Families of algorithms related to the inversion of a Symmetric Positive Definite matrix
ACM Transactions on Mathematical Software (TOMS)
Out-of-Core Computation of the QR Factorization on Multi-core Processors
Euro-Par '09 Proceedings of the 15th International Euro-Par Conference on Parallel Processing
Using desktop computers to solve large-scale dense linear algebra problems
The Journal of Supercomputing
ACM Transactions on Mathematical Software (TOMS)
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The focus of this study was to observe and characterize the behavior of certain types of errors present in the gravity field model estimation process, as they relate to fields created from the recently launched Gravity Recovery and Climate Experiment (GRACE). The instruments and configuration of the GRACE satellites are different from any other previously flown gravity mission, so the impact that these error sources have on the GRACE gravity solutions is not fully understood. The high resolution gravity perturbations detectable by GRACE also mean that many of these errors can only be fully explored through the use of high spherical harmonic degree and order solutions. When this study first began, a software estimation tool did not exist that was capable of handling the extremely large problem sizes that the GRACE mission can create. To address this issue, a parallel application called the Advanced Equation Solver for Parallel Systems (AESoP) was developed that was designed to accommodate the computational requirements of GRACE. An outline of the functionality and methodologies employed by AESoP is provided, as well as detailed descriptions of the parallel algorithms created as part of its development. Using this new software tool, several types of errors inherent to the GRACE gravity field estimation process were analyzed. Investigations into the errors of omission and commission were performed using both real and simulated GRACE data. Additional studies into the combination of the CPS and inter-satellite ranging measurements were also conducted in an attempt to maximize the contribution of each data type as well as to improve processing efficiency. The results of these studies outline several processing strategies by which many of the error sources investigated can be significantly reduced while simultaneously decreasing the processing time and disk storage requirements by roughly 75% for an average GRACE solution.