Vector-Multiprocessing Algorithm For The Solution Of Large Geophysical Inverse Problems

The primary objective of the proposed investigation is to develop numerical tools capable of producing scalable algorithms for efficient solution of a general class of large geophysical inverse problem in a massively parallel processing (MPP) computing environment. An example problem is the rigorous solution of the Earth's gravity field using massive satellite data. Currently, such a solution can easily exhaust the central memory of conventional supercomputers (Cray Y-MP/C90) and storage requirements (tera-byte storage). The proposed investigation will apply coarsely-grained MPP (1) techniques to develop tools capable of generating scalable, parallel, and system-independent algorithms (1) to accumulate and to process very large data sets for a least squares system, and (2) to solve the resulting large linear system of equations. The proposed approach include developing tools parallel to build parallel codes for efficient computation of recursive spherical functions and for parallel processing of massive data sets. The MPP utilities to be used for the tool development include the Parallel Virtual Memory (PVM) and Distributed Queuing System (DQS). Phase I objectives identified include the overall design of the proposed algorithm development and the initial proof-of-concept effort to apply the tools to an established large-scale linear system software system (LLISS) in a small array of MPP computing environment (workstations) to solve an example problem. Anticipated Benefits/Potential Applications - The anticipated results of the investigation include tools that can produce a new class of generalized parallel and scalable algorithms capable of solving a very large least squares system. The solution of the identified example problem, i.e., the rigorous solution of Earth's gravity field, will provide scientific advancements in areas of geophysics and computational mathematics. Anticipated re have potential commercial applications such as oil exploration and precise navigation of space vehicles.