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NASA Lunar Surface Operations & Power Grid

The National Aeronautics and Space Administration (NASA) Artemis Program is developing, testing, and demonstrating new capabilities and technologies required to support a sustainable human presence on the lunar surface and a longer-term vision of sending astronauts to Mars. Artemis lunar surface operations will begin with robotically exploring the lunar south polar regions for locations suitable for harvesting lunar surface resources. Over time activities on the lunar surface will expand beyond robotic operations to human lunar surface operations with the delivery of a lunar habitat and in-situ resource utilization (ISRU) assets increasing the need for highly reliable and available electrical power. As operations move beyond the Artemis technology demonstrations and exploration activities towards full commercial lunar surface activities, the ability to expand the original envisioned Artemis power system and repurpose power system components to support commercial activities will be crucial. One technology that will be necessary to support commercial lunar operations is a power grid. A lunar surface power grid would offer the ability to integrate various power sources to maximize power availability, including fission surface power (nuclear), solar arrays, batteries, and regenerative fuel cells. Newly designed terrestrial microgrids are flexible and can be designed to allow for islanded operation, where power is utilized near the loads to minimize power distribution losses or in a power sharing mode where power is transmitted longer distances. This capability is crucial during failures where overall power availability is reduced, and load demand exceeds generation/storage capability. These terrestrial microgrids will also allow for the power system to grow and evolve over time, meeting the need to expand beyond initial lunar surface activities. This presentation will discuss the NASA Artemis plans, potential power system architectures, and power distribution options that will enable growth from initial technology demonstrations towards a lunar economy with a lunar surface power grid that offers many of the advantages of terrestrial microgrids.

Microgrids

A Review of Unmanned Aerial Vehicle Technology in Power Line Inspection

The electric power industry is one of the heaviest adopters of Unmanned Aerial Vehicles (UAV) technology, utilizing their versatility to enhance power line maintenance programs. For reliable power grids, routine maintenance operations and rapid repair operations are required across substantial geographical distances. Both maintenance and repair decisions are driven by assessment operations, such as inspections of mechanical structures with visible-band sensors, inspections for the presence of high voltage coronas and hot spots with multispectral sensors, and surveying of equipment and adjacent features (particularly vegetation) with photogrammetric and Light Detection and Ranging (LiDAR) sensors. Assessment was historically accomplished with manned helicopter flights or foot patrols. Recently, this critical economic segment harnessed advances in Unmanned Aerial Systems (UAS)technology to accomplish assessment tasks with faster results, lower cost, and higher levels of safety than historical methods. Adoption of UAVs in high-voltage electric power transmission activities is well underway. Adoption of UAVs for low voltage distribution activities is still emerging, with the important exception of post-storm damage assessment following major hurricanes (Harvey and Maria in 2017 and Michael in 2018). This report reviews the broad UAS adoption in high-voltage electric power transmission operations and early attempts at adoption in distribution operations. The ability to fly beyond visual line of sight (BVLOS) may increase the advantages of UAV inspection over former options, and in the United States, regulators have approved two pilot projects to demonstrate BVLOS methods and their benefits in operating and maintaining the power grid.

UAV

Ion accelerator systems for high power 30 cm thruster operation

Two and three-grid accelerator systems for high power ion thruster operation were investigated. Two-grid translation tests show that over compensation of the 30 cm thruster SHAG grid set spacing the 30 cm thruster radial plasma density variation and by incorporating grid compensation only sufficient to maintain grid hole axial alignment, it is shown that beam current gains as large as 50% can be realized. Three-grid translation tests performed with a simulated 30 cm thruster discharge chamber show that substantial beamlet steering can be reliably affected by decelerator grid translation only, at net-to-total voltage ratios as low as 0.05.

Aston, G.

Space Weather Products and Tools Used in Auroral Monitoring and Forecasting at CCMC/SWRC

Key points discussed in this chapter are (1) the importance of aurora research to scientific advances and space weather applications, (2) space weather products at CCMC that are relevant to aurora monitoring and forecasting, and (3) the need for more effort from the whole community to achieve a better and long‐lead‐time forecast of auroral activity. Aurora, as manifestations of solar wind−magnetosphere−ionosphere coupling that occurs in a region of space that is relatively easy to access for sounding rockets, satellites, and other types of observational platforms, serves as a natural laboratory for studying the underlying physics of the complex system. From a space weather application perspective, auroras can cause surface charging of technological assets passing through the region, result in scintillation effects affecting communication and navigation, and cause radar cluttering that hinders military and civilian applications. Indirectly, an aurora and its currents can induce geomagnetically induced currents (GIC) on the ground, which poses major concerns for the wellbeing and operation of power grids, particularly during periods of intense geomagnetic activity. In addition, accurate auroral forecasting is desired for auroral tourism. In this chapter, we first review some of the existing auroral models and discuss past validation efforts. Such efforts are crucial in transitioning a model(s) from research to operations and for further model improvement and development that also benefits scientific endeavors. Then we will focus on products and tools that are used for auroral monitoring and forecasting at the Space Weather Research Center (SWRC). As part of the CCMC (Community Coordinated Modeling Center), SWRC has been providing space weather services since 2010.

Zheng, Yihua

Space Weather Products and Tools Used in Auroral Monitoring and Forecasting at CCMC/SWRC

Key points discussed in this chapter are (1) the importance of aurora research to scientific advances and space weather applications, (2) space weather products at CCMC that are relevant to aurora monitoring and forecasting, and (3) the need for more effort from the whole community to achieve a better and long-lead- time forecast of auroral activity. Aurora, as manifestations of solar wind-magnetosphere-ionosphere coupling that occurs in a region of space that is relatively easy to access for sounding rockets, satellites, and other types of observational platforms, serves as a natural laboratory for studying the underlying physics of the complex system. From a space weather application perspective, auroras can cause surface charging of technological assets passing through the region, result in scintillation effects affecting communication and navigation, and cause radar cluttering that hinders military and civilian applications. Indirectly, an aurora and its currents can induce geomagnetically induced currents (GIC) on the ground, which poses major concerns for the wellbeing and operation of power grids, particularly during periods of intense geomagnetic activity. In addition, accurate auroral forecasting is desired for auroral tourism. In this chapter, we first review some of the existing auroral models and discuss past validation efforts. Such efforts are crucial in transitioning a model(s) from research to operations and for further model improvement and development that also benefits scientific endeavors. Then we will focus on products and tools that are used for auroral monitoring and forecasting at the Space Weather Research Center (SWRC). As part of the CCMC (Community Coordinated Modeling Center), SWRC has been providing space weather services since 2010.

Zheng, Yihua

Solar Eruptive Events

It s long been known that the Sun plays host to the most energetic explosions in the solar system. But key insights into the forms that energy takes have only recently become available. Solar flares have been phenomena of both academic and practical interest since their discovery in 1859. From the academic point of view, they are the nearest events for studying the explosive release of energy in astrophysical magnetized plasmas. From the practical point of view, they disrupt communication channels on Earth, from telegraph communications in 1859 to radio and television signals today. Flares also wreak havoc on the electrical power grid, satellite operations, and GPS signals, and energetic charged particles and radiation are dangerous to passengers on high-altitude polar flights and to astronauts. Flares are not the only explosive phenomena on the Sun. More difficult to observe but equally energetic are the large coronal mass ejections (CMEs), the ejection of up to ten billion tons of magnetized plasma into the solar wind at speeds that can exceed 1000 km/s. CMEs are primarily observed from the side, with coronagraphs that block out the bright disk of the Sun and lower solar atmosphere so that light scattered from the ejected mass can be seen. Major geomagnetic storms are now known to arise from the interaction of CMEs with Earth's magnetosphere. Solar flares are observed without CMEs, and CMEs are observed without flares. The two phenomena often occur together, however, and almost always do in the case of large flares and fast CMEs. The term solar eruptive event refers to the combination of a flare and a CME. Solar eruptive events generate a lot of heat: They can heat plasma to temperatures as high at 50 million Kelvin, producing radiation across the electromagnetic spectrum. But that s not all. A fascinating aspect of solar eruptive events is the acceleration of electrons and ions to suprathermal often relativistic energies. The accelerated particles are primarily observed through their emissions in the higher energy x-ray, gamma-ray, and rf regimes. The radio and x-ray emissions are both from mildly relativistic electrons with energies of tens of keV and above. Gamma-ray line emission comes indirectly from accelerated protons and heavier ions with MeV and higher energies. The difficulty in collecting spatially and spectrally resolved x-ray and gamma-ray data has long been a barrier to learning about the accelerated particles. Considerable progress has been made in the last decade in understanding the relationship between the flare, the CME, energy release, and particle acceleration. But many new questions have also arisen. In this article, I describe those new insights and our evolving understanding of solar eruptive events.

Holman, Gordon D.

Ion accelerator systems for high power 30-cm thruster operation

An investigation of two- and three-grid accelerator systems for high power ion thruster operation has been performed. Two-grid translation tests show that overcompensation of the 30-cm thruster SHAG (Small Hole Accelerator Grid) leads to a premature impingement limit. By better matching the SHAG grid set spacing to the 30-cm thruster radial plasma density variation and by incorporating grid compensation only sufficient to maintain grid hole axial alignment, it is shown that beam current gains as large as 50% can be realized. Three-grid translation tests performed with a simulated 30-cm thruster discharge chamber show that substantial beamlet steering can be reliably affected by decelerator grid translation only, at net-to-total voltage ratios as low as 0.05.

Aston, G.

Lunar Microgrid Trade Studies to Define Interface Converter Requirements

The National Aeronautics and Space Administration (NASA) is interested in developing an incremental lunar power grid to support continuous human/robotic operations under the Artemis missions and can scale to global power utilization and industrial power levels. The initial lunar surface power system will be composed primarily of assets that contain their own power generation and energy storage. These assets can be connected to form a grid, which allows power to be shared between the system’s distributed energy resources. This grid can provide backup power to existing assets as well as primary power to future assets. A trade study was conducted for an Artemis scale grid, which has identified 3 kVAC as an ideal transmission voltage. This paper documents the analysis and findings from these trade studies. These studies were used to define the operating voltage and develop a common interface for connecting lunar surface assets to the power grid. The Universal Modular Interface Converter (UMIC) connects lunar surface assets to the high voltage grid. Products from this grid definition and UMIC development work will enable highly reliable and available power for Artemis and future planetary surface missions, which is key to achieving NASA’s long-term vision of space exploration.

Planetary surface power

Methodology for Time-Domain Estimation of Storm Time Geoelectric Fields Using the 3-D Magnetotelluric Response Tensors

Geoelectric fields at the Earth's surface caused by magnetic storms constitute a hazard to the operation of electric power grids and related infrastructure. The ability to estimate these geoelectric fields in close to real time and provide local predictions would better equip the industry to mitigate negative impacts on their operations. Here we report progress toward this goal: development of robust algorithms that convolve a magnetic storm time series with a frequency domain impedance for a realistic three-dimensional (3-D) Earth, to estimate the local, storm time geoelectric field. Both frequency domain and time domain approaches are presented and validated against storm time geoelectric field data measured in Japan. The methods are then compared in the context of a real-time application.

Kelbert, Anna

Enabling Universal Access to Power on the Lunar Surface

The National Aeronautics and Space Administration (NASA) Artemis Missions will return human astronauts to the lunar surface, demonstrate technologies that establish a sustained presence on the lunar surface and enable human missions to Mars, and help create a lunar commercial economy. Creating a sustained permanent presence on the lunar surface will require access to continuous and highly reliable power to support mission needs. During Artemis, lunar surface operations will evolve and grow over time (years), requiring an increase in the amount of power needed (100s of kW) and distance that the power must be transmitted (up to 10 km during early Artemis missions). A lunar commercial economy is likely to exceed this power demand to the MW level and distance in the 100s of km. This increased distance and demand for highly reliable power drives the need to create an electric power grid by connecting localized lunar power systems (e.g., habitats, in-situ resource utilization plants, etc.), each containing one or more loads and/or sources. Developing a lunar surface power grid will allow lunar surface operations to resemble electrical utility operations on Earth; it allows power to be generated where it is convenient and allows power to be consumed where it is convenient and required. A lunar surface electric power grid will facilitate the growth of a lunar commercial economy because it provides a means to connect new loads to an existing electrical power system. A common standardized interface to the grid and a set of standardized voltages is required to take full advantage of the benefits of an electric power grid, similar to the terrestrial power grid. NASA Glenn Research Center is leading an effort to create universal access to power through the development of the Universal Modular Interface Converter (UMIC). The UMIC is designed to have a common interface that connects sources and loads compliant with the International Space Power System Interoperability Standard (ISPSIS) to a higher voltage AC transmission system or power grid. This presentation will further discuss the evolution of power during the Artemis missions, challenges associated with creating a sustained presence on the lunar surface, progress made on the UMIC, and future opportunities for technology development and standards.

space power systems

Development and Testing of a Prototype Grid-Tied Photovoltaic Power System

The NASA Glenn Research Center (GRC) has developed and tested a prototype 2 kW DC grid-tied photovoltaic (PV) power system at the Center. The PV system has generated in excess of 6700 kWh since operation commenced in July 2006. The PV system is providing power to the GRC grid for use by all. Operation of the prototype PV system has been completely trouble free. A grid-tied PV power system is connected directly to the utility distribution grid. Facility power can be obtained from the utility system as normal. The PV system is synchronized with the utility system to provide power for the facility, and excess power is provided to the utility. The project transfers space technology to terrestrial use via nontraditional partners. GRC personnel glean valuable experience with PV power systems that are directly applicable to various space power systems, and provide valuable space program test data. PV power systems help to reduce harmful emissions and reduce the Nation s dependence on fossil fuels. Power generated by the PV system reduces the GRC utility demand, and the surplus power aids the community. Present global energy concerns reinforce the need for the development of alternative energy systems. Modern PV panels are readily available, reliable, efficient, and economical with a life expectancy of at least 25 years. Modern electronics has been the enabling technology behind grid-tied power systems, making them safe, reliable, efficient, and economical with a life expectancy of at least 25 years. Based upon the success of the prototype PV system, additional PV power system expansion at GRC is under consideration. The prototype grid-tied PV power system was successfully designed and developed which served to validate the basic principles described, and the theoretical work that was performed. The report concludes that grid-tied photovoltaic power systems are reliable, maintenance free, long life power systems, and are of significant value to NASA and the community.

Eichenberg, Dennis J.

Extended operating range of the 30-cm ion thruster with simplified power processor requirements

A two grid 30 cm diameter mercury ion thruster was operated with only six power supplies over the baseline J series thruster power throttle range with negligible impact on thruster performance. An analysis of the functional model power processor showed that the component mass and parts count could be reduced considerably and the electrical efficiency increased slightly by only replacing power supplies with relays. The input power, output thrust, and specific impulse of the thruster were then extended, still using six supplies, from 2660 watts, 0.13 newtons, and 2980 seconds to 9130 watts, 0.37 newtons, and 3820 seconds, respectively. Increases in thrust and power density enable reductions in the number of thrusters and power processors required for most missions. Preliminary assessments of the impact of thruster operation at increased thrust and power density on the discharge characteristics, performance, and lifetime of the thruster were also made.

Rawlin, V. K.

Analysis of Electrical Grid Capacity in Major U.S. Metropolitan Areas for Urban Air Mobility

A wide range of challenges must be overcome to conduct Urban Air Mobility (UAM) operations at scale with electric vertical takeoff and landing aircraft as envisioned. This paper documents an analysis of one potential infrastructure challenge for UAM: available electrical grid power capacity. The success of UAM depends on the availability of electricity, which will be increasingly impacted by the proliferation of ground electric vehicles (EVs) over time. Under the worst-case assumption that each U.S. Metropolitan Statistical Area (MSA) can only access and utilize the electricity generated by power plants within its boundaries, it is estimated that the maximum number of UAM aircraft that can charge simultaneously in the 25 most populous MSAs will decrease by about 61% from about 129,000 in the year 2021 to about 51,000 in the year 2050, due to the projected increase in ground EVs. Also, it is estimated that the number of these MSAs that may lack any available electrical grid power capacity for UAM operations will increase from zero MSAs in 2021 to eleven MSAs in 2050—including three MSAs that prospective UAM operators have announced as target markets (Los Angeles, Miami, and Orlando)—unless electricity demand for other purposes is reduced.

electrical grid

Analysis of Electrical Grid Capacity in Major U.S. Metropolitan Areas for Urban Air Mobility

A wide range of challenges must be overcome to conduct Urban Air Mobility (UAM) operations at scale with electric vertical takeoff and landing aircraft as envisioned. This paper documents an analysis of one potential infrastructure challenge for UAM: available electrical grid power capacity. The success of UAM depends on the availability of electricity, which will be increasingly impacted by the proliferation of ground electric vehicles (EVs) over time. Under the worst-case assumption that each U.S. Metropolitan Statistical Area (MSA) can only access and utilize the electricity generated by power plants within its boundaries, it is estimated that the maximum number of UAM aircraft that can charge simultaneously in the 25 most populous MSAs will decrease by about 61% from about 129,000 in the year 2021 to about 51,000 in the year 2050, due to the projected increase in ground EVs. Also, it is estimated that the number of these MSAs that may lack any available electrical grid power capacity for UAM operations will increase from zero MSAs in 2021 to eleven MSAs in 2050—including three MSAs that prospective UAM operators have announced as target markets (Los Angeles, Miami, and Orlando)—unless electricity demand for other purposes is reduced.

electrical grid

Micro-grid for Future Planetary Surface Needs

Under the current Artemis Program, the National Aeronautics and Space Administration (NASA) will send its next set of astronauts (first woman and next man) to the Moon by 2024 and establish a sustainable presence on the lunar surface by 2028. The challenge of creating a sustained lunar surface presence is significantly different than previous efforts. Lunar surface operations will require access to continuous and highly reliable power to support mission needs, such as to support ISRU operations. Adding to this challenge, the lunar surface operations are not going to be established over a single effort, rather the system and operations will evolve and grow over time (years). The first initial loads that arrive on the lunar surface will be integrated to their own dedicated power sources. As the lunar surface operations grow, so will the demand for power and at some point these individual loads will require more power than can be generated with any single power device. This power demand drives the need for inter-connecting the loads and power devices to share power between them, resulting in a micro-grid. One of the advantages of developing a lunar surface micro-grid is that allows lunar surface operations to resemble electrical utility operations on Earth; it allows power to be generated where it is convenient and allows power to be consumed where it is convenient, rather than negotiating between generation and consumption. The micro-grid concept also provides another benefit of affording the ability to increase overall system reliability by integrating dissimilar power generation and energy storage devices together, for example modifying the power generation strategy to include both solar arrays and nuclear. Creating a lunar surface micro-grid has its advantages, however there are significant challenges associated with an evolvable micro-grid concept. The challenges include how to efficiently transmit large amounts of power (10kW+) long distances (1kW+), how to effectively integrate dissimilar power generation and energy storage devices to maximize power consumption and minimize downtime, and how to physically connect these devices together with a connector that can survive the lunar environment (dust, extreme cold temperatures) and is capable of both astronaut and robotic operation. The basic components of the micro-grid have to be designed to ensure the system is sustainable, modular, and reconfigurable. An interface to the micro-grid has to be designed that allows for additional technologies, some of which may not yet be fully designed, to easily integrate into the micro-grid concept. This presentation discusses these lunar challenges in some more depth and offers a path forward in designing an evolvable micro-grid to meet the needs of the lunar surface operations and proposes a Universal Micro-grid Interface Converter to connect these dissimilar power sources and mission loads to the micro-grid.

Jeffrey Csank

Initial Thrust Measurements of Marshall's Ion-ioN Thruster

Electronegative ion thrusters are a variation of traditional gridded ion thruster technology differentiated by the production and acceleration of both positive and negative ions. Benefits of electronegative ion thrusters include the elimination of lifetime-limiting cathodes from the thruster architecture and the ability to generate appreciable thrust from both charge species. While much progress has been made in the development of electronegative ion thruster technology, direct thrust measurements are required to unambiguously demonstrate the efficacy of the concept and support continued development. In the present work, direct thrust measurements of the thrust produced by the MINT (Marshall's Ion-ioN Thruster) are performed using an inverted-pendulum thrust stand in the High-Power Electric Propulsion Laboratory's Vacuum Test Facility-1 at the Georgia Institute of Technology with operating pressures ranging from 4.8 x 10(exp -5) and 5.7 x 10(exp -5) torr. Thrust is recorded while operating with a propellant volumetric mixture ratio of 5:1 argon to nitrogen with total volumetric flow rates of 6, 12, and 24 sccm (0.17, 0.34, and 0.68 mg/s). Plasma is generated using a helical antenna at 13.56 MHz and radio frequency (RF) power levels of 150 and 350 W. The acceleration grid assembly is operated using both sinusoidal and square waveform biases of +/-350 V at frequencies of 4, 10, 25, 125, and 225 kHz. Thrust is recorded for two separate thruster configurations: with and without the magnetic filter. No thrust is discernable during thruster operation without the magnetic filter for any volumetric flow rate, RF forward Power level, or acceleration grid biasing scheme. For the full thruster configuration, with the magnetic filter installed, a brief burst of thrust of approximately 3.75 mN +/- 3 mN of error is observed at the start of grid operation for a volumetric flow rate of 24 sccm at 350 W RF power using a sinusoidal waveform grid bias at 125 kHz and +/- 350 V. Similar bursts in thrust are observed using a square waveform grid bias at 10 kHz and +/- 350 V for volumetric flow rates of 6, 10, and 12 sccm at 150, 350, and 350 W respectively. The only operating condition that exhibits repeated thrust spikes throughout thruster operation is the 24 sccm condition with a 5:1 mixture ratio at 150 W RF power using the 10 kHz square waveform acceleration grid bias. Thrust spikes for this condition measure 3 mN with an error of +/- 2.5 mN. There are no operating conditions tested that show continuous thrust production.

Caruso, Natalie R. S.

Development and Testing of the Glenn Research Center Visitor's Center Grid-Tied Photovoltaic Power System

The NASA Glenn Research Center (GRC) has developed, installed, and tested a 12 kW DC grid-tied photovoltaic (PV) power system at the GRC Visitor s Center. This system utilizes a unique ballast type roof mount for installing the photovoltaic panels on the roof of the Visitor s Center with no alterations or penetrations to the roof. The PV system has generated in excess of 15000 kWh since operation commenced in August 2008. The PV system is providing power to the GRC grid for use by all. Operation of the GRC Visitor s Center PV system has been completely trouble free. A grid-tied PV power system is connected directly to the utility distribution grid. Facility power can be obtained from the utility system as normal. The PV system is synchronized with the utility system to provide power for the facility, and excess power is provided to the utility. The project transfers space technology to terrestrial use via nontraditional partners. GRC personnel glean valuable experience with PV power systems that are directly applicable to various space power systems, and provides valuable space program test data. PV power systems help to reduce harmful emissions and reduce the Nation s dependence on fossil fuels. Power generated by the PV system reduces the GRC utility demand, and the surplus power aids the community. Present global energy concerns reinforce the need for the development of alternative energy systems. Modern PV panels are readily available, reliable, efficient, and economical with a life expectancy of at least 25 years. Modern electronics has been the enabling technology behind grid-tied power systems, making them safe, reliable, efficient, and economical with a life expectancy of at least 25 years. Based upon the success of the GRC Visitor s Center PV system, additional PV power system expansion at GRC is under consideration. The GRC Visitor s Center grid-tied PV power system was successfully designed and developed which served to validate the basic principles described, and the theoretical work that was performed. The report concludes that grid-tied photovoltaic power systems are reliable, maintenance free, long life power systems, and are of significant value to NASA and the community.

Eichenberg, Dennis J.

Optimal Padding for the Two-Dimensional Fast Fourier Transform

One-dimensional Fast Fourier Transform (FFT) operations work fastest on grids whose size is divisible by a power of two. Because of this, padding grids (that are not already sized to a power of two) so that their size is the next highest power of two can speed up operations. While this works well for one-dimensional grids, it does not work well for two-dimensional grids. For a two-dimensional grid, there are certain pad sizes that work better than others. Therefore, the need exists to generalize a strategy for determining optimal pad sizes. There are three steps in the FFT algorithm. The first is to perform a one-dimensional transform on each row in the grid. The second step is to transpose the resulting matrix. The third step is to perform a one-dimensional transform on each row in the resulting grid. Steps one and three both benefit from padding the row to the next highest power of two, but the second step needs a novel approach. An algorithm was developed that struck a balance between optimizing the grid pad size with prime factors that are small (which are optimal for one-dimensional operations), and with prime factors that are large (which are optimal for two-dimensional operations). This algorithm optimizes based on average run times, and is not fine-tuned for any specific application. It increases the amount of times that processor-requested data is found in the set-associative processor cache. Cache retrievals are 4-10 times faster than conventional memory retrievals. The tested implementation of the algorithm resulted in faster execution times on all platforms tested, but with varying sized grids. This is because various computer architectures process commands differently. The test grid was 512 512. Using a 540 540 grid on a Pentium V processor, the code ran 30 percent faster. On a PowerPC, a 256x256 grid worked best. A Core2Duo computer preferred either a 1040x1040 (15 percent faster) or a 1008x1008 (30 percent faster) grid. There are many industries that can benefit from this algorithm, including optics, image-processing, signal-processing, and engineering applications.

Dean, Bruce H.