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NASA NTRS1990

Defect Clustering and Nano-Phase Structure Characterization of Multi-Component Rare Earth Oxide Doped Zirconia-Yttria Thermal Barrier Coatings

Advanced oxide thermal barrier coatings have been developed by incorporating multi- component rare earth oxide dopants into zirconia-yttria to effectively promote the creation of the thermodynamically stable, immobile oxide defect clusters and/or nano-scale phases within the coating systems. The presence of these nano-sized defect clusters has found to significantly reduce the coating intrinsic thermal conductivity, improve sintering resistance, and maintain long-term high temperature stability. In this paper, the defect clusters and nano-structured phases, which were created by the addition of multi-component rare earth dopants to the plasma- sprayed and electron-beam physical vapor deposited thermal barrier coatings, were characterized by high-resolution transmission electron microscopy (TEM). The defect cluster size, distribution, crystallographic and compositional information were investigated using high-resolution TEM lattice imaging, selected area diffraction (SAD), and energy dispersive spectroscopy (EDS) analysis techniques. The results showed that substantial defect clusters were formed in the advanced multi-component rare earth oxide doped zirconia-yttria systems. The size of the oxide defect clusters and the cluster dopant segregation was typically ranging fiom 5 to 50 nm. These multi-component dopant induced defect clusters are an important factor for the coating long-term high temperature stability and excellent performance.

Zhu, Dongming↗

DOE OSTI2025

Role of glucuronoxylomannan and steryl glucosides in protecting against cryptococcosis

The development of vaccines for fungal diseases, including cryptococcosis, is an emergent line of research and development. In previous studies, we showed that a Cryptococcus mutant lacking the SGL1 gene (∆sgl1) accumulates certain glycolipids called steryl glucosides (SGs) on the fungal capsule, promoting an effective immunostimulation that totally protects the host from a secondary cryptococcal infection. However, this protection is lost when the cryptococcal capsule is absent in the ∆sgl1 background. The cryptococcal capsule is mainly composed of glucuronoxylomannan (GXM), a polysaccharide microfiber consisting of glucuronic acid, xylose, and mannose linked by glycosidic bonds forming specific triads. In this study, we engineered cells to lack each of the GXM components and tested the effect of these deletions on protection under the condition of SG accumulation. We found that glucuronic acid and xylose are required for protection, and their absence abrogates the production of IFNγ and IL-17A by γδ T cells, which are necessary stimulants for the protective phenotype of the ∆sgl1. We analyzed the structure of the GXM microfibers and found that although the deletion of SGL1 only slightly affects the size and distribution of these microfibers, it significantly changes the ratio of mannose to other components. In conclusion, this study identifies the structural modifications that the deletion of SGL1 and the consequent accumulation of SGs impart to the GXM structure of C. neoformans. This provides significant insights into the protective mechanisms mediated by SG accumulation on the capsule, with important implications for the future development of an efficacious cryptococcal vaccine.

Cryptococcus neoformans↗

NASA NTRS1993

An efficient formulation of the coupled finite element-integral equation technique for solving large 3D scattering problems

It is often desirable to calculate the electromagnetic fields inside and about a complicated system of scattering bodies, as well as in their far-field region. The finite element method (FE) is well suited to solving the interior problem, but the domain has to be limited to a manageable size. At the truncation of the FE mesh one can either impose approximate (absorbing) boundary conditions or set up an integral equation (IE) for the fields scattered from the bodies. The latter approach is preferable since it results in higher accuracy. Hence, the two techniques can be successfully combined by introducing a surface that encloses the scatterers, applying a FE model to the inner volume and setting up an IE for the tangential fields components on the surface. Here the continuity of the tangential fields is used bo obtain a consistent solution. A few coupled FE-IE methods have recently appeared in the literature. The approach presented here has the advantage of using edge-based finite elements, a type of finite elements with degrees of freedom associated with edges of the mesh. Because of their properties, they are better suited than the conventional node based elements to represent electromagnetic fields, particularly when inhomogeneous regions are modeled, since the node based elements impose an unnatural continuity of all field components across boundaries of mesh elements. Additionally, our approach is well suited to handle large size problems and lends itself to code parallelization. We will discuss the salient features that make our approach very efficient from the standpoint of numerical computation, and the fields and RCS of a few objects are illustrated as examples.

Cwik, T.↗

DOE OSTI2017

Global Value Chain and Manufacturing Analysis on Geothermal Power Plant Turbines: Preprint

The global geothermal electricity market has significantly grown over the last decade and is expected to reach a total installed capacity of 18.4 GWe in 2021 (GEA, 2016). Currently, geothermal project developers customize the size of the power plant to fit the resource being developed. In particular, the turbine is designed and sized to optimize efficiency and resource utilization for electricity production; most often, other power plant components are then chosen to complement the turbine design. These custom turbine designs demand one-off manufacturing processes, which result in higher manufacturing setup costs, longer lead-times, and higher capital costs overall in comparison to larger-volume line manufacturing processes. In contrast, turbines produced in standard increments, manufactured in larger volumes, could result in lower costs per turbine. This study focuses on analysis of the global supply chain and manufacturing costs for Organic Rankine Cycle (ORC) turboexpanders and steam turbines used in geothermal power plants. In this study, we developed a manufacturing cost model to identify requirements for equipment, facilities, raw materials, and labor. We analyzed three different cases 1) 1 MWe geothermal ORC turboexpander 2) 5 MWe ORC turboexpander and 3) 20 MWe geothermal steam turbine, and calculated the cost of manufacturing the major components, such as the impellers/blades, shaft/rotor, nozzles, inlet guide lanes, disks, and casings. Then we used discounted cash flow (DCF) analysis to calculate the minimum sustainable price (MSP). MSP is the minimum price that a company must sell its product for in order to pay back the capital and operating expenses during the plant lifetime (CEMAC, 2017). The results showed that MSP could highly vary between 893 dollar/kW and 30 dollar/kW based on turbine size, standardization and volume of manufacturing. The analysis also showed that the economy of scale applies both to the size of the turbine and the number manufactured in a single run. Sensitivity analysis indicated these savings come largely from reduced labor costs for design and engineering and manufacturing setup.

15 GEOTHERMAL ENERGY↗

DOE OSTI2017

Global Value Chain and Manufacturing Analysis on Geothermal Power Plant Turbines

15 GEOTHERMAL ENERGY↗

NASA NTRS2015

Oxide_Oxide Ceramic Matrix Composite (CMC) Exhaust Mixer Development in the NASA Environmentally Responsible Aviation (ERA) Project

Rolls-Royce North American Technologies, Inc. (LibertyWorksLW) began considering the development of CMC exhaust forced mixers in 2008, as a means of obtaining reduced weight and hotter operating temperature capability, while minimizing shape distortion during operation, which would improve mixing efficiency and reduce fuel burn. Increased component durability, enhanced ability to fabricate complex-shaped components, and engine noise reduction are other potential advantages of CMC mixers (compared to metallic mixers). In 2010, NASA was pursuing the reduction of NOx emissions, fuel burn, and noise from turbine engines in Phase I of the Environmentally Responsible Aviation (ERA) Project. ERA subtasks, including those focused on CMC components, were formulated with the goal of maturing technology from proof of concept validation (TRL 3) to a systemsubsystem or prototype demonstration in a relevant environment (TRL 6). In April 2010, the NASA Glenn Research Center (GRC) and LibertyWorks jointly initiated a CMC Exhaust System Validation Program within the ERA Project, teaming on CMC exhaust mixer development for subsonic jet engines capable of operating with increased performance. Our initial focus was on designing, fabricating, and characterizing the thrust and acoustic performance of a roughly quarter-scale 16-lobe oxide oxide CMC mixer and tail cone along with a conventional low bypass exhaust nozzle. Support Services, LLC (Allendale, MI) and ATK COI Ceramics, Inc. (COIC, in San Diego, CA) supported the design of a subscale nozzle assembly that consisted of an oxide oxide CMC mixer and center body, with each component mounted on a metallic attachment ring. That design was based upon the operating conditions a mixer would experience in a turbofan engine. Validation of the aerodynamic and acoustic performance of the subscale mixer via testing and the achievement of TRL 4 encouraged the NASALWCOIC team to move to the next phase where a full scale CMC mixer sized for a RR AE3007 engine and a compatible attachment flange were designed, followed by CMC component fabrication by COIC, and vibration testing at GRC under conditions simulating the structural and dynamic environment encountered during engine operation. AFRL (WPAFB) supported this testing by performing 3D laser vibrometry to identify the mixer mode shapes and modal frequencies. The successful fabrication and testing of such a component has been achieved. The CMC mixer demonstrated good durability during vibration testing at room and elevated temperature (TRL5). This has cleared the article for a ground-based test on a Rolls-Royce AE3007 engine, where the performance and benefits of the component can be further assessed.

exhaust nozzles↗

NASA NTRSDate not supplied

An Eddy Current Case Study using NASA’s Transfer Function and Limited-Sample Probability of Detection Guidebooks

Probability of detection (POD) requirements for NASA fracture-critical human-rated systems can be met by (1) claiming ‘similarity’ to NASA Standard Nondestructive Evaluation (NDE) flaw sizes or (2) by inspector-specific POD demonstration, known as NASA Special NDE. Standard NDE flaw sizes are intended to represent the detection capability of most qualified inspectors, and were primarily based on POD studies in the development of the Space Shuttle Program Orbiter fracture control plan. However, these Standard NDE flaw sizes were based on fatigue cracks in flat panels of one material alloy over a limited range of panel thicknesses. While the POD study was comprehensive, the inspection conditions are relatively narrow. An evaluation of similarity between the Standard NDE POD study and flight component conditions is required to apply Standard NDE to specific flight component inspections. A similarity evaluation may include differences in materials, surface finish, component geometry (e.g., curvature, corners, welds), and inspection access. Similarity is typically based on a qualitative engineering evaluation. Recently, NASA published a quantitative methodology to assess similarity. If similarity is not supported by test and analysis, then the methodology provides a transfer function of flaw size for Special NDE POD demonstration. NASA recommends that Special POD demonstrations use flaws that are flight-like or more difficult to detect than flight component flaws, which are commonly induced fatigue cracks. Often, it is not feasible to induce fatigue cracks in flight component geometry, and therefore, a simpler representative geometry is used, commonly a flat panel, for POD demonstration. Inducing cracks in simple geometry specimens can be time-consuming and expensive, and thus, minimizing the number of flawed specimens is desired. Traditionally, NASA Special NDE demonstration was limited to MIL-HDBK-1823A methods or the binomial point-estimate method (PEM), commonly known as 29/29. Recently, NASA published a limited-sample POD (LS-POD) methodology for signal-response NDE techniques (e.g., eddy current) that provides POD demonstration with fewer specimens than previous approaches. LS-POD suggests a minimum of 10 flawed specimens, compared to 29 in the PEM and the suggested minimum of 40 from MIL-HDBK-1823A. The methodology also includes new guidance on evaluating the probability of false calls. In this presentation, these new transfer function and LS-POD methodologies are described and illustrated through an eddy current detection capability of far-side flaws on thin welded panels. A geometry-based transfer function is developed using electro-discharge machined (EDM) notches in flight component and simple geometry to estimate the Special NDE flaw size that is representative of the critical initial flaw size required by the fracture analysis. Then, fatigue cracks are induced in simple flat panels of the transferred flaw size, and the LS-POD methodology is used for Special NDE demonstration.

P. A. Parker↗

DOE OSTI2021

Humidified single-scattering albedometer (H-CAPS-PM SSA ): Design, data analysis, and validation

In this work, we report the development and validation of a new humidified aerosol single-scattering albedometer to quantify the effects of water uptake on submicrometer particle optical properties. The instrument simultaneously measures in situ aerosol light extinction ( σ ep ) and scattering ( σ sp ) using a cavity-attenuated phase shift-single scattering albedo particulate matter (PM) monitor (CAPS-PM SSA , Aerodyne Research, Inc., Billerica, MA, USA). It retrieves by difference aerosol light absorption ( σ ap ) and directly quantifies aerosol single-scattering albedo (SSA), the aerosol “brightness.” We custom built a relative humidity (RH) control system using a water vapor-permeable membrane humidifier and coupled it to the CAPS-PM SSA to enable humidified aerosol observations. Our humidified instrument (H-CAPS-PM SSA ) overcomes problems with noise caused by mirror purge-flow humidification, heating, and characterizing cell RH. Careful angular truncation corrections in scattering, particularly for larger particles, were combined with empirical observations. Results show that the optimal operational size to be D p < 400 nm. The H-CAPS-PM SSA was evaluated with several pure single-component aerosols including ammonium sulfate ((NH 4 ) 2 SO 4 ), absorbing nigrosin, and levoglucosan, an organic biomass smoke tracer. The measured σ ep , σ sp , and the derived optical hygroscopicity parameter ( κ ) for size-selected ammonium sulfate are in good agreement with literature values. For dry size-selected nigrosin in the 100 < D p < 400 nm range, SSA values increased from ~0.3 to 0.65 with increasing D p . The enhancement in nigrosin σ ap at RH = 80% was a factor of 1.05–1.20 relative to dry conditions, with the larger particles showing greater enhancement. SSA increased with RH with the largest fractional enhancement measured for the smallest particles. For polydisperse levoglucosan, we measured an optical κ of 0.26 for both light extinction and scattering and negligible absorption. Our new instrument enables reliable observations of the effects of ambient humidity on mixed aerosol optical properties, particularly for light-absorbing aerosols whose climate forcing is uncertain due to measurement gaps.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Diagnostics for Burning Plasmas

Here, recent progress in the design and manufacturing development of in-vessel diagnostic components by the U.S. ITER team is reported. Design and manufacturing choices are driven by engineering challenges stemming from ITER’s burning plasma mission, which entails levels of plasma neutron emission, pulse lengths, and size scales well beyond the existing database. Challenges include port access limitations, neutron irradiation and activation risks, nuclear heating of components, complex interfaces, remote handling compatibility, and constraints on component and processing materials. Responses to these challenges are presented using examples from the low field side reflectometer, toroidal interferometer polarimeter, and electron cyclotron emission diagnostics. Relevance of the experience from ITER diagnostics engineering to the design of future integrated fusion facilities based on burning plasmas is addressed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2018

Dependences of the Tunnel Magnetoresistance and Spin Transfer Torque on the Sizes and Concentration of Nanoparticles in Magnetic Tunnel Junctions

Dependences of the tunnel magnetoresistance and in-plane component of the spin transfer torque on the applied voltage in a magnetic tunnel junction have been calculated in the approximation of ballistic transport of conduction electrons through an insulating layer with embedded magnetic or nonmagnetic nanoparticles. A single-barrier magnetic tunnel junction with a nanoparticle embedded in an insulator forms a double-barrier magnetic tunnel junction. It has been shown that the in-plane component of the spin transfer torque in the double-barrier magnetic tunnel junction can be higher than that in the single-barrier one at the same thickness of the insulating layer. The calculations show that nanoparticles embedded in the tunnel junction increase the probability of tunneling of electrons, create resonance conditions, and ensure the quantization of the conductance in contrast to the tunnel junction without nanoparticles. The calculated dependences of the tunnel magnetoresistance correspond to experimental data demonstrating peak anomalies and suppression of the maximum magnetoresistances at low voltages.

36 MATERIALS SCIENCE↗

NASA NTRS1992

Size of metallic and polyethylene debris particles in failed cemented total hip replacements

Reports of differing failure rates of total hip prostheses made of various metals prompted us to measure the size of metallic and polyethylene particulate debris around failed cemented arthroplasties. We used an isolation method, in which metallic debris was extracted from the tissues, and a non-isolation method of routine preparation for light and electron microscopy. Specimens were taken from 30 cases in which the femoral component was of titanium alloy (10), cobalt-chrome alloy (10), or stainless steel (10). The mean size of metallic particles with the isolation method was 0.8 to 1.0 microns by 1.5 to 1.8 microns. The non-isolation method gave a significantly smaller mean size of 0.3 to 0.4 microns by 0.6 to 0.7 microns. For each technique the particle sizes of the three metals were similar. The mean size of polyethylene particles was 2 to 4 microns by 8 to 13 microns. They were larger in tissue retrieved from failed titanium-alloy implants than from cobalt-chrome and stainless-steel implants. Our results suggest that factors other than the size of the metal particles, such as the constituents of the alloy, and the amount and speed of generation of debris, may be more important in the failure of hip replacements.

Non-NASA Center↗

NASA NTRSDate not supplied

Cruise Propulsion System Thermal Analysis for NASA’s X-57 “Maxwell” Mod II Configuration

The X-57 “Maxwell” is NASA’s flight demonstrator for distributed electric propulsion technologies. The X-57 Mod II configuration is designed to test the electric cruise propulsion system for X-57 and features an electric cruise motor mounted in an integral nacelle on each wing. The electric motors and associated control equipment for X-57 Mod II are air-cooled; therefore, they require adequate cooling airflow to stay within temperature limits in all relevant flight conditions within the operational ambient temperature limits set by the X-57 project. A computational flow analysis was conducted to estimate the internal flow properties of the X-57 Mod II cruise nacelles in three critical flight conditions. These flow properties were then used to determine the boundary conditions for individual component thermal models, which were used to estimate individual component operating temperatures. The results indicated that the low-speed, low-altitude initial takeoff climb during hot day conditions was the sizing condition from a cooling perspective. The analysis found that the cooling flowpaths in the X-57 Mod II cruise nacelles are adequate to provide cooling to all components with the appropriate amount of thermal margin except two of the low-voltage control boards in the cruise motor controller. These components would violate required thermal margins by less than two degrees Celsius in the Project Hot Day reference atmosphere.

Nicholas K Borer↗

DOE OSTI2016

Measurements of impurity concentrations and transport in the Lithium Tokamak Experiment

This thesis presents new measurements of core impurity concentrations and transport in plasmas with lithium coatings on all-metal plasma facing components (PFCs) in the Lithium Tokamak Experiment (LTX). LTX is a modest-sized spherical tokamak uniquely capable of operating with large area solid and/or liquid lithium coatings essentially surrounding the entire plasma (as opposed to just the divertor or limiter region in other devices). Lithium (Li) wall-coatings have improved plasma performance and confinement in several tokamaks with carbon (C) PFCs, including the National Spherical Torus Experiment (NSTX). In NSTX, contamination of the core plasma with Li impurities was very low (<0.1%) despite extensive divertor coatings. Low Li levels in NSTX were found to be largely due to neoclassical forces from the high level of C impurities. Studying impurity levels and transport with Li coatings on stainless steel surfaces in LTX is relevant to future devices (including future enhancements to NSTX-Upgrade) with all-metal PFCs. The new measurements in this thesis were enabled by a refurbished Thomson scattering system and improved impurity spectroscopy, primarily using a novel visible spectrometer monitoring several Li, C, and oxygen (O) emission lines. A simple model was used to account for impurities in unmeasured charge states, assuming constant density in the plasma core and constant concentration in the edge. In discharges with solid Li coatings, volume averaged impurity concentrations were low but non-negligible, with~2-4% Li, ~0.6-2% C, ~0.4-0.7% O, and Z_eff<1.2. Transport was assessed using the TRANSP, NCLASS, and MIST codes. Collisions with the main H ions dominated the neoclassical impurity transport, unlike in NSTX, where collisions with C dominated. Furthermore, neoclassical transport coefficients calculated with NCLASS were similar across all impurity species and differed no more than a factor of two, in contrast to NSTX where they differed by an order of magnitude. However, time-independent simulations with MIST indicated that unlike NSTX, neoclassical theory did not fully capture the impurity transport and anomalous transport likely played a significant role in determining impurity profiles.

Lithium plasma facing components↗

DOE OSTI2018

Characterization of Flexible Operation Performance of N-R HES Components in support of a Model-Based Pre-conditioner

The concept of Nuclear-Renewable Hybrid Energy Systems (N-R HES) is meant to combine different energy technologies in synergistic ways to achieve a more secure and economical energy supply. The N-R HES unit is constituted by a small-sized pressurized water reactor coupled with a Rankine energy conversion cycle, a gas-fired turbine, an energy storage component, and a hydrogen production plant.

08 HYDROGEN↗

NASA NTRS1992

An accelerated development, reduced cost approach to lunar/Mars exploration using a modular NTR-based space transportation system

Benefits and rationale for developing a common, modular lunar/Mars space transporation system (STS) based on nuclear thermal rocket (NTR) are presented. The modular NTR is based on three key components including a 50 klbf NERVA-derived engine used in clusters of 2 or 3, two standardized tank sizes developed for the First Lunar Outpost and Mars cargo vehicle applications, and a preintegrated truss/propellant feed system used for transferring LH2 from the drop tanks into the 'in-line' tank. It is concluded that, by using these components in a 'building block' fashion, a variety of single and multi-engine lunar and Mars vehicles can be configured to satisfy particular mission requirements.

Borowski, S.↗

NASA NTRS2018

Particle Size Distributions in Chondritic Meteorites: Evidence for Pre-Planetesimal Histories

Magnesium-rich silicate chondrules and calcium-, aluminum-rich refractory inclusions (CAIs) are fundamental components of primitive chondritic meteorites. It has been suggested that concentration of these early-formed particles by nebular sorting processes may lead to accretion of planetesimals, the planetary bodies that represent the building blocks of the terrestrial planets. In this case, the size distributions of the particles may constrain the accretion process. Here we present new particle size distribution data for Northwest Africa 5717, a primitive ordinary chondrite (ungrouped 3.05) and the well-known carbonaceous chondrite Allende (CV3). Instead of the relatively narrow size distributions obtained in previous studies (Ebel et al., 2016; Friedrich et al., 2015; Paque and Cuzzi, 1997, and references therein), we observed broad size distributions for all particle types in both meteorites. Detailed microscopic image analysis of Allende shows differences in the size distributions of chondrule subtypes, but collectively these subpopulations comprise a composite "chondrule" size distribution that is similar to the broad size distribution found for CAIs. Also, we find accretionary 'dust' rims on only a subset (approximately 15-20 percent) of the chondrules contained in Allende, which indicates that subpopulations of chondrules experienced distinct histories prior to planetary accretion. For the rimmed subset, we find positive correlation between rim thickness and chondrule size. The remarkable similarity between the size distributions of various subgroups of particles, both with and without fine grained rims, implies a common size sorting process. Chondrite classification schemes, astrophysical disk models that predict a narrow chondrule size population and/or a common localized formation event, and conventional particle analysis methods must all be critically reevaluated. We support the idea that distinct "lithologies" in NWA 5717 are nebular aggregates of chondrules. If greater than or equal to centimeter-sized aggregates of chondrules can form it will have implications for planet formation and suggests the sticking stage is where the preferential size physics is operating.

chondritic meteorites↗

DOE OSTI2024

Diverse organic carbon dynamics captured by radiocarbon analysis of distinct compound classes in a grassland soil

Soil organic carbon (SOC) is a large, dynamic reservoir composed of a complex mixture of plant- and microbe-derived compounds with a wide distribution of cycling timescales and mechanisms. The distinct residence times of individual carbon components within this reservoir depend on a combination of factors, including compound reactivity, mineral association, and climate conditions. To better constrain SOC dynamics, bulk radiocarbon measurements are commonly used to trace biosphere inputs into soils and to estimate timescales of SOC cycling. However, understanding the mechanisms driving the persistence of organic compounds in bulk soil requires analyses of SOC pools that can be linked to plant sources and microbial transformation processes. Here, we adapt approaches, previously developed for marine sediments, to isolate organic compound classes from soils for radiocarbon ( 14 C) analysis. We apply these methods to a soil profile from an annual grassland in Hopland, California (USA), to assess changes in SOC persistence with depth (down to 1 m). We measured the radiocarbon values of water-extractable organic carbon (WEOC), total lipid extracts (TLEs), total hydrolyzable amino acids (AAs), and an acid-insoluble (AI) fraction from bulk and physically separated size fractions (< 2 mm, 2 mm–63 µm, and < 63 µm). Our results show that Δ 14 C values of bulk soil, size fractions, and extracted compound classes became more depleted with depth, and individual SOC components have distinct age–depth distributions that suggest distinguishable cycling rates. We found that AAs and TLEs cycle faster than the bulk soils and the AI fraction. The AI was the most 14 C-depleted fraction, indicating that it is the most chemically inert in this soil. Our approach enables the isolation and measurement of SOC fractions that separate functionally distinct SOC pools that can cycle relatively quickly (e.g., plant and microbial residues) from more passive or inert SOC pools (associated with minerals or petrogenic) from bulk soils and soil physical fractions. With the effort to move beyond SOC bulk analysis, we find that compound class 14 C analysis can improve our understanding of SOC cycling and disentangle the physical and chemical factors driving OC cycling rates and persistence.

58 GEOSCIENCES↗

NASA NTRS1994

An analysis of spectral envelope-reduction via quadratic assignment problems

A new spectral algorithm for reordering a sparse symmetric matrix to reduce its envelope size was described. The ordering is computed by associating a Laplacian matrix with the given matrix and then sorting the components of a specified eigenvector of the Laplacian. In this paper, we provide an analysis of the spectral envelope reduction algorithm. We described related 1- and 2-sum problems; the former is related to the envelope size, while the latter is related to an upper bound on the work involved in an envelope Cholesky factorization scheme. We formulate the latter two problems as quadratic assignment problems, and then study the 2-sum problem in more detail. We obtain lower bounds on the 2-sum by considering a projected quadratic assignment problem, and then show that finding a permutation matrix closest to an orthogonal matrix attaining one of the lower bounds justifies the spectral envelope reduction algorithm. The lower bound on the 2-sum is seen to be tight for reasonably 'uniform' finite element meshes. We also obtain asymptotically tight lower bounds for the envelope size for certain classes of meshes.

George, Alan↗