Brian Christopher Gunter

Parallel out-of-core computation and updating of the QR factorization

This article discusses the high-performance parallel implementation of the computation and updating of QR factorizations of dense matrices, including problems large enough to require out-of-core computation, where the matrix is stored on disk. The algorithms presented here are scalable both in problem size and as the number of processors increases. Implementation using the Parallel Linear Algebra Package (PLAPACK) and the Parallel Out-of-Core Linear Algebra Package (POOCLAPACK) is discussed. The methods are shown to attain excellent performance, in some cases attaining roughly 80&percent; of the “realizable” peak of the architectures on which the experiments were performed.

Families of algorithms related to the inversion of a Symmetric Positive Definite matrix

We study the high-performance implementation of the inversion of a Symmetric Positive Definite (SPD) matrix on architectures ranging from sequential processors to Symmetric MultiProcessors to distributed memory parallel computers. This inversion is traditionally accomplished in three “sweeps”: a Cholesky factorization of the SPD matrix, the inversion of the resulting triangular matrix, and finally the multiplication of the inverted triangular matrix by its own transpose. We state different algorithms for each of these sweeps as well as algorithms that compute the result in a single sweep. One algorithm outperforms the current ScaLAPACK implementation by 20-30 percent due to improved load-balance on a distributed memory architecture.

Parallel out-of-core cholesky and QR factorizations with POOCLAPACK

In this paper the parallel implementation of out-of-core Cholesky factorization is used to introduce the Parallel Outof-Core Linear Algebra Package (POOCLAPACK), a flexible infrastructure for parallel implementation of out-ofcore linear algebra operations. POOCLAPACK builds on the Parallel Linear Algebra Package (PLAPACK) for incore parallel dense linear algebra computation. Despite the extreme simplicity of POOCLAPACK, the out-of-core Cholesky factorization implementation is shown to achieve up to 80% of peak performance on a 64 node configuration of the Cray T3E-600. The insights gained from examining the Cholesky factorization are also applied to the much more difficult and important QR factorization operation. Preliminary results for parallel implementation of the resulting OOC QR factorization algorithm are included.

GEOScan: A global, real-time geoscience facility

GEOScan is a proposed space-based facility of globally networked instruments that will provide revolutionary, massively dense global geosciences observations. Major scientific research projects are typically conducted using two approaches: community facilities, and investigator lead focused missions. While science from space is almost exclusively conducted within the mission model, GEOScan is a new concept designed as a constellation facility from space utilizing a suite of space-based sensors that optimizes the scientific value across the greatest number of scientific disciplines in the earth and geosciences, while constraining cost and accommodation related parameters. Our grassroots design processes target questions that have not, and will not be answered until simultaneous global measurements are made. The relatively small size, mass, and power of the GEOScan instruments make them an ideal candidate for a hosted payload aboard a global constellation of communication satellites, such as the Iridium NEXTs 66-satellite constellation. This paper will focus on the design and planning components of this new type of heterogeneous, multi-node facility concept, such as: costing, design for manufacture, science synergy, and operations of this non-traditional mission concept. We will demonstrate that this mission design concept has distinct advantages over traditional monolithic satellite missions for a number of scientific measurement priorities and data products due to the constellation configuration, scaled manufacturing and facility model.

Relative Orbital Element Estimation and Observability Analysis for Formation Flying Satellites using Inter-Satellite Range Measurements Only

The goal of this study is to explore those applications which can best utilize a network of orbiting satellites working as a distributed computing array. The satellites are presumed to be low-cost minior micro-satellites orbiting Earth or some other celestial body (i.e., an asteroid, moon, etc.), and should have a (near) constant communication link between the satellites, such that any given satellite can continuously send data to any other satellite in the network; however, as a low-cost and potentially remotely operated mission scenario, it is assumed that the downlink bandwidth via Earth-based ground stations will be very limited. As such, the goal of the networked array of satellites is to directly compute the data or science product in-space, as opposed to the traditional scheme of downloading all of the raw data and processing the results on the ground. Not all observations techniques will benefit from this space-based distributed computing approach, but case studies involving gravity field determination will be provided to highlight the potential of such systems.The goal of this study is to explore those applications which can best utilize a network of orbiting satellites working as a distributed computing array. The satellites are presumed to be low-cost mini- or micro-satellites orbiting Earth or some other celestial body (i.e., an asteroid, moon, etc.), and should have a (near) constant communication link between the satellites, such that any given satellite can continuously send data to any other satellite in the network; however, as a low-cost and potentially remotely operated mission scenario, it is assumed that the downlink bandwidth via Earth-based ground stations will be very limited. As such, the goal of the networked array of satellites is to directly compute the data or science product in-space, as opposed to the traditional scheme of downloading all of the raw data and processing the results on the ground. Not all observations techniques will benefit from this space-based distributed computing approach, but case studies involving gravity field determination will be provided to highlight the potential of such systems.

Evaluation of GRACE and ICESat Mass Change Estimates Over Antarctica

The goal of this study is to examine some of the many corrections and processing strategies that can have a significant influence on the ice mass change estimates computed from GRACE and ICESat mission data. These two missions, when combined, have the potential to generate new insights into the mass balance and geophysical processes of regions such as Antarctica, where such quantities are currently not well understood. Key to this combination is the identification of the major sources of uncertainty in the data processing. For the ICESat data, this includes an analysis into the calculation of the campaign biases, assumptions regarding the firn density, and a comparison between height rates derived from crossover and repeat track analysis. For the GRACE data, the focus will be on the impact of various GIA models and other a priori input values (i.e., C 20, geocenter motion, etc.). Comparisons with the latest data releases for both missions will be presented for the 4 year period spanning from October 2003 to October 2007. Recommendations for future work will also be discussed.

GEOScan: A GEOScience Facility From Space

GEOScan is a grassroots effort, proposed as globally networked orbiting observation facility utilizing the main Iridium NEXT 66-satellite constellation. This will create a revolutionary new capability of massively dense, global geoscience observations and targets elusive questions that scientists have not previously been able to answer, and will not answer, until simultaneous global measurements are made. This effort is enabled by Iridium as part of its Hosted Payload Program. By developing a common sensor suite the logistical and cost barriers for transmitting massive amounts of data from 66 satellites configured in 6 orbital planes with 11 evenly spaced slots per plane is removed. Each sensor suite of GEOScans networked orbital observation facility consists of 6 system sensors: a Radiometer to measure Earths total outgoing radiation; a GPS Compact Total Electron Content Sensor to image Earths plasma environment and gravity field; a MicroCam Multispectral Imager to measure global cloud cover, vegetation, land use, and bright aurora, and also take the first uniform instantaneous image of the Earth; a Radiation Belt Mapping System (dosimeters) to measure energetic electron and proton distributions; a Compact Earth Observing Spectrometer to measure aerosol-atmospheric composition and vegetation; and MEMS Accelerometers to deduce non-conservative forces aiding gravity and neutral drag studies. Our analysis shows that the instrument suites evaluated in a constellation configuration onboard the Iridium NEXT satellites are poised to provide major breakthroughs in Earth and geospace science. GEOScan commercial-of-the-shelf instruments provide low-cost space situational awareness and intelligence, surveillance, and reconnaissance opportunities.

Space-Based Distributed Computing Using a Networked Constellation of Small Satellites

The goal of this study is to explore the feasibility of utilizing a network of orbiting satellites working as a distributed-computing array. The satellites are presumed to be low-cost mini- or microsatellites orbiting Earth or some other celestial body (i.e., an asteroid, moon, etc.), and should have regular communication links between the satellites such that any given satellite can transmit data to any other satellite in the network; however, as a low-cost and potentially remotely operated mission scenario, it is assumed that the downlink bandwidth via Earth-based ground stations will be very limited. As such, the goal of the networked array of satellites is to directly compute the data or science product in orbit as opposed to the traditional scheme of downloading all of the raw data and processing the results on the ground. Not all observation techniques will benefit from this space-based distributed-computing approach, but case studies involving the gravity-field determination of Earth and other plan...