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At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Efficient Measurement-Driven Eigenenergy Estimation with Classical Shadows

Quantum algorithms exploiting real-time evolution under a target Hamiltonian have demonstrated remarkable efficiency in extracting key spectral information. However, the broader potential of these methods, particularly beyond ground-state calculations, is underexplored. In this work, we introduce the framework of multiobservable dynamic mode decomposition (MODMD), which combines the observable dynamic mode decomposition (DMD), a measurement-driven eigensolver tailored for near-term implementation, with classical shadow tomography. MODMD leverages random scrambling in the classical shadow technique to construct, with exponentially reduced resource requirements, a signal subspace that encodes rich spectral information. Notably, we replace typical Hadamard-test circuits with a protocol designed to predict low-rank observables, thereby broadening the use of classical shadow tomography for predicting many low-rank observables. We establish theoretical guarantees on the spectral approximation from MODMD, taking into account distinct sources of error. In the ideal case, we prove that the spectral error scales as exp (−Δ⁢𝐸⁢𝑡 max ), where Δ⁢𝐸 is the Hamiltonian spectral gap and 𝑡 max is the maximal simulation time. This analysis provides a rigorous justification of the rapid convergence observed across simulations. To demonstrate the utility of our framework, we consider its application to fundamental tasks, such as determining the low-lying, i.e., ground or excited, energies of representative many-body systems. Our work paves the path for efficient designs of measurement-driven algorithms on near-term and early fault-tolerant quantum devices.

quantum algorithms & computation↗
DOE OSTI2022

Near-field radiative heat transfer between irregularly shaped dielectric particles modeled with the discrete system Green's function method

Near-field radiative heat transfer (NFRHT) between irregularly shaped dielectric particles made of SiO 2 and morphology characterized by Gaussian random spheres is studied. Particles are modeled using the discrete system Green's function (DSGF) approach, which is a volume integral numerical method based on fluctuational electrodynamics. This method is applicable to finite, three-dimensional objects, and all system interactions are defined independent of thermal excitation by a generalized system Green's function. The DSGF method is deemed suitable to model NFRHT between irregularly shaped particles after verification against the analytical solution for chains of two and three SiO 2 spheres. The NFRHT results reveal that geometric irregularity in particles leads to a reduction of the total conductance from that of comparable perfect spheres at vacuum separation distances smaller than the particle size, a regime in which NFRHT is a surface phenomenon. At vacuum separation distances larger than the particle size, NFRHT becomes a volumetric process, and the total conductance between irregularly shaped particles converges to that of comparable perfect spheres. Spectral analysis reveals, however, that particle irregularity leads to damping and broadening of resonances at all separation distances, thereby highlighting the importance of the DSGF method for spectral engineering in the near field. The reduced spectral coherence when particle size is larger than the vacuum separation distance is attributed to coupling of surface phonon-polaritons within the randomly generated, distorted particle features. For particle size smaller than the vacuum separation distance, resonance broadening and damping are linked with the multiple localized surface phonon modes supported by the composite spherical harmonic morphologies of the Gaussian random spheres. In conclusion, this paper has direct implications for thermal management of packed particle systems, with applications in radiative property control, electronics, energy conversion, and nanomanufacturing.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1974

Analysis of complex elastic structures by a Rayleigh-Ritz component modes method using Lagrange multipliers

The free vibrations of elastic structures of arbitrary complexity were analyzed in terms of their component modes. The method was based upon the use of the normal unconstrained modes of the components in a Rayleigh-Ritz analysis. The continuity conditions were enforced by means of Lagrange Multipliers. Examples of the structures considered are: (1) beams with nonuniform properties; (2) airplane structures with high or low aspect ratio lifting surface components; (3) the oblique wing airplane; and (4) plate structures. The method was also applied to the analysis of modal damping of linear elastic structures. Convergence of the method versus the number of modes per component and/or the number of components is discussed and compared to more conventional approaches, ad-hoc methods, and experimental results.

Klein, L. R.↗
NASA NTRS1984

Aerospace engineering design by systematic decomposition and multilevel optimization

A method for systematic analysis and optimization of large engineering systems, by decomposition of a large task into a set of smaller subtasks that is solved concurrently is described. The subtasks may be arranged in hierarchical levels. Analyses are carried out in each subtask using inputs received from other subtasks, and are followed by optimizations carried out from the bottom up. Each optimization at the lower levels is augmented by analysis of its sensitivity to the inputs received from other subtasks to account for the couplings among the subtasks in a formal manner. The analysis and optimization operations alternate iteratively until they converge to a system design whose performance is maximized with all constraints satisfied. The method, which is still under development, is tentatively validated by test cases in structural applications and an aircraft configuration optimization.

Sobieszczanski-Sobieski, J.↗
NASA NTRS1984

Automated mesoscale winds derived from GOES multispectral imagery

An automated technique for extracting mesoscale winds from sequences of GOES VISSR image pairs was developed, tested and configured for quasi-real time/research applications on a computing system which gives mesoscale wind estimates at the highest spatial/temporal resolution possible from the VISSR imagery down to a wind vector separation of 10 km. Preprocessing of imagery using IR resampling, VIS edge preserving filtering, and reduced VIS resolution averaging improved height assignments and vector extraction for 10, 15, and 30 min imagery. An objective quality control system provides much greater than 99% accuracy in eliminating questionable wind estimates. Automated winds generally have better spatial coverage and density, and have random error estimates half as large as the manual winds. Dynamical analysis of cloud wind divergence revealed temporally consistent convergence centers on the meso beta scale that are highly correlated with on going and future developing convective storms. The entire system of computer codes was successfully vectorized for execution on an array processor resulting in job turnaround in less than one hour.

Wilson, G. S.↗
NASA NTRS1984

Aerospace engineering design by systematic decomposition and multilevel optimization

This paper describes a method for systematic analysis and optimization of large engineering systems, e.g., aircraft, by decomposition of a large task into a set of smaller, self-contained subtasks that can be solved concurrently. The subtasks may be arranged in many hierarchical levels with the assembled system at the top level. Analyses are carried out in each subtask using inputs received from other subtasks, and are followed by optimizations carried out from the bottom up. Each optimization at the lower levels is augmented by analysis of its sensitivity to the inputs received from other subtasks to account for the couplings among the subtasks in a formal manner. The analysis and optimization operations alternate iteratively until they converge to a system design whose performance is maximized with all constraints satisfied. The method, which is still under development, is tentatively validated by test cases in structural applications and an aircraft configuration optimization. It is pointed out that the method is intended to be compatible with the typical engineering organization and the modern technology of distributed computing.

Sobieszczanski-Sobieski, J.↗
NASA NTRS1992

Magnetic flipping - Reconnection in three dimensions without null points

In three dimensions, magnetic reconnection may take place in a sheared magnetic field at any singular field line, where the nearby field has X-type topology in planes perpendicular to the field line and where an electric field is present parallel to the field line. In the ideal region around the singular line there will, in general, be singularities in the plasma flow and electric field, both at the singular line and at 'magnetic flipping layers', which are remnants of local magnetic separatrices. In the absence of a three-dimensional magnetic neutral point or null point, reconnection of field lines can still occur by a process of magnetic flipping, in which the plasma crosses the flipping layers but the field lines rapidly flip along them by magnetic diffusion. Depending on the boundary conditions, there may be two or four flipping layers which converge on the singular line. A boundary layer analysis of a flipping layer is given, in which the magnetic field parallel to the layer decreases as one crosses it while the plasma pressure (or magnetic pressure associated with the field along the singular line) increases. The width of the flipping layer decreases with distance from the singular line.

Priest, E. R.↗
NASA NTRS1995

Comparison between global latent heat flux computed from multisensor (SSM/I and AVHRR) and from in situ data

Comprehensive Ocean-Atmosphere Data Set (COADS) and satellite-derived parameters are input to a similarity theory-based model and treated in completely equivalent ways to compute global latent heat flux (LHF). In order to compute LHF exclusively from satellite measurements, an empirical relationship (Q-W relationship) is used to compute the air mixing ratio from Special Sensor Microwave/Imager (SSM/I) precipitable water W and a new one is derived to compute the air temperature also from retrieved W(T-W relationship). First analyses indicate that in situ and satellite LHF computations compare within 40%, but systematic errors increase the differences up to 100% in some regions. By investigating more closely the origin of the discrepancies, the spatial sampling of ship reports has been found to be an important source of error in the observed differences. When the number of in situ data records increases (more than 20 per month), the agreement is about 50 W/sq m rms (40 W/sq m rms for multiyear averages). Limitations of both empirical relationships and W retrieval errors strongly affect the LHF computation. Systematic LHF overestimation occurs in strong subsidence regions and LHF underestimation occurs within surface convergence zones and over oceanic upwelling areas. The analysis of time series of the different parameters in these regions confirms that systematic LHF discrepancies are negatively correlated with the differences between COADS and satellite-derived values of the air mixing ratio and air temperature. To reduce the systematic differences in satellite-derived LHF, a preliminary ship-satellite blending procedure has been developed for the air mixing ratio and air temperature.

Jourdan, Didier↗
NASA NTRS1992

Small Business Innovations (Helicopters)

The amount of engine power required for a helicopter to hover is an important, but difficult, consideration in helicopter design. The EHPIC program model produces converged, freely distorted wake geometries that generate accurate analysis of wake-induced downwash, allowing good predictions of rotor thrust and power requirements. Continuum Dynamics, Inc., the Small Business Innovation Research (SBIR) company that developed EHPIC, also produces RotorCRAFT, a program for analysis of aerodynamic loading of helicopter blades in forward flight. Both helicopter codes have been licensed to commercial manufacturers.

Source record↗
NASA NTRS2008

Bounded Linear Stability Margin Analysis of Nonlinear Hybrid Adaptive Control

This paper presents a bounded linear stability analysis for a hybrid adaptive control that blends both direct and indirect adaptive control. Stability and convergence of nonlinear adaptive control are analyzed using an approximate linear equivalent system. A stability margin analysis shows that a large adaptive gain can lead to a reduced phase margin. This method can enable metrics-driven adaptive control whereby the adaptive gain is adjusted to meet stability margin requirements.

Nguyen, Nhan T.↗
NASA NTRS2011

Convergence of Defect-Correction and Multigrid Iterations for Inviscid Flows

Convergence of multigrid and defect-correction iterations is comprehensively studied within different incompressible and compressible inviscid regimes on high-density grids. Good smoothing properties of the defect-correction relaxation have been shown using both a modified Fourier analysis and a more general idealized-coarse-grid analysis. Single-grid defect correction alone has some slowly converging iterations on grids of medium density. The convergence is especially slow for near-sonic flows and for very low compressible Mach numbers. Additionally, the fast asymptotic convergence seen on medium density grids deteriorates on high-density grids. Certain downstream-boundary modes are very slowly damped on high-density grids. Multigrid scheme accelerates convergence of the slow defect-correction iterations to the extent determined by the coarse-grid correction. The two-level asymptotic convergence rates are stable and significantly below one in most of the regions but slow convergence is noted for near-sonic and very low-Mach compressible flows. Multigrid solver has been applied to the NACA 0012 airfoil and to different flow regimes, such as near-tangency and stagnation. Certain convergence difficulties have been encountered within stagnation regions. Nonetheless, for the airfoil flow, with a sharp trailing-edge, residuals were fast converging for a subcritical flow on a sequence of grids. For supercritical flow, residuals converged slower on some intermediate grids than on the finest grid or the two coarsest grids.

Diskin, Boris↗
NASA NTRS2011

Adaptation of G-TAG Software for Validating Touch-and-Go Comet Surface Sampling Design Methodology

The G-TAG software tool was developed under the R&TD on Integrated Autonomous Guidance, Navigation, and Control for Comet Sample Return, and represents a novel, multi-body dynamics simulation software tool for studying TAG sampling. The G-TAG multi-body simulation tool provides a simulation environment in which a Touch-and-Go (TAG) sampling event can be extensively tested. TAG sampling requires the spacecraft to descend to the surface, contact the surface with a sampling collection device, and then to ascend to a safe altitude. The TAG event lasts only a few seconds but is mission-critical with potentially high risk. Consequently, there is a need for the TAG event to be well characterized and studied by simulation and analysis in order for the proposal teams to converge on a reliable spacecraft design. This adaptation of the G-TAG tool was developed to support the Comet Odyssey proposal effort, and is specifically focused to address comet sample return missions. In this application, the spacecraft descends to and samples from the surface of a comet. Performance of the spacecraft during TAG is assessed based on survivability and sample collection performance. For the adaptation of the G-TAG simulation tool to comet scenarios, models are developed that accurately describe the properties of the spacecraft, approach trajectories, and descent velocities, as well as the models of the external forces and torques acting on the spacecraft. The adapted models of the spacecraft, descent profiles, and external sampling forces/torques were more sophisticated and customized for comets than those available in the basic G-TAG simulation tool. Scenarios implemented include the study of variations in requirements, spacecraft design (size, locations, etc. of the spacecraft components), and the environment (surface properties, slope, disturbances, etc.). The simulations, along with their visual representations using G-View, contributed to the Comet Odyssey New Frontiers proposal effort by indicating problems and/or benefits of different approaches and designs.

Mandic, Milan↗
NASA NTRS2020

AERoBOND Project Summary

Under NASA’s Convergent Aeronautics Solutions (CAS) project, the Adhesive-Free Bonding of Complex Composites (AERoBOND) project investigated off-stoichiometric epoxy polymers for fast, reliable assembly of epoxy matrix composite structures. The project goal was to demonstrate feasibility of the AERoBOND joining method by demonstrating mechanical properties greater than 80% of conventional co-cured materials while reducing structure weight by 1%. The project consisted of three convergent research areas: material and process development, systems analysis, and material and process modeling. Material and process development was the largest component of AERoBOND with approximately 6 FTE and 1WYE of support to formulate and characterize new resins, prepare carbon fiber prepregs, fabricate laminates, measure mechanical properties, analyze failure results, and select material and process improvements. The systems analysis activity estimated the potential reduction in part count and aircraft weight by comparing models of composite wing boxes with no fasteners (co-cured structure), fasteners in major joints (co-cured stringers), and fasteners in all joints. The materials and process modeling activity included a molecular model of the AERoBOND materials system to predict mechanical properties of resins with offset stoichiometry and a process model to predict the effect of resin formulation and processing conditions on the extent of mixing and degree of cure in a finished joint. As the number of airline passenger trips doubles in the next 20 years (IATA/Tourism Economics Air Passenger Forecasts, April 2019), the increased demand for new commercial aircraft is now the single greatest technical challenge to the airframe manufacturing industry. To meet efficiency requirements, new aircraft must be fabricated primarily from high performance structural composites, but manufacturing processes are inherently slow with the largest bottleneck attributed to assembly and installation of fasteners (NASA/TM–2019-220428). Manufactures of commercial transport aircraft are compelled to install more than 100,000 redundant fasteners into bonded joints to prevent failures due to unpredictable weak bonds. In structural adhesive bonds, the interface between adherend and adhesive is nearly two-dimensional making it susceptible to minute quantities of contamination, which can cause weak bonds. Currently, bond strength assessment is only possible through destructive testing (i.e., breaking the joint). For these reasons, regulatory organizations such as the Federal Aviation Administration (FAA) often require redundant load paths in secondary-bonded, primary-structures to alleviate concerns with bond performance. The AERoBOND process enables reflow of matrix resin during assembly to eliminate the material discontinuity at the interface, thereby eliminating the dependence of mechanical performance on interfacial adhesion. The AERoBOND joint is equivalent to the interlaminar region obtained during a co-cure process, so joint performance depends on the cohesive properties of the matrix resin. Conventional co-cured structures, although too costly and complex for large-scale manufacturing, are trusted by manufacturers and regulators, and are certified for flight with few or no redundant fasteners.Systems analysis performed on a composite wing model at the scale of a single-aisle commercial transport aircraft indicated that >20,000 redundant fasteners per wing could be eliminated by implementing the AERoBOND joining method. A total weight reduction of 15% was predicted in a wing box by eliminating fasteners and thinning components that must no longer support localized fastener loads and accommodate fastener dimensions. Interlaminar shear fracture toughness measured by the end-notched flexure test was greater than 1 kJ/m2 (nearly 140% of the co-cured benchmark property), which is greatly in excess of the project goals for mechanical properties. Testing was planned to measure interlaminar tensile fracture toughness as well as interlaminar tensile and shear strengths using the same AERoBOND configuration, but was delayed due to closure of LaRC facilities during the COVID-19 pandemic. The AERoBOND process model is partially validated and available for experimental use. It allows the user to input AERoBOND process parameters such as material composition, laminate configuration, and cure cycle to predict the final cure state of the AERoBOND joint. A preliminary, multi-scale material model was developed to predict AERoBOND joint mechanical properties (stiffness and strength) based on the cure state of the joint provided by the process model. The timing for transition of this technology within NASA is excellent as NASA initiates new enduring projects to address composites manufacturing rate challenges. AERoBOND technology is well suited to AAVP/AATT objectives for rapid manufacturing of a composite wing. A minimal effort (1 FTE/$15k procurement/0 WYE) is proposed in FY21 to continue a minor mechanical testing effort and maintain a SAA with ASX composites to develop commercial quality prepreg material. An RFI with the composites industry is suggested to quantify the technology gap between the current TRL and the TRL needed for transition to industry. A moderate effort [3-4 FTE/$150k/1 WYE (~$115k)] is proposed in FY22 for the “high rate composites manufacturing” project currently in planning. The partnership with ASX Composites will be expanded to produce material for sub-element/element-scale “panel-off” activities. Industry partnerships with airframe manufacturers is an expected component to explore damage tolerance and environmental stability. Further development of multi-scale modeling tools (process model, meso-scale model, and molecular model) is planned to enhance and deliver tools for rapid manufacturing infusion.

Frank Louis Palmieri↗
NASA NTRS2018

Overview of the Spacecraft Design for the Psyche Mission Concept

In January 2017, Psyche and a second mission concept were selected by NASA for flight as part of the 14th Discovery mission competition. Assigned for an initial launch date in 2023, the Psyche team was given direction shortly after selection to research the possibility for earlier opportunities. Ultimately, the team was able to identify a launch opportunity in 2022 with a reduced flight time to its destination. This was accomplished in large part to crosscutting trades centered on the electrical power subsystem. These trades were facilitated through the Psyche mission's planned use of Solar Electric Propulsion (SEP), which enables substantial flexibility with respect to trajectory design. In combination with low-thrust trajectory analysis tools, the team was able to robustly converge to solutions with a higher fidelity and accuracy of results. These trades also took advantage of the 1300 series product line produced by Space Systems Loral (SSL), which enabled power growth while maintaining strong system-level heritage through its modular design that has been utilized on a large number of geostationary (GEO) communications satellites. This paper presents an overview of the Psyche mission concept, and the unique architecture that enables the use of commercially developed electric propulsion and space power systems from Space Systems Loral to provide flexibility in mission design. This paper then discusses the trades that allowed the Psyche team to meet a 2022 launch date.

Prikl, Zachary↗
NASA NTRS2013

Statistical Analysis of CFD Solutions From the Fifth AIAA Drag Prediction Workshop

A graphical framework is used for statistical analysis of the results from an extensive N-version test of a collection of Reynolds-averaged Navier-Stokes computational fluid dynamics codes. The solutions were obtained by code developers and users from North America, Europe, Asia, and South America using a common grid sequence and multiple turbulence models for the June 2012 fifth Drag Prediction Workshop sponsored by the AIAA Applied Aerodynamics Technical Committee. The aerodynamic configuration for this workshop was the Common Research Model subsonic transport wing-body previously used for the 4th Drag Prediction Workshop. This work continues the statistical analysis begun in the earlier workshops and compares the results from the grid convergence study of the most recent workshop with previous workshops.

Statistical analysis↗
NASA NTRS2010

Accuracy Analysis for Finite-Volume Discretization Schemes on Irregular Grids

A new computational analysis tool, downscaling test, is introduced and applied for studying the convergence rates of truncation and discretization errors of nite-volume discretization schemes on general irregular (e.g., unstructured) grids. The study shows that the design-order convergence of discretization errors can be achieved even when truncation errors exhibit a lower-order convergence or, in some cases, do not converge at all. The downscaling test is a general, efficient, accurate, and practical tool, enabling straightforward extension of verification and validation to general unstructured grid formulations. It also allows separate analysis of the interior, boundaries, and singularities that could be useful even in structured-grid settings. There are several new findings arising from the use of the downscaling test analysis. It is shown that the discretization accuracy of a common node-centered nite-volume scheme, known to be second-order accurate for inviscid equations on triangular grids, degenerates to first order for mixed grids. Alternative node-centered schemes are presented and demonstrated to provide second and third order accuracies on general mixed grids. The local accuracy deterioration at intersections of tangency and in flow/outflow boundaries is demonstrated using the DS tests tailored to examining the local behavior of the boundary conditions. The discretization-error order reduction within inviscid stagnation regions is demonstrated. The accuracy deterioration is local, affecting mainly the velocity components, but applies to any order scheme.

Diskin, Boris↗
DOE OSTI2023

Requirements and Recommendations for a Physical Attack Characterization Framework

This study seeks to identify existing frameworks or develop requirements and recommendations for a new framework that can consistently characterize physical attacks, analogous to MITRE ATT&CK®. MITRE ATT&CK is widely used across government, research organizations, and the cyber security community to characterize cyber attack tactics, techniques, and procedures (TTPs) in a consistent and commonly understood manner. While physical attack taxonomies, methodologies, and other tools for evaluating physical security do exist, many are sector and/or facility-type specific—and therefore not able to provide comparable scenarios across sectors—or are more focused on security assessment instead of the characterization of attacks themselves. A MITRE ATT&CK analog for physical attacks on critical infrastructure would provide a common language and structure for analysis of physical attacks. Existing attack characterization methodologies do not robustly address cyber-physical security risks. To fully understand a facility’s security needs, it is important to understand the entire vulnerability landscape from both a physical and a cyber perspective. To underscore this need, organizations such as the Cybersecurity and Infrastructure Security Agency (CISA) are calling for a coordinated approach to cyber and physical security, which they refer to as cyber and physical security convergence. A physical attack characterization framework that could be used jointly with MITRE ATT&CK would help support a more robust analysis in support of convergence, enabling the consistent characterization of attacks that utilize both cyber and physical tactics and techniques. This could provide analysts and stakeholders with a clearer understanding of how security mitigations deployed in the physical realm impact security risks in the cyber realm, and vice versa. In this study, the project team evaluates existing physical security taxonomies and methodologies to assess whether an existing method can be used to create a “physical half” of MITRE ATT&CK. This study then provides requirements and recommendations for a framework that can leverage aspects of existing methodologies. The goal of the final framework is for it to be widely adopted and referenced, regardless of critical infrastructure sector, facility type, or facility components. This study also identifies applicable use cases for when and how a framework could be applied across the various critical infrastructure sectors for a variety of attack types or motivations. Through a literature review of existing security-focused methodologies and taxonomies, engagement with relative stakeholders, evaluation of potential physical attack framework use cases, and subsequent identification of requirements, this study identified the following key findings and recommendations: There is a need for a new physical attack characterization framework; A physical attack framework should be interoperable with the MITRE ATT&CK framework; A physical attack framework should be broadly applicable, but with detailed tactics, techniques, and procedures that encompass the entire attack path; A physical attack framework should be based on observed or feasible events; A physical attack framework should adapt features from existing methodologies, frameworks, and taxonomies; A physical attack framework should be owned, overseen, and maintained by one organization.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
NASA NTRS2002

Higher Order, Hybrid BEM/FEM Methods Applied to Antenna Modeling

In this presentation, the authors address topics relevant to higher order modeling using hybrid BEM/FEM formulations. The first of these is the limitation on convergence rates imposed by geometric modeling errors in the analysis of scattering by a dielectric sphere. The second topic is the application of an Incomplete LU Threshold (ILUT) preconditioner to solve the linear system resulting from the BEM/FEM formulation. The final tOpic is the application of the higher order BEM/FEM formulation to antenna modeling problems. The authors have previously presented work on the benefits of higher order modeling. To achieve these benefits, special attention is required in the integration of singular and near-singular terms arising in the surface integral equation. Several methods for handling these terms have been presented. It is also well known that achieving ~he high rates of convergence afforded by higher order bases may als'o require the employment of higher order geometry models. A number of publications have described the use of quadratic elements to model curved surfaces. The authors have shown in an EFIE formulation, applied to scattering by a PEC .sphere, that quadratic order elements may be insufficient to prevent the domination of modeling errors. In fact, on a PEC sphere with radius r = 0.58 Lambda(sub 0), a quartic order geometry representation was required to obtain a convergence benefi.t from quadratic bases when compared to the convergence rate achieved with linear bases. Initial trials indicate that, for a dielectric sphere of the same radius, - requirements on the geometry model are not as severe as for the PEC sphere. The authors will present convergence results for higher order bases as a function of the geometry model order in the hybrid BEM/FEM formulation applied to dielectric spheres. It is well known that the system matrix resulting from the hybrid BEM/FEM formulation is ill -conditioned. For many real applications, a good preconditioner is required to obtain usable convergence from an iterative solver. The authors have examined the use of an Incomplete LU Threshold (ILUT) preconditioner . to solver linear systems stemming from higher order BEM/FEM formulations in 2D scattering problems. Although the resulting preconditioner provided aD excellent approximation to the system inverse, its size in terms of non-zero entries represented only a modest improvement when compared with the fill-in associated with a sparse direct solver. Furthermore, the fill-in of the preconditioner could not be substantially reduced without the occurrence of instabilities. In addition to the results for these 2D problems, the authors will present iterative solution data from the application of the ILUT preconditioner to 3D problems.

Fink, P. W.↗