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Parallel computation of large-scale network equilibria and variational inequalities.
Equilibrium of a network is obtained when each user who competes to optimize his utility can not improve his utility any further. Equilibrium problems governed by distinct equilibrium concepts can be formulated in one general framework--that of variational inequalities. The synthesis of variational inequalities and networks induces the creation of highly efficient algorithms which are especially suited for the large-scale equilibrium problems. Motivated by the recent technological advances in parallel computing architectures, parallel algorithms of large-scale equilibrium problems were developed using the theory of variational inequalities. In the case where the feasible constraint set of a network equilibrium problem can be expressed as a Cartesian product of subsets, the application of variational inequality decomposition algorithms for the parallel computation becomes possible. A new spatial price equilibrium model, which is not based on the path flows, but, rather, on the link flows to allow the decomposition by time periods, was developed and used as a prototype of large-scale network equilibrium problems. The variational inequality formulations were decomposed first by commodities, then by time periods, and, subsequently, by markets. The coarse grain parallel architectures used were the IBM 3090-600E and the IBM 3090-600J at the Cornell Theory Center with six processors each. The maximum speed-ups obtained were 1.93 for two processors, 3.74 for four processors, and 5.15 for six processors. The market subproblems were further decomposed by links, resulting in a fine grain parallel implementation. The Thinking Machine\u27s Connection Machine, CM-2, with 32,768 processors was used for the numerical experimentation. The fine grain parallel algorithm solved input/output matrix problems more than 20 times faster, when compared to the results on the IBM 3090-600J. It is expected that further enhancements to parallel languages and parallel architectures will make even more efficient implementations realizable, and that parallel computing and the theory of variational inequalities can be successfully applied to solve more efficiently other large-scale problems with an underlying network structure, such as traffic equilibrium problems, general economic equilibrium problems, and financial equilibrium problems
Probabilistic structural mechanics research for parallel processing computers
Aerospace structures and spacecraft are a complex assemblage of structural components that are subjected to a variety of complex, cyclic, and transient loading conditions. Significant modeling uncertainties are present in these structures, in addition to the inherent randomness of material properties and loads. To properly account for these uncertainties in evaluating and assessing the reliability of these components and structures, probabilistic structural mechanics (PSM) procedures must be used. Much research has focused on basic theory development and the development of approximate analytic solution methods in random vibrations and structural reliability. Practical application of PSM methods was hampered by their computationally intense nature. Solution of PSM problems requires repeated analyses of structures that are often large, and exhibit nonlinear and/or dynamic response behavior. These methods are all inherently parallel and ideally suited to implementation on parallel processing computers. New hardware architectures and innovative control software and solution methodologies are needed to make solution of large scale PSM problems practical
Efficient Data Structures and Algorithms for Scientific Computations.
Large-scale numerically intensive scientific applications can require tremendous amounts of computer time and space. Two general methods are presented for reducing the computer resources required in scientific computing. The first is a numerical database system which is built on a space and time optimal data structure called a weighted search tree and that allows for the storage and retrieval of valuable intermediate information so costly redundant calculations can be avoided. The second is a matrix algorithm based on a new space optimal representation of sparse matrices that for typical scientific applications can be expected to dramatically decrease the cost of multiplying sparse matrices. Codes and tests for each are given. Both methods can be implemented in a broad range of large-scale scientific applications
A Theoretical Approach Involving Recurrence Resolution, Dependence Cycle Statement Ordering and Subroutine Transformation for the Exploitation of Parallelism in Sequential Code.
To exploit parallelism in Fortran code, this dissertation consists of a study of the following three issues: (1) recurrence resolution in Do-loops for vector processing, (2) dependence cycle statement ordering in Do-loops for parallel processing, and (3) sub-routine parallelization. For recurrence resolution, the major findings include: (1) the node splitting algorithm cannot be used directly to break an essential antidependence link, of which the source variable that results in antidependence is itself the sink variable of another true dependence so a correction method is proposed, (2) a sink variable renaming technique is capable of breaking an antidependence and/or output-dependence link, (3) for recurrences formed by only true dependences, a dynamic dependence concept and the derived technique are powerful, and (4) by integrating related techniques, an algorithm for resolving a general multistatement recurrence is developed. The performance of a parallel loop is determined by the level of parallelism and the time delay due to interprocessor communication and synchronization. For a dependence cycle of a single parallel loop executed in a general synchronization mode, the parallelism exposed varies with the alignment of statements. Statements are reordered on the basis of execution-time of the loop as estimated at compile-time. An improved timing formula and a derived statement ordering algorithm are proposed. Further extension of this algorithm to multiple perfectly nested Do-loops with simple global dependence cycle is also presented. The subroutine is a potential source for parallel processing. Several problems must be solved for subroutine parallelization: (1) the precedence of parallel executions of subroutines, (2) identification of the optimum execution mode for each subroutine and (3) the restructuring of a serial program. A five-step approach to parallelize called subroutines for a calling subroutine is proposed: (1) computation of control dependence, (2) approximation of the global effects of subroutines, (3) analysis of data dependence, (4) identification of execution mode, and (5) restructuring of calling and called subroutines. Application of these five steps in a recursive manner to different levels of calling subroutines in a program addresses the parallelization of subroutines
Architecture independent environment for developing engineering software on MIMD computers
Engineers are constantly faced with solving problems of increasing complexity and detail. Multiple Instruction stream Multiple Data stream (MIMD) computers have been developed to overcome the performance limitations of serial computers. The hardware architectures of MIMD computers vary considerably and are much more sophisticated than serial computers. Developing large scale software for a variety of MIMD computers is difficult and expensive. There is a need to provide tools that facilitate programming these machines. First, the issues that must be considered to develop those tools are examined. The two main areas of concern were architecture independence and data management. Architecture independent software facilitates software portability and improves the longevity and utility of the software product. It provides some form of insurance for the investment of time and effort that goes into developing the software. The management of data is a crucial aspect of solving large engineering problems. It must be considered in light of the new hardware organizations that are available. Second, the functional design and implementation of a software environment that facilitates developing architecture independent software for large engineering applications are described. The topics of discussion include: a description of the model that supports the development of architecture independent software; identifying and exploiting concurrency within the application program; data coherence; engineering data base and memory management
Earth and environmental science in the 1980's: Part 1: Environmental data systems, supercomputer facilities and networks
Overview descriptions of on-line environmental data systems, supercomputer facilities, and networks are presented. Each description addresses the concepts of content, capability, and user access relevant to the point of view of potential utilization by the Earth and environmental science community. The information on similar systems or facilities is presented in parallel fashion to encourage and facilitate intercomparison. In addition, summary sheets are given for each description, and a summary table precedes each section
Equilibration operators for the solution of constrained matrix problems
Includes bibliographical references (p. 24-28).Supported by a Faculty Research Grant from the University of Massachusetts. Supported by the National Science Foundation, VPW program. RII-880361by A. Nagurney and A. Robinson
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