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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 559 records · Page 31
All sourcesNASA NTRSDOE OSTI
NASA NTRS2001

Hydrogen/Air Fuel Nozzle Emissions Experiments

The use of hydrogen combustion for aircraft gas turbine engines provides significant opportunities to reduce harmful exhaust emissions. Hydrogen has many advantages (no CO2 production, high reaction rates, high heating value, and future availability), along with some disadvantages (high current cost of production and storage, high volume per BTU, and an unknown safety profile when in wide use). One of the primary reasons for switching to hydrogen is the elimination of CO2 emissions. Also, with hydrogen, design challenges such as fuel coking in the fuel nozzle and particulate emissions are no longer an issue. However, because it takes place at high temperatures, hydrogen-air combustion can still produce significant levels of NOx emissions. Much of the current research into conventional hydrocarbon-fueled aircraft gas turbine combustors is focused on NOx reduction methods. The Zero CO2 Emission Technology (ZCET) hydrogen combustion project will focus on meeting the Office of Aerospace Technology goal 2 within pillar one for Global Civil Aviation reducing the emissions of future aircraft by a factor of 3 within 10 years and by a factor of 5 within 25 years. Recent advances in hydrocarbon-based gas turbine combustion components have expanded the horizons for fuel nozzle development. Both new fluid designs and manufacturing technologies have led to the development of fuel nozzles that significantly reduce aircraft emissions. The goal of the ZCET program is to mesh the current technology of Lean Direct Injection and rocket injectors to provide quick mixing, low emissions, and high-performance fuel nozzle designs. An experimental program is planned to investigate the fuel nozzle concepts in a flametube test rig. Currently, a hydrogen system is being installed in cell 23 at NASA Glenn Research Center's Research Combustion Laboratory. Testing will be conducted on a variety of fuel nozzle concepts up to combustion pressures of 350 psia and inlet air temperatures of 1200 F. Computational fluid dynamics calculations, with the Glenn developed National Combustor Code, are being performed to optimize the fuel nozzle designs.

Smith, Timothy D.↗
NASA NTRS2009

Microstrip Antenna for Remote Sensing of Soil Moisture and Sea Surface Salinity

This compact, lightweight, dual-frequency antenna feed developed for future soil moisture and sea surface salinity (SSS) missions can benefit future soil and ocean studies by lowering mass, volume, and cost of the antenna system. It also allows for airborne soil moisture and salinity remote sensors operating on small aircraft. While microstrip antenna technology has been developed for radio communications, it has yet to be applied to combined radar and radiometer for Earth remote sensing. The antenna feed provides a key instrument element enabling high-resolution radiometric observations with large, deployable antennas. The design is based on the microstrip stacked-patch array (MSPA) used to feed a large, lightweight, deployable, rotating mesh antenna for spaceborne L-band (approximately equal to 1 GHz) passive and active sensing systems. The array consists of stacked patches to provide dual-frequency capability and suitable radiation patterns. The stacked-patch microstrip element was designed to cover the required L-band center frequencies at 1.26 GHz (lower patch) and 1.413 GHz (upper patch), with dual-linear polarization capabilities. The dimension of patches produces the required frequencies. To achieve excellent polarization isolation and control of antenna sidelobes for the MSPA, the orientation of each stacked-patch element within the array is optimized to reduce the cross-polarization. A specialized feed-distribution network was designed to achieve the required excitation amplitude and phase for each stacked-patch element.

Ramhat-Samii, Yahya↗
NASA NTRS2015

3D Printing Multi-Functionality: Embedded RF Antennas and Components

Significant research and press has recently focused on the fabrication freedom of Additive Manufacturing (AM) to create both conceptual models and final end-use products. This flexibility allows design modifications to be immediately reflected in 3D printed structures, creating new paradigms within the manufacturing process. 3D printed products will inevitably be fabricated locally, with unit-level customization, optimized to unique mission requirements. However, for the technology to be universally adopted, the processes must be enhanced to incorporate additional technologies; such as electronics, actuation, and electromagnetics. Recently, a novel 3D printing platform, Multi3D manufacturing, was funded by the presidential initiative for revitalizing manufacturing in the USA using 3D printing (America Makes - also known as the National Additive Manufacturing Innovation Institute). The Multi3D system specifically targets 3D printed electronics in arbitrary form; and building upon the potential of this system, this paper describes RF antennas and components fabricated through the integration of material extrusion 3D printing with embedded wire, mesh, and RF elements.

antennas↗
NASA NTRS2019

Analytical Techniques for Assessing Gateway and Other Spacecraft Antenna Line-of-Sight

NASA’s Artemis program is committed to landing the next man and the first woman on the Moon by 2024. A critical piece of infrastructure for the mission, the Gateway will inaugurate a sustainable crewed presence beyond low-Earth orbit in cis-lunar space and serve as a staging point for a lunar landing system. The Near Rectilinear Halo Orbit of the Gateway offers numerous operational benefits in terms of its Earth access via the Orion Multipurpose Crew Vehicle, the degree of lunar visibility and surface access it provides, and favorable conditions for station-keeping. To minimize burns during station-keeping and conserve propellant, the Gateway will continually align itself to a solar pressure equilibrium attitude with the Sun; this is convenient for solar array orientation and power generation, but causes difficulties in terms of communication line-of-sight with the Earth, Moon, and visiting vehicles, which appear to be continually rotating about the Gateway’s local frame. A fixed antenna on the Gateway is continually subject to a moving target and can find itself obstructed by the Gateway’s own geometry frequently if not placed carefully. To understand the performance of either Earth-pointing or Moon-pointing antenna placements for a given Gateway geometry, a transient solar system simulation of the Gateway is used to step through orbital ephemeris data and determine the periods in which line-of-sight to a chosen target is achieved and lost. Antenna placements can be tested in the simulation and optimized to increase the average line-of-sight exposure to the target, while also minimizing the maximum duration cut-out in line-of-sight communication experienced; long durations without a successful communication link could pose threats to operations, safety, and mission success. It may be necessary to deviate from the Gateway’s solar pressure equilibrium attitude for short periods of time in order to continue a successful line-of-sight link to a chosen target. Communication coverage spheres can offer insight into what these necessary attitude adjustments may be and are generated by using a 3D mesh of the Gateway and an implementation of the Möller-Trumbore intersection algorithm. This paper outlines the analytical techniques used to perform such antenna placements on the Gateway, offering examples of how line-of-sight strength can be enhanced with an understanding of the Gateway geometry and attitude constraints. These techniques have had direct impact on the writing of communication requirements for NASA and international partner-owned Gateway elements.

Kennedy, William J.↗
NASA NTRS2019

Analytical Techniques for Assessing Gateway and Other Spacecraft Antenna Line-of-Sight

NASA’s Artemis program is committed to landing the next man and the first woman on the Moon by 2024. A critical piece of infrastructure for the mission, the Gateway will inaugurate a sustainable crewed presence beyond low-Earth orbit in cis-lunar space and serve as a staging point for a lunar landing system. The Near Rectilinear Halo Orbit of the Gateway offers numerous operational benefits in terms of its Earth access via the Orion Multipurpose Crew Vehicle, the degree of lunar visibility and surface access it provides, and favorable conditions for station-keeping. To minimize burns during station-keeping and conserve propellant, the Gateway will continually align itself to a solar pressure equilibrium attitude with the Sun; this is convenient for solar array orientation and power generation, but causes difficulties in terms of communication line-of-sight with the Earth, Moon, and visiting vehicles, which appear to be continually rotating about the Gateway’s local frame. A fixed antenna on the Gateway is continually subject to a moving target and can find itself obstructed by the Gateway’s own geometry frequently if not placed carefully. To understand the performance of either Earth-pointing or Moon-pointing antenna placements for a given Gateway geometry, a transient solar system simulation of the Gateway is used to step through orbital ephemeris data and determine the periods in which line-of-sight to a chosen target is achieved and lost. Antenna placements can be tested in the simulation and optimized to increase the average line-of-sight exposure to the target, while also minimizing the maximum duration cut-out in line-of-sight communication experienced; long durations without a successful communication link could pose threats to operations, safety, and mission success. It may be necessary to deviate from the Gateway’s solar pressure equilibrium attitude for short periods of time in order to continue a successful line-of-sight link to a chosen target. Communication coverage spheres can offer insight into what these necessary attitude adjustments may be and are generated by using a 3D mesh of the Gateway and an implementation of the Möller-Trumbore intersection algorithm. This paper outlines the analytical techniques used to perform such antenna placements on the Gateway, offering examples of how line-of-sight strength can be enhanced with an understanding of the Gateway geometry and attitude constraints. These techniques have had direct impact on the writing of communication requirements for NASA and international partner-owned Gateway elements.

Kennedy, William J.↗
NASA NTRSDate not supplied

2020 International Astronautical Congress Conference Presentation - ANALYTICAL TECHNIQUES FOR ASSESSING GATEWAY AND OTHER SPACECRAFT ANTENNA LINE-OF-SIGHT FOR THE ARTEMIS PROGRAM

NASA’s Artemis program is committed to landing the next man and the first woman on the Moon by 2024. The Gateway, a critical piece of infrastructure for the long-term Artemis mission profiles, will inaugurate a sustainable crewed presence beyond low-Earth orbit in cis-lunar space and serve as a staging point for a lunar landing system. The Near Rectilinear Halo Orbit of the Gateway offers numerous operational benefits in terms of its Earth access via the Orion Multipurpose Crew Vehicle, its degree of Earth and lunar visibility, the versatile surface access it provides, and favorable conditions for station-keeping. To minimize burns during station-keeping and conserve propellant, the Gateway will continually align itself to a solar pressure equilibrium attitude with the Sun; this is convenient for solar array orientation and power generation, but causes difficulties in terms of communication line-of-sight with the Earth, Moon, and visiting vehicles, which appear to be continually rotating about the Gateway’s local frame. A fixed antenna on the Gateway is continually subject to a moving target and can find itself obstructed by the Gateway’s own geometry frequently if not placed carefully. To understand the performance of either Earth-pointing or Moon-pointing antenna placements for a given Gateway geometry, a transient solar system simulation of the Gateway is used to step through orbital ephemeris data and determine the periods in which line-of-sight to a chosen target is achieved and lost. Antenna placements can be tested in the simulation and optimized to increase the average line-of-sight exposure to the target, while also minimizing the maximum duration drop-out in line-of-sight communication experienced; long durations without a successful communication link could pose threats to operations, safety, and mission success. It may be necessary to deviate from the Gateway’s solar pressure equilibrium attitude for short periods of time in order to continue a successful line-of-sight link to a chosen target. Communication coverage spheres can offer insight into what these necessary attitude adjustments may be and are generated by using a 3D mesh of the Gateway and an implementation of the Möller-Trumbore intersection algorithm. This paper outlines the analytical techniques used to perform such antenna placements on the Gateway, offering examples of how line-of-sight strength can be enhanced with an understanding of the Gateway geometry and attitude constraints. These techniques have had direct impact on the writing of communication requirements for NASA and international partner-owned Gateway elements.

Gateway↗
DOE OSTI2026

Numerical Simulation of a Natural Convection–Driven Air-Cooled Reactor Cavity Cooling System Experiment

Ensuring the efficient removal of decay heat from the reactor vessel is essential for the safety of advanced reactor technologies. Several Generation-IV concepts incorporate variations in the reactor vessel cooling systems to achieve this objective. High-temperature gas-cooled reactors utilize a reactor cavity cooling system (RCCS), a passive ex-vessel system designed to operate without active components or external power during accident conditions. The RCCS removes decay heat primarily through radiative and convective heat transfer mechanisms. Here, this study presents a comprehensive validation of a computational fluid dynamics Reynolds-averaged Navier-Stokes model for the University of Wisconsin-Madison air-cooled RCCS facility. Validation was conducted for both high- and low-power natural convection cases under a uniform heating profile. Near-wall resolution was found to be critical for accurately modeling natural convection in the RCCS; employing an all-𝑦 + wall treatment resulted in wall temperature discrepancies exceeding 50 °⁢𝐶 compared to a wall-resolved mesh. Thermal-hydraulic behaviors under natural and forced convection conditions were compared within the heated cavity and RCCS. A turbulence model sensitivity analysis indicated that low-Reynolds number k-ɛ, k-ω shear stress transport (SST), and Reynolds stress transport models produce similar wall temperature predictions. A buoyancy modeling sensitivity study revealed that the Boussinesq approximation significantly underpredicted thermal-hydraulic behavior in the RCCS. Based on these findings, modeling recommendations are provided. The validated data set along with identified sensitivities refine the modeling of natural convection in the RCCS. The information produced by this study supports RCCS design, optimization, and safety evaluations, enabling the calibration and verification of reduced-order thermal-hydraulic models.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Embedded training of neural-network subgrid-scale turbulence models

We report that the weights of a deep neural-network model are optimized in conjunction with the governing flow equations to provide a model for subgrid-scale stresses in a temporally developing plane turbulent jet at Reynolds number Re 0 = 6000 . The objective function for training is first based on the instantaneous filtered velocity fields from a corresponding direct numerical simulation, and the training is by a stochastic gradient descent method, which uses the adjoint Navier-Stokes equations to provide the end-to-end sensitivities of the model weights to the velocity fields. In-sample and out-of-sample testing on multiple dual-jet configurations show that its required mesh density in each coordinate direction for prediction of mean flow, Reynolds stresses, and spectra is half that needed by the dynamic Smagorinsky model for comparable accuracy. The same neural-network model trained directly to match filtered subgrid-scale stresses, without the constraint of being embedded within the flow equations during the training, fails to provide a qualitatively correct prediction. The coupled formulation is generalized to train based only on mean-flow and Reynolds stresses, which are more readily available in experiments. The mean-flow training provides a robust model, which is important, though a somewhat less accurate prediction for the same coarse meshes, as might be anticipated due to the reduced information available for training in this case. The anticipated advantage of the formulation is that the inclusion of resolved physics in the training increases its capacity to extrapolate. This is assessed for the case of passive scalar transport, for which it outperforms established models due to improved mixing predictions.

42 ENGINEERING↗
DOE OSTI2022

User-Oriented Improvements in the MOOSE framework in support of Multiphysics Simulation

The MOOSE Framework is a foundational capability used by NEAMS to create over 15 different simulation tools for advanced nuclear reactors. Due to this ubiquity, improvements to the framework in support of modeling and simulation goals are critical to the program. These improvements can take many forms including optimization, improved user experience, streamlined APIs, parallelism, and new capability. The work transcribed in the report was in direct support of the simulation tools and is already deployed or will be deployed in the coming months. The capabilities implemented were, in the same order as this report, chainable execution objects or executors, support for transfers between applications at the same level in a coupling scheme, support for boundary/subdomain restricted transfers, support for transfers between applications with different coordinate or unit systems, support for MOOSE applications in the NEAMS workbench, deployment of MOOSE application of the INL HPC OnDemand platform, addition of a triangular meshing library in libMesh and increased support of face variables.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Progressive collapse analysis of stiffened panel structure with consideration of actual welding distortion and residual stresses

To date, inclusion of welding distortion and residual stresses in determining the strength of marine structures is based on empirical formulations due to welding complexity. In this study, a more feasible numerical model was developed from the perspective of inherent strain theory. The accuracy of this simplified numerical model was confirmed by transient thermo-elastic–plastic finite element analysis using a novel dynamic mesh refining and iterative substructure method which is 50 times faster than conventional finite element method. Welding distortion by the two numerical approaches was validated with experimental measurement. The collapse analyses indicated that the inherent strain model predicted a compressive strength and load-displacement curve with high accuracy, as validated by the transient thermo-mechanical model. The global stiffness and the ultimate strength of the welded structure would be overestimated by about 22% if no welding effects were considered. The proposed computation procedure for determining the ultimate strength of welded structures is accurate, simple, and practical and enables improvement of ultimate strength through optimization of welding joint design to reduce the welding residual stress and distortion.

Huang, Hui↗
NASA NTRS1995

Bending strength model for internal spur gear teeth

Internal spur gear teeth are normally stronger than pinion teeth of the same pitch and face width since external teeth are smaller at the base. However, ring gears which are narrower have an unequal addendum or are made of a material with a lower strength than that of the meshing pinion may be loaded more critically in bending. In this study, a model for the bending strength of an internal gear tooth as a function of the applied load pressure angle is presented which is based on the inscribed Lewis constant strength parabolic beam. The bending model includes a stress concentration factor and an axial compression term which are extensions of the model for an external gear tooth. The geometry of the Lewis factor determination is presented, the iteration to determine the factor is described, and the bending strength J factor is compared to that of an external gear tooth. This strength model will assist optimal design efforts for unequal addendum gears and gears of mixed materials.

Savage, Michael↗
NASA NTRS2024

Smallsat 2024 - Starling Cubesat Swarm Technology Demonstration Flight Results

The Starling swarm of four 6U CubeSats launched in July 2023 to test four key technologies to enable future swarm missions: 1) Mobile Ad-Hoc Networking (MANET) over a crosslink radio network 2) Autonomous onboard decision-making for operations 3) Optical-based absolute and relative navigation 4) Autonomous maneuver planning and execution The Starling team implemented the Better Approach to Mobile Ad-hoc Networking (B.A.T.M.A.N.) protocol to automatically manage the crosslink network of four satellites. The B.A.T.M.A.N. protocol uses a decentralized approach to managing a multi-hop mesh network of devices, in this case, a satellite swarm. The four satellites were able to successfully establish a network at multiple data rates and demonstrate file transfer and command issuance between spacecraft over the network. Starling incorporated Distributed Spacecraft Autonomy's (DSA) software to demonstrate onboard decision-making. The DSA software takes L1/L2 band GPS measurements and uses them to estimate the relative Total Electron Count (TEC) in the ionosphere. The onboard software then determines if there are any features of interest and provides that information to the other satellites over the crosslink network. The swarm of satellites then reaches a consensus on the optimal TEC observation strategy and adjusts its measurement collection tactics autonomously. The Starling Formation-Flying Optical Experiment (StarFOX), produced by Stanford's Space Rendezvous Laboratory, uses the onboard star trackers to collect images of the other swarm spacecraft and produce angles-only navigation estimates. This system is envisioned to be valuable in applications in which Global Navigation Satellite Systems (GNSS) are not available, such as in cis-lunar or deep space. StarFOX successfully applied its algorithms to multiple simultaneous spacecraft targets using the star tracker imagery. Finally, Starling used Emergent Space's Cluster Flight Application (CFA) software suite for the Reconfiguration and Orbit Maintenance Experiments Onboard (ROMEO) demonstration of autonomously planning and executing propulsive maneuvers. Large swarms will need to be able to maintain formation requirements with minimal operator involvement, especially as the size of the swarm scales up. Results from the ROMEO experiment are presented. Starling is funded by the Small Spacecraft Technology (SST) program out of NASA's Space Technology Mission Directorate (STMD).

distributed systems↗
DOE OSTI2024

Impact of LWR assembly structural features on cladding burst behavior under LOCA conditions

This provides an initial scoping study on clad balloon and burst behavior for burnup extension of reactor fuel. The associated issues with burnup extension are fuel fragmentation, relocation, and dispersal in the event of cladding failure. The general finding of this work is that the structural features, spacer grids and mixing vanes, locally suppress cladding deformation but have little impact on the overall clad performance during loss-of-coolant accidents. The work detailed in a previous report by Capps et al. focused on core optimization via neutronics, thermal hydraulics and thermomechanical analysis for burnups beyond 62 GWD/tU and enrichments above 5%. Uncertainty of fuel fragmentation relocation and dispersal in high-burnup rods during accident conditions was also investigated. The dispersal aspect of fuel fragmentation depends on cladding rupture. Thus, assessing uncertainties in the rupture behavior is helpful in estimating the dispersal of high-burnup fuel. This study builds on the previous work by assessing the impact of assembly structural features on cladding balloon and burst behavior in a full-length fuel rod. In this work, the BISON fuel performance code was used to generate 2D radial and height meshes containing structural features commonly used in nuclear fuel assemblies. First, meshes were generated with spacer grids. Results were then compared to the cladding burst temperature and balloon strain results from the previous work. A mesh sensitivity study was performed to ensure that mixing vanes and spacer grid effects were appropriately considered, resulting in a more refined mesh than the previous study. The balloon deformation and burst times of the cladding were compared to the original case. Consideration was also given to the effect of rod initial pressure. In conclusion, 3D quarter rod simulations were also performed and found good agreement with the 2D simulations in clad deformation and reasonable agreement in burst times.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS2005

Face Gear Technology for Aerospace Power Transmission Progresses

The use of face gears in an advanced rotorcraft transmission design was first proposed by the McDonnell Douglas Helicopter Company during their contracted effort with the U.S. Army under the Advanced Rotorcraft Transmission (ART) program. Face gears would be used to turn the corner between the horizontal gas turbine engine and the vertical output rotor shaft--a function currently done by spiral bevel gears. This novel gearing arrangement would substantially lower the drive system weight partly because a face gear mesh would be used to split the input power between two output gears. However, the use of face gears and their ability to operate successfully at the speeds and loads required for an aerospace environment was unknown. Therefore a proof-of-concept phase with an existing test stand at the NASA Lewis Research Center was pursued. Hardware was designed that could be tested in Lewis' Spiral Bevel Gear Test Rig. The initial testing indicated that the face gear mesh was a feasible design that could be used at high speeds and load. Surface pitting fatigue was the typical failure mode, and that could lead to tooth fracture. An interim project was conducted to see if slight modifications to the gear tooth geometry or an alternative heat treating process could overcome the surface fatigue problems. From the initial and interim tests, it was apparent that for the surface fatigue problems to be overcome the manufacturing process used for this component would have to be developed to the level used for spiral bevel gears. The current state of the art for face gear manufacturing required using less than optimal gear materials and manufacturing techniques because the surface of the tooth form does not receive final finishing after heat treatment as it does for spiral bevel gears. This resulted in less than desirable surface hardness and manufacturing tolerances. An Advanced Research and Projects Agency (ARPA) Technology Reinvestment Project has been funded to investigate the effects of manufacturing process improvements on the operating characteristics of face gears. The program is being conducted with McDonnell Douglas Helicopter Co., Lucas Western Inc., the University of Illinois at Chicago, and a NASA/U.S. Army team. The goal of the project is develop the grinding process, experimentally verify the improvement in face gear fatigue life, and conduct a full-scale helicopter transmission test. The theory and methodology to grind face gears has been completed, and manufacture of the test hardware is ongoing. Experimental verification on test hardware is scheduled to begin in fiscal 1996.

Source record↗
DOE OSTI2024

Early experiences on the OLCF Frontier system with AthenaPK and Parthenon–Hydro

The Oak Ridge Leadership Computing Facility (OLCF) has been preparing the nation's first exascale system, Frontier, for production and end users. Frontier is based on HPE Cray's new EX architecture and Slingshot interconnect and features 74 cabinets of optimized 3rd Gen AMD EPYC CPUs for HPC and AI and AMD Instinct 250X accelerators. As a part of this preparation, “real-world” user codes have been selected to help assess the functionality, performance, and usability of the system. This article describes early experiences using the system in collaboration with the Hamburg Observatory for two selected codes, which have since been adopted in the OLCF test harness. Experiences discussed include efforts to resolve performance variability and per-cycle slowdowns. Results are shown for a performance portable astrophysical magnetohydronamics code, AthenaPK, and a mini-application stressing the core functionality of a performance portable block-structured adaptive mesh refinement framework, Parthenon-Hydro. Here, these results show good scaling characteristics to the full system. At the largest scale, the Parthenon-Hydro miniapp reaches a total of $1.7$ $\times$ $10^{13}$ zone-cycles/s on 9216 nodes (73,728 logical GPUs) at ≈92% weak scaling parallel efficiency (starting from a single node using a second-order, finite-volume method).

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1989

Operator induced multigrid algorithms using semirefinement

A variant of multigrid, based on zebra relaxation, and a new family of restriction/prolongation operators is described. Using zebra relaxation in combination with an operator-induced prolongation leads to fast convergence, since the coarse grid can correct all error components. The resulting algorithms are not only fast, but are also robust, in the sense that the convergence rate is insensitive to the mesh aspect ratio. This is true even though line relaxation is performed in only one direction. Multigrid becomes a direct method if an operator-induced prolongation is used, together with the induced coarse grid operators. Unfortunately, this approach leads to stencils which double in size on each coarser grid. The use of an implicit three point restriction can be used to factor these large stencils, in order to retain the usual five or nine point stencils, while still achieving fast convergence. This algorithm achieves a V-cycle convergence rate of 0.03 on Poisson's equation, using 1.5 zebra sweeps per level, while the convergence rate improves to 0.003 if optimal nine point stencils are used. Numerical results for two and three dimensional model problems are presented, together with a two level analysis explaining these results.

Decker, Naomi↗
NASA NTRS1989

Operator induced multigrid algorithms using semirefinement

A variant of multigrid, based on zebra relaxation, and a new family of restriction/prolongation operators is described. Using zebra relaxation in combination with an operator-induced prolongation leads to fast convergence, since the coarse grid can correct all error components. The resulting algorithms are not only fast, but are also robust, in the sense that the convergence rate is insensitive to the mesh aspect ratio. This is true even though line relaxation is performed in only one direction. Multigrid becomes a direct method if an operator-induced prolongation is used, together with the induced coarse grid operators. Unfortunately, this approach leads to stencils which double in size on each coarser grid. The use of an implicit three point restriction can be used to factor these large stencils, in order to retain the usual five or nine point stencils, while still achieving fast convergence. This algorithm achieves a V-cycle convergence rate of 0.03 on Poisson's equation, using 1.5 zebra sweeps per level, while the convergence rate improves to 0.003 if optimal nine point stencils are used. Numerical results for two- and three-dimensional model problems are presented, together with a two level analysis explaining these results.

Decker, Naomi Henderson↗