrological, topological, aircraft performance, and flight path scheduling databases supporting a National Air Space Simulation systems}; (3) Coupling large-scale computing and data systems to scientific and engineering instruments (e.g., realtime interaction with experiments through real-time data analysis and interpretation presented to the experimentalist in ways that allow direct interaction with the experiment (instead of just with instrument control); (5) Highly interactive, augmented reality and virtual reality remote collaborations (e.g., Ames / Boeing Remote Help Desk providing field maintenance use of coupled video and NDI to a remote, on-line airframe structures expert who uses this data to index into detailed design databases, and returns 3D internal aircraft geometry to the field); (5) Single computational problems too large for any single system (e.g. the rotocraft reference calculation). Grids also have the potential to provide pools of resources that could be called on in extraordinary / rapid response situations (such as disaster response) because they can provide common interfaces and access mechanisms, standardized management, and uniform user authentication and authorization, for large collections of distributed resources (whether or not they normally function in concert). IPG development and deployment is addressing requirements obtained by analyzing a number of different application areas, in particular from the NASA Aero-Space Technology Enterprise. This analysis has focussed primarily on two types of users: the scientist / design engineer whose primary interest is problem solving (e.g. determining wing aerodynamic characteristics in many different operating environments), and whose primary interface to IPG will be through various sorts of problem solving frameworks. The second type of user is the tool designer: the computational scientists who convert physics and mathematics into code that can simulate the physical world. These are the two primary users of IPG, and they have rather different requirements. The results of the analysis of the needs of these two types of users provides a broad set of requirements that gives rise to a general set of required capabilities. The IPG project is intended to address all of these requirements. In some cases the required computing technology exists, and in some cases it must be researched and developed. The project is using available technology to provide a prototype set of capabilities in a persistent distributed computing testbed. Beyond this, there are required capabilities that are not immediately available, and whose development spans the range from near-term engineering development (one to two years) to much longer term R&D (three to six years). Additional information is contained in the original.

Johnston, William E.↗
NASA NTRSDate not supplied

Assessing and Advancing the Potential of Quantum Computing: A NASA Case Study

Quantum computing is one of the most enticing computational paradigms with the potential to revolutionize diverse areas of future-generation computational systems. While quantum computing hardware has advanced rapidly, from tiny laboratory experiments to quantum chips that can outperform even the largest supercomputers on specialized computational tasks, these noisy- intermediate scale quantum (NISQ) processors are still too small and non-robust to be directly useful for any real-world applications. In this paper, we describe NASA’s work in assessing and advancing the potential of quantum computing. We discuss advances in algorithms, both near- and longer-term, and the results of our explorations on current hardware as well as with simulations, including illustrating the benefits of algorithm-hardware codesign in the NISQ era. This work also includes physics-inspired classical algorithms that can be used at application scale today. We discuss innovative tools supporting the assessment and advancement of quantum computing, and describe improved methods for simulating quantum systems of various types on high performance computing systems that incorporate realistic error models. We provide an overview of recent methods for benchmarking, evaluating, and characterizing quantum hardware for error mitigation, computational purposes.

quantum computing↗
DOE OSTI2026

A mathematical framework for thermodynamic computing with applications to chemical reaction networks

The widespread adoption of energy-intensive computing applications has led to a growing need for energy-efficient computing approaches. Thermodynamic computing offers a promising approach for low-energy computation by leveraging the intrinsic computational capabilities of physical, chemical, or biological systems. However, the mathematical foundations of thermodynamic computing require further development to fully realize the potential energy efficiencies, as well as to assess factors like noise and operational speed. In this paper, we establish a mathematical framework for utilizing thermodynamic processes to perform fundamental operations, including addition, subtraction, multiplication, and division. We highlight the use of chemical reactions as potential computational units and explore synthetic chemical and biochemical systems as practical implementations. Additionally, we demonstrate how these principles can be applied to solving complex mathematical problems, such as ordinary differential equations (ODEs) and suggest the necessary components to implement the thermodynamic computing framework using chemical reactions based in a microfluidic device. This work enhances our understanding of thermodynamic processes for natural computing as a basis for scalable, energy-efficient computation in paradigm disruptive next-generation systems.

Cannon, William R. [Pacific Northwest National Lab↗
DOE OSTI2024

Computing with a Chemical Reservoir

Contemporary computation is expensive, with large language models and artificial intelligence becoming more common in daily life. However, high-performance computing is reaching the limits in speed and energy expenditure, and domain science requires ever-increasing computational capacity, with simulations and data analysis pipelines ever-growing in complexity. As we progress towards post-exascale computation, with the associated high energy costs, new methods of energy-conscious computation are required. Novel analog and hybrid digital-analog systems can overcome these challenges, and chemical reactions offer a promising avenue. Computers based on chemistry can provide compact desktop devices with immense computational power. These devices are readily scalable by considering greater reaction systems or vessels, meeting the high-performance requirements for scientific workflows. In this article, we present ChemComp, a compilation pipeline for the conversion of ordinary differential equations into implementable chemical reactions. We then demonstrate the solving capabilities of ChemComp by emulating a potential chemical reservoir device. We leverage the multi-layer intermediate representation (MLIR) compiler framework to implement an expressive chemical reaction abstraction and propose a path for chemical reaction networks (CRNs) to represent mathematical problems effectively. Combined, we demonstrate a potential workflow that can harness chemistry’s computing power to create energy-efficient, high-performance computation systems for contemporary computing needs.

artificial intelligence↗
DOE OSTI2024

Shifting Between Compute and Memory Bounds: A Compression-Enabled Roofline Model

In the evolving landscape of high-performance computing, especially to fight the end of Moore’s Law and Dennard’s Scaling, the ability to shift between compute-bound and memory-bound states is critical for enhancing adaptability and flexibility to diverse system and domain-specific architectures. Such capability is vital for optimizing performance across distinguished hardware configurations, such as accelerators, memory hierarchies, and cache systems. Despite that ad hoc optimization techniques, such as compressed/approximate computation, have been enabled for compute-/data-intensive computing for improved performance in distinct hardware settings, there lacks an understanding of 1) the rational behind performance improvement; 2) capability of different optimizations; 3) what optimization to respond to specific computational and memory demands. This work proposes a compression-enabled roofline model to facilitate this adaptability with data compression techniques to balance and transform between computational and memory demands. This model enables applications to adjust in response to the specific strengths and limitations of the underlying hardware and system to optimize resource utilization. The effectiveness of this approach is demonstrated with matrix multiplication kernels on different input sizes, with turning on/off various compression techniques, including 1) low-precision floating point; 2) sparse matrix formulation; and 3) compressed arrays with ZFP. By reducing memory transfer volumes and cache misses and increasing data locality and computational intensity through compression, the specific roofline model can transform between compute and memory bounds to align more efficiently with system capabilities. This advancement not only improves overall performance but also maximizes adaptability in diverse computing environments.

Naraparaju, Ramasoumya [University of Washington]↗
DOE OSTI2024

Quantum Computing for Energy-Related Applications

Growing interest in quantum computing and simulations have created opportunities for its deployment to improve processes pertaining to energy production, distribution, and consumption. While quantum computing is considered as a paradigm shift in our basic understanding of physical computation, effective implementation of quantum computing in energy applications also depends on progress and development in the dimensions of both quantum computing hardware and quantum computing algorithms. To fully address the status and future challenges of quantum information science (QIS) applied within the energy sector, in this presentation, we firstly summarize recent advancements on the applications of quantum computing to energy infrastructure and materials, complex energy system processes, advanced manufacturing, and energy system security. Then, we will demonstrate the results of quantum computing both on a simulator and a quantum device accessing from OLCF. Our first example is to use the variational quantum eigensolver (VQE) with a unitary coupled cluster with singles and doubles (UCCSD) ansatz to simulate a series of LixHyq molecules (q=-1, 0, +1). The obtained results showed that the quantum computing VQE-UCCSD is comparable to classical CCSD for small systems like LiH with respect to full configuration interaction (FCI). Targeting on CO2 capture application, our second example is to use VQE to quantify molecular vibrational energies and reaction pathways between CO2 and a simplified amine-based solvent model—NH3 to form H2NCOOH. This research showcases quantum computing applications in the study of CO2 capture reactions.

Duan, Yuhua↗
NASA NTRS1993

Fast parallel algorithms that compute transitive closure of a fuzzy relation

The notion of a transitive closure of a fuzzy relation is very useful for clustering in pattern recognition, for fuzzy databases, etc. The original algorithm proposed by L. Zadeh (1971) requires the computation time O(n(sup 4)), where n is the number of elements in the relation. In 1974, J. C. Dunn proposed a O(n(sup 2)) algorithm. Since we must compute n(n-1)/2 different values s(a, b) (a not equal to b) that represent the fuzzy relation, and we need at least one computational step to compute each of these values, we cannot compute all of them in less than O(n(sup 2)) steps. So, Dunn's algorithm is in this sense optimal. For small n, it is ok. However, for big n (e.g., for big databases), it is still a lot, so it would be desirable to decrease the computation time (this problem was formulated by J. Bezdek). Since this decrease cannot be done on a sequential computer, the only way to do it is to use a computer with several processors working in parallel. We show that on a parallel computer, transitive closure can be computed in time O((log(sub 2)(n))2).

Kreinovich, Vladik YA.↗
NASA NTRS1995

Exploring the use of I/O nodes for computation in a MIMD multiprocessor

As parallel systems move into the production scientific-computing world, the emphasis will be on cost-effective solutions that provide high throughput for a mix of applications. Cost effective solutions demand that a system make effective use of all of its resources. Many MIMD multiprocessors today, however, distinguish between 'compute' and 'I/O' nodes, the latter having attached disks and being dedicated to running the file-system server. This static division of responsibilities simplifies system management but does not necessarily lead to the best performance in workloads that need a different balance of computation and I/O. Of course, computational processes sharing a node with a file-system service may receive less CPU time, network bandwidth, and memory bandwidth than they would on a computation-only node. In this paper we begin to examine this issue experimentally. We found that high performance I/O does not necessarily require substantial CPU time, leaving plenty of time for application computation. There were some complex file-system requests, however, which left little CPU time available to the application. (The impact on network and memory bandwidth still needs to be determined.) For applications (or users) that cannot tolerate an occasional interruption, we recommend that they continue to use only compute nodes. For tolerant applications needing more cycles than those provided by the compute nodes, we recommend that they take full advantage of both compute and I/O nodes for computation, and that operating systems should make this possible.

Kotz, David↗
NASA NTRS1996

Computational Analysis of Static and Dynamic Behaviour of Magnetic Suspensions and Magnetic Bearings

Static modelling of magnetic bearings is often carried out using magnetic circuit theory. This theory cannot easily include nonlinear effects such as magnetic saturation or the fringing of flux in air-gaps. Modern computational tools are able to accurately model complex magnetic bearing geometries, provided some care is exercised. In magnetic suspension applications, the magnetic fields are highly three-dimensional and require computational tools for the solution of most problems of interest. The dynamics of a magnetic bearing or magnetic suspension system can be strongly affected by eddy currents. Eddy currents are present whenever a time-varying magnetic flux penetrates a conducting medium. The direction of flow of the eddy current is such as to reduce the rate-of-change of flux. Analytic solutions for eddy currents are available for some simplified geometries, but complex geometries must be solved by computation. It is only in recent years that such computations have been considered truly practical. At NASA Langley Research Center, state-of-the-art finite-element computer codes, 'OPERA', 'TOSCA' and 'ELEKTRA' have recently been installed and applied to the magnetostatic and eddy current problems. This paper reviews results of theoretical analyses which suggest general forms of mathematical models for eddy currents, together with computational results. A simplified circuit-based eddy current model proposed appears to predict the observed trends in the case of large eddy current circuits in conducting non-magnetic material. A much more difficult case is seen to be that of eddy currents in magnetic material, or in non-magnetic material at higher frequencies, due to the lower skin depths. Even here, the dissipative behavior has been shown to yield at least somewhat to linear modelling. Magnetostatic and eddy current computations have been carried out relating to the Annular Suspension and Pointing System, a prototype for a space payload pointing and vibration isolation system, where the magnetic actuator geometry resembles a conventional magnetic bearing. Magnetostatic computations provide estimates of flux density within airgaps and the iron core material, fringing at the pole faces and the net force generated. Eddy current computations provide coil inductance, power dissipation and the phase lag in the magnetic field, all as functions of excitation frequency. Here, the dynamics of the magnetic bearings, notably the rise time of forces with changing currents, are found to be very strongly affected by eddy currents, even at quite low frequencies. Results are also compared to experimental measurements of the performance of a large-gap magnetic suspension system, the Large Angle Magnetic Suspension Test Fixture (LAMSTF). Eddy current effects are again shown to significantly affect the dynamics of the system. Some consideration is given to the ease and accuracy of computation, specifically relating to OPERA/TOSCA/ELEKTRA.

Britcher, Colin P.↗