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Includes bibliographical references (p. 359-370)and index

We describe a new, parallel programming version of the scalar field simulation program LATTICEEASY. The new C++ program, CLUSTEREASY, can simulate arbitrary scalar field models on distributed-memory clusters. The speed and memory requirements scale well with the number of processors. As with the serial version of LATTICEEASY, CLUSTEREASY can run simulations in one, two, or three dimensions, with or without expansion of the universe, with customizable parameters and output. The program and its full documentation are available on the LATTICEEASY website at http://www.science.smith.edu/departments/Physics/fstaff/gfelder/latticeeasy/. In this paper we provide a brief overview of what CLUSTEREASY does and the ways in which it does and doesn't differ from the serial version of LATTICEEASY.

Comment in response to Phys. Rev. Lett. 112, 046401 (2014)

Includes bibliographical references

Scan Directed Load Balancing is a new, locality-preserving, dynamic load balancing algorithm for grid based computations on mesh connected parallel computers. Scans are used to efficiently determine what areas of the machine are heavily loaded and what areas are lightly loaded, and to organize the movement of data. Data is shifted along the mesh in a regular fashion to balance the load. The Locality Property of the algorithm guarantees that all the neighbors of a data point on the grid are stored either on the same processor, or on a processor that is directly connected to it. Scan Directed Load Balancing is applicable to both SIMD and MIMD mesh-connected parallel computers, and has been implemented on the MasPar MP-1. We present some theoretical bounds achieved by the algorithm as well as the algorithm's performance on a particular image processing problem, edge-directed diffusion. Our experiments show that the algorithm is effective in improving the load distribution for real problems, while the efficiency of the original grid-based computation is preserved by the locality property.

Installation and Operating Manual C.E.D. Distributors Ltd

Installation and Operating Manual C.E.D. Distributors Ltd

This paper addresses the reservoir design problem in the context of delay-based reservoir computers for multidimensional input signals, parallel architectures, and real-time multitasking. First, an approximating reservoir model is presented in those frameworks that provides an explicit functional link between the reservoir parameters and architecture and its performance in the execution of a specific task. Second, the inference properties of the ridge regression estimator in the multivariate context is used to assess the impact of finite sample training on the decrease of the reservoir capacity. Finally, an empirical study is conducted that shows the adequacy of the theoretical results with the empirical performances exhibited by various reservoir architectures in the execution of several nonlinear tasks with multidimensional inputs. Our results confirm the robustness properties of the parallel reservoir architecture with respect to task misspecification and parameter choice that had already been documented in the literature.

5 p. 28 cm

Includes index

Hashing techniques have long been used to efficiently store and locate data indexed by key. Recently, parallel hashing algorithms have been developed that allow table insertion of many keys in a few parallel steps. The analyses of these algorithms have focused on the expected number of steps required, ignoring the issue of work complexity. As a result, these algorithms have not been work efficient. In this paper, we present a parallel hashing algorithm that is shown to be work efficient because it performs no more work than its serial counterpart. An analysis of its behavior shows that it performs S = 0(logn) expected parallel steps and W = 0(n) expected work. Many parallel algorithms can make use of hashing as a core step. Procedures such as histogramming, set difference, keyed reduction and dictionary lookup can be formulated using a general hash routine. Thus, parallel hashing is an important fundamental parallel operation. The above applications may also be implemented using sorting as the core step. While the use of parallel hashing has been generally accepted in the folklore of parallel computing, a dearth of literature about the expected performance of such algorithms has led many to favor the use of sorting. This paper sheds light on the performance that may be achieved using parallel hashing algorithms and should lend credibility to their use.

This research investigated the important issues related to the analysis and design of real-time systems targeted to parallel architectures. In particular, the software specification models for real-time systems on parallel architectures were evaluated. A survey of current formal methods for uniprocessor real-time systems specifications was conducted to determine their extensibility in specifying real-time systems on parallel architectures. In this research, a specification model called Parallel REal Time specification Language (PRETsEL) was defined. It leverages off of existing models while adding the necessary syntax and semantics lacking in existing models in supporting specification of real-time systems for parallel architectures. Examples of utilizing the PRETSEL language are presented.

Shared memory parallel machines are relatively easy to program, but it is difficult to scale up their performance by increasing the number of processors because the bandwidth of the shared memory is limited. Although distributed memory parallel computers are more difficult to program, they have the potential to provide very large speedup, since their performance can scale up when the number of processors increases. This research effort evaluated how large scale scientific computational problems can be solved on two different distributed memory parallel systems at Carnegie Mellon - the Warp and Nectar systems. Three applications were chosen. The first problem from the biological sciences and the second application involving chemical process modeling were implemented on Warp. The third application of representing 3-dimensional models was implemented on both Warp and Nectar.

The purpose of this study was to evaluate the parallel processing impact of MIMD (Multiple-Instruction Multiple-Data Path) computers on Flight Simulation Software. Basic mathematical functions and arithmetic expressions from typical Flight Simulation Software were selected and run on a MIMD computer to evaluate the improvement in execution time that results from the parallel architecture of this type of computer. Recommendations as to the types of tasks which are optimally suitable for this computer architecture are made, together with the improvement in execution speed to be expected. (Author)

The purpose of this study was to evaluate the parallel processing impact of MIMD (Multiple-Instruction Multiple-Data Path) computers on Flight Simulation Software. Basic mathematical functions and arithmetic expressions from typical Flight Simulation Software were selected and run on a MIMD computer to evaluate the improvement in execution time that results from the parallel architecture of this type of computer. Recommendations as to the types of tasks which are optimally suitable for this computer architecture are made, together with the improvement in execution speed to be expected. (Author)

Network based parallel computing using personal computers is currently a popular choice for concurrent scientific computing. This work evaluates the capabilities and the performance of the AFIT Bimodal Cluster (ABC); a heterogeneous cluster of PCs connected by switched fast Ethernet and using MPICH 1.1 for interprocess communication for parallel digital signal processing using Space Time Adaptive Processing (STAP) as the case study. The MITRE RT_STAP Benchmark version 1.1 is ported and executed on the ABC, as well as on a cluster of six Sun SPARC workstations connected by a Myrinet network (the AFIT NOW), and on a IBM SP for comparison. Modifications to the RT_STAP benchmark source code are done to accommodate the BLAS routines obtained from the ASCI Red project and the FFTPACK from the Netlib repository. Comparative performance analysis of the original and modified versions of the benchmarks executed on the ABC running the LINUX OS is performed, and shows improvements in the sustained Gflop/sec rates. Inter-platform comparative analysis demonstrates ABC's superior computation rates, but also reveals limited machine scalability as a result of severe communication overheads imposed by RT_STAP cornerturn operations. Analysis of experimental data indicates that ABC outperforms AFIT NOW but needs interconnection network improvements to be globally competitive to MPPs such as the IBM SP.

Network based parallel computing using personal computers is currently a popular choice for concurrent scientific computing. This work evaluates the capabilities and the performance of the AFIT Bimodal Cluster (ABC); a heterogeneous cluster of PCs connected by switched fast Ethernet and using MPICH 1.1 for interprocess communication for parallel digital signal processing using Space Time Adaptive Processing (STAP) as the case study. The MITRE RT_STAP Benchmark version 1.1 is ported and executed on the ABC, as well as on a cluster of six Sun SPARC workstations connected by a Myrinet network (the AFIT NOW), and on a IBM SP for comparison. Modifications to the RT_STAP benchmark source code are done to accommodate the BLAS routines obtained from the ASCI Red project and the FFTPACK from the Netlib repository. Comparative performance analysis of the original and modified versions of the benchmarks executed on the ABC running the LINUX OS is performed, and shows improvements in the sustained Gflop/sec rates. Inter-platform comparative analysis demonstrates ABC's superior computation rates, but also reveals limited machine scalability as a result of severe communication overheads imposed by RT_STAP cornerturn operations. Analysis of experimental data indicates that ABC outperforms AFIT NOW but needs interconnection network improvements to be globally competitive to MPPs such as the IBM SP.

The present status of numerical methods for partial differential equations on vector and parallel computers was reviewed. The relevant aspects of these computers are discussed and a brief review of their development is included, with particular attention paid to those characteristics that influence algorithm selection. Both direct and iterative methods are given for elliptic equations as well as explicit and implicit methods for initial boundary value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms. Application areas utilizing these computers are briefly discussed.

The present status of numerical methods for partial differential equations on vector and parallel computers was reviewed. The relevant aspects of these computers are discussed and a brief review of their development is included, with particular attention paid to those characteristics that influence algorithm selection. Both direct and iterative methods are given for elliptic equations as well as explicit and implicit methods for initial boundary value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms. Application areas utilizing these computers are briefly discussed.

The performance of hypercubes were evaluated on a computational fluid dynamics problem and the parallel environment issues were considered that must be addressed, such as algorithm changes, implementation choices, programming effort, and programming environment. The evaluation focuses on a widely used fluid dynamics code, FLO52, which solves the two dimensional steady Euler equations describing flow around the airfoil. The code development experience is described, including interacting with the operating system, utilizing the message-passing communication system, and code modifications necessary to increase parallel efficiency. Results from two hypercube parallel computers (a 16-node iPSC/2, and a 512-node NCUBE/ten) are discussed and compared. In addition, a mathematical model of the execution time was developed as a function of several machine and algorithm parameters. This model accurately predicts the actual run times obtained and is used to explore the performance of the code in interesting but yet physically realizable regions of the parameter space. Based on this model, predictions about future hypercubes are made.

A novel approach to parallelize the well-known Hoshen-Kopelman algorithm has been chosen, suitable for simulating huge lattices in high dimensions on massively-parallel computers with distributed memory and message passing. This method consists of domain decomposition of the simulated lattice into strips perpendicular to the hyperplane of investigation that is used in the Hoshen-Kopelman algorithm. Systems of world record sizes, up to L=4000256 in two dimensions, L=20224 in three, and L=1036 in four, gave precise estimates for the Fisher exponent tau, the corrections to scaling Delta_1, and for the critical number density n_c.

The work presented in this report deals with the development of a fast and fairly accurate Computer-Aided Design software for simulating very-large-scale-integrated (VLSI) circuits. The methods rely on piecewise linearized nonlinear elements in the circuits. The piecewise linear approaches explored in this work are: (1) a fast piecewise linear Gauss-Seidel waveform relaxation method; (2) a slower but more accurate piecewise linear method based on simplices; and (3) a Gauss-Seidel piecewise linear method with dynamic partitioning. Also described is a mixed method which combines the fast piecewise linear method and the dynamic partitioning method. The circuit to be analyzed is partitioned into dc-connected subcircuits and then sequenced for analysis. Small subcircuits are solved using the fast piecewise linear method while large subcircuits, including the strongly connected components in the circuit, are solved using the dynamic partitioning method. A parallel implementation of the Gauss-Seidel piecewise linear method with dynamic partitioning on a uniprocessor computer is studied. Algorithms for the parallel implementation of the dynamic partitioning approach on a multiprocessor with shared memory (Alliant FX/8) are also explained in detail. The piecewise linear methods presented in this work have been implemented in a set of programs called PLATINUM. The waveforms generated by PLATINUM are fairly accurate as compared to those for SPICE2, and the speedup for a uniprocessor machine is over two orders of magnitude, while the parallel implementation gives an additional 4 to 6 times speed improvements.

At the Earth's surface, the magnetic field that is observed is similar to that that would be generated by a simple bar magnet running through the Earth's axis. This idea (permanent magnetism) was commonly believed a century ago. Because the temperature of the core is so high, permanent magnetism is not possible. Therefore, the magnetic field should decay, over tens of thousands of years. Since it does not, the field must be regenerating. Since the turn of the century, the idea that the core is molten iron which by moving generates a magnetic field arose. The set of equations to describe this are extremely non-linear and complex. Only in the last five to ten years have computers been able to solve these equations.

This final report describes the status of work performed during the months of Sept 1995 through Jan 1999 on the Algorithmic Research And Software Development For An Industrial Strength Sparse Matrix Library For Parallel Computers. The objective of this effort was to: 1. research and demonstrate new algorithms for the solution of systems of linear equations in parallel; and 2. research and demonstrate a new parallel approach for the real symmetric sparse generalized eigenvalue problem.

This report covers work conducted under grant NAG1-1562 for the NASA High Performance Computing and Communications Program (HPCCP) from December 7, 1993, to December 31, 1997. The objective of the research was to develop new multidisciplinary design optimization (MDO) techniques which exploit parallel computing to reduce the computational burden of aircraft MDO. The design of the High-Speed Civil Transport (HSCT) air-craft was selected as a test case to demonstrate the utility of our MDO methods. The three major tasks of this research grant included: development of parallel multipoint approximation methods for the aerodynamic design of the HSCT, use of parallel multipoint approximation methods for structural optimization of the HSCT, mathematical and algorithmic development including support in the integration of parallel computation for items (1) and (2). These tasks have been accomplished with the development of a response surface methodology that incorporates multi-fidelity models. For the aerodynamic design we were able to optimize with up to 20 design variables using hundreds of expensive Euler analyses together with thousands of inexpensive linear theory simulations. We have thereby demonstrated the application of CFD to a large aerodynamic design problem. For the predicting structural weight we were able to combine hundreds of structural optimizations of refined finite element models with thousands of optimizations based on coarse models. Computations have been carried out on the Intel Paragon with up to 128 nodes. The parallel computation allowed us to perform combined aerodynamic-structural optimization using state of the art models of a complex aircraft configurations.

This report covers work conducted under grant NAG1-1562 for the NASA High Performance Computing and Communications Program (HPCCP) from December 7, 1993, to December 31, 1997. The objective of the research was to develop new multidisciplinary design optimization (MDO) techniques which exploit parallel computing to reduce the computational burden of aircraft MDO. The design of the High-Speed Civil Transport (HSCT) air-craft was selected as a test case to demonstrate the utility of our MDO methods. The three major tasks of this research grant included: development of parallel multipoint approximation methods for the aerodynamic design of the HSCT, use of parallel multipoint approximation methods for structural optimization of the HSCT, mathematical and algorithmic development including support in the integration of parallel computation for items (1) and (2). These tasks have been accomplished with the development of a response surface methodology that incorporates multi-fidelity models. For the aerodynamic design we were able to optimize with up to 20 design variables using hundreds of expensive Euler analyses together with thousands of inexpensive linear theory simulations. We have thereby demonstrated the application of CFD to a large aerodynamic design problem. For the predicting structural weight we were able to combine hundreds of structural optimizations of refined finite element models with thousands of optimizations based on coarse models. Computations have been carried out on the Intel Paragon with up to 128 nodes. The parallel computation allowed us to perform combined aerodynamic-structural optimization using state of the art models of a complex aircraft configurations.

The purpose of this study is to evaluate the feasibility of remote memory access (RMA) programming on shared memory parallel computers. We discuss different RMA based implementations of selected CFD application benchmark kernels and compare them to corresponding message passing based codes. For the message-passing implementation we use MPI point-to-point and global communication routines. For the RMA based approach we consider two different libraries supporting this programming model. One is a shared memory parallelization library (SMPlib) developed at NASA Ames, the other is the MPI-2 extensions to the MPI Standard. We give timing comparisons for the different implementation strategies and discuss the performance.

The computational complexity for parallel implementation of multidomain spectral methods is studied to derive the optimal number of subdomains, q, and spectral order, n, for numerical solution of hyperbolic problems. The complexity analysis is based upon theoretical results which predict error as a function of (q, n) for problems having wave-like solutions. These are combined with a linear communication cost model to study the impact of communication overhead and imposed granularity on the optimal choice of (q, n) as a function of the number of processors. It is shown that, for present day multicomputers, the impact of communication overhead does not significantly shift (q, n) from the optimal uniprocessor values, and that the effects of granularity are more important.

The computational complexity for parallel implementation of multidomain spectral methods is studied to derive the optimal number of subdomains, q, and spectral order, n, for numerical solution of hyperbolic problems. The complexity analysis is based upon theoretical results which predict error as a function of (q, n) for problems having wave-like solutions. These are combined with a linear communication cost model to study the impact of communication overhead and imposed granularity on the optimal choice of (q, n) as a function of the number of processors. It is shown that, for present day multicomputers, the impact of communication overhead does not significantly shift (q, n) from the optimal uniprocessor values, and that the effects of granularity are more important.

The computational complexity for parallel implementation of multidomain spectral methods is studied to derive the optimal number of subdomains, q, and spectral order, n, for numerical solution of hyperbolic problems. The complexity analysis is based upon theoretical results which predict error as a function of (q, n) for problems having wave-like solutions. These are combined with a linear communication cost model to study the impact of communication overhead and imposed granularity on the optimal choice of (q, n) as a function of the number of processors. It is shown that, for present day multicomputers, the impact of communication overhead does not significantly shift (q, n) from the optimal uniprocessor values, and that the effects of granularity are more important.

The computational complexity for parallel implementation of multidomain spectral methods is studied to derive the optimal number of subdomains, q, and spectral order, n, for numerical solution of hyperbolic problems. The complexity analysis is based upon theoretical results which predict error as a function of (q, n) for problems having wave-like solutions. These are combined with a linear communication cost model to study the impact of communication overhead and imposed granularity on the optimal choice of (q, n) as a function of the number of processors. It is shown that, for present day multicomputers, the impact of communication overhead does not significantly shift (q, n) from the optimal uniprocessor values, and that the effects of granularity are more important.

The computational complexity for parallel implementation of multidomain spectral methods is studied to derive the optimal number of subdomains, q, and spectral order, n, for numerical solution of hyperbolic problems. The complexity analysis is based upon theoretical results which predict error as a function of (q, n) for problems having wave-like solutions. These are combined with a linear communication cost model to study the impact of communication overhead and imposed granularity on the optimal choice of (q, n) as a function of the number of processors. It is shown that, for present day multicomputers, the impact of communication overhead does not significantly shift (q, n) from the optimal uniprocessor values, and that the effects of granularity are more important.

The implementation of Pan and Reif's Parallel Nested Dissection (PND) algorithm on mesh connected parallel computers is described. This is the first known algorithm that allows very large, sparse linear systems of equations to be solved efficiently in polylog time using a small number of processors. How the processor bound of PND can be matched to the number of processors available on a given parallel computer by slowing down the algorithm by constant factors is described. Also, for the important class of problems where G(A) is a grid graph, a unique memory mapping that reduces the inter-processor communication requirements of PND to those that can be executed on mesh connected parallel machines is detailed. A description of an implementation on the Goodyear Massively Parallel Processor (MPP), located at Goddard is given. Also, a detailed discussion of data mappings and performance issues is given.

This article presents a procedure for computing the aeroelasticity of wing-body configurations on multiple-instruction, multiple-data parallel computers. In this procedure, fluids are modeled using Euler equations discretized by a finite difference method, and structures are modeled using finite element equations. The procedure is designed in such a way that each discipline can be developed and maintained independently by using a domain decomposition approach. A parallel integration scheme is used to compute aeroelastic responses by solving the coupled fluid and structural equations concurrently while keeping modularity of each discipline. The present procedure is validated by computing the aeroelastic response of a wing and comparing with experiment. Aeroelastic computations are illustrated for a high speed civil transport type wing-body configuration.

This article presents a procedure for computing the aeroelasticity of wing-body configurations on multiple-instruction, multiple-data parallel computers. In this procedure, fluids are modeled using Euler equations discretized by a finite difference method, and structures are modeled using finite element equations. The procedure is designed in such a way that each discipline can be developed and maintained independently by using a domain decomposition approach. A parallel integration scheme is used to compute aeroelastic responses by solving the coupled fluid and structural equations concurrently while keeping modularity of each discipline. The present procedure is validated by computing the aeroelastic response of a wing and comparing with experiment. Aeroelastic computations are illustrated for a high speed civil transport type wing-body configuration.

This article presents a procedure for computing the aeroelasticity of wing-body configurations on multiple-instruction, multiple-data parallel computers. In this procedure, fluids are modeled using Euler equations discretized by a finite difference method, and structures are modeled using finite element equations. The procedure is designed in such a way that each discipline can be developed and maintained independently by using a domain decomposition approach. A parallel integration scheme is used to compute aeroelastic responses by solving the coupled fluid and structural equations concurrently while keeping modularity of each discipline. The present procedure is validated by computing the aeroelastic response of a wing and comparing with experiment. Aeroelastic computations are illustrated for a high speed civil transport type wing-body configuration.

We present a method for electronic structure calculations that retains all of the advantages of real space and addresses the inherent inefficiency of a regular grid, which has equal precision everywhere. The computations are carried out on a {\em regular} mesh in {\em curvilinear space}, which allows natural and efficient decomposition on parallel computers, and effective use of iterative numerical methods. A novel feature is the use of error analysis to optimize the curvilinear grid for highly inhomogeneous electronic distributions. We report accurate all-electron calculations for H$_2$, O, and O$_{2}$.

The purpose of this study was to evaluate the parallel processing impact of MIMD (Multiple-Instruction Multiple-Data Path) computers on Flight Simulation Software. Basic mathematical functions and arithmetic expressions from typical Flight Simulation Software were selected and run on a MIMD computer to evaluate the improvement in execution time that results from the parallel architecture of this type of computer. Recommendations as to the types of tasks which are optimally suitable for this computer architecture are made, together with the improvement in execution speed to be expected. (Author)

State-of-the-art report on the activities in parallel computation nd computers as it pertains to artificial intellgence

The objective of the current work is to build a prototype software system which will automated the process of running CFD jobs on Information Power Grid (IPG) resources. This system should remove the need for user monitoring and intervention of every single CFD job. It should enable the use of many different computers to populate a massive run matrix in the shortest time possible. Such a software system has been developed, and is known as the AeroDB script system. The approach taken for the development of AeroDB was to build several discrete modules. These include a database, a job-launcher module, a run-manager module to monitor each individual job, and a web-based user portal for monitoring of the progress of the parameter study. The details of the design of AeroDB are presented in the following section. The following section provides the results of a parameter study which was performed using AeroDB for the analysis of a reusable launch vehicle (RLV). The paper concludes with a section on the lessons learned in this effort, and ideas for future work in this area.

A new parallel algorithm for the solution of a general linear recurrence is described. Its relation to the work of Kogge and Stone is discussed.

This paper presents parallel implementations of two codes used in a combined CFD/Kirchhoff methodology to predict the aerodynamics and aeroacoustics properties of helicopters. The rotorcraft Navier-Stokes code, TURNS, computes the aerodynamic flowfield near the helicopter blades and the Kirchhoff acoustics code computes the noise in the far field, using the TURNS solution as input. The overall parallel strategy adds MPI message passing calls to the existing serial codes to allow for communication between processors. As a result, the total code modifications required for parallel execution are relatively small. The biggest bottleneck in running the TURNS code in parallel comes from the LU-SGS algorithm that solves the implicit system of equations. We use a new hybrid domain decomposition implementation of LU-SGS to obtain good parallel performance on the SP-2. TURNS demonstrates excellent parallel speedups for quasi-steady and unsteady three-dimensional calculations of a helicopter blade in forward flight. The execution rate attained by the code on 114 processors is six times faster than the same cases run on one processor of the Cray C-90. The parallel Kirchhoff code also shows excellent parallel speedups and fast execution rates. As a performance demonstration, unsteady acoustic pressures are computed at 1886 far-field observer locations for a sample acoustics problem. The calculation requires over two hundred hours of CPU time on one C-90 processor but takes only a few hours on 80 processors of the SP2. The resultant far-field acoustic field is analyzed with state of-the-art audio and video rendering of the propagating acoustic signals.

Astrophysics is a science where controlled experiments are intrinsically challenging. Numerical laboratories on a computer are often the next best alternative. I describe our group's efforts to understand the supermassive black hole in the center of the Milky Way through global 3-D numerical simulations, which are performed on the 30,000 core SciNet cluster, and on GPU clusters. ©2011 Microsoft Corporation. All rights reserved.

A procedure to support parallel refinement and redistribution of two dimensional unstructured finite element meshes on distributed memory computers is presented. The procedure uses the mesh topological entity hierarchy as the underlying data structures to easily support the required adjacency information. Mesh refinement is done by employing links back to the geometric representation to place new nodes on the boundary of the domain directly on the curved geometry. The refined mesh is then redistributed by an iterative heuristic based on the Leiss/Reddy 9 load balancing criteria. A fast parallel tree edge-coloring algorithm is used to pair processors having adjacent partitions and forming a tree structure as a result of Leiss/Reddy load request criteria. Excess elements are iteratively migrated from heavily loaded to less loaded processors until load balancing is achieved. The system is implemented on a massively parallel MasPar MP-1 system with a SIMD style of computation and uses message passing primitives to migrate elements during the mesh redistribution phase. Performance results of the redistribution heuristics on various test meshes are given.

This final report is a cumulative summary of our group's research accomplishments under the AFOSR grant number F49620-92-J-O126. Over the past three years, our work has spanned the areas of architectures, operating system policies, performance analysis and algorithms for parallel processing.

A general purpose solver for large, sparse, banded systems of equations has been developed and tested on the CM5E. This tool can be applied to any problem arising in finite element analysis such as structures, machinery, acoustic-structure interaction among many others. For a very large problem a factorization and solution takes 10 to 12 minutes; solutions for additional right hand sides will take on the order of one minute each.

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Problems which can arise with vector and parallel computers are discussed in a user oriented context. Emphasis is placed on the algorithms used and the programming techniques adopted. Three recently developed supercomputers are examined and typical application examples are given in CRAY FORTRAN, CYBER 205 FORTRAN and DAP (distributed array processor) FORTRAN. The systems performance is compared. The addition of parts of two N x N arrays is considered. The influence of the architecture on the algorithms and programming language is demonstrated. Numerical analysis of magnetohydrodynamic differential equations by an explicit difference method is illustrated, showing very good results for all three systems. The prognosis for supercomputer development is assessed.

The results of the implementation of a Navier-Stokes algorithm on three parallel/vector computers are presented. The object of this research is to determine how well, or poorly, a single numerical algorithm would map onto three different architectures. The algorithm is a compact difference scheme for the solution of the incompressible, two-dimensional, time-dependent Navier-Stokes equations. The computers were chosen so as to encompass a variety of architectures. They are the following: the MPP, an SIMD machine with 16K bit serial processors; Flex/32, an MIMD machine with 20 processors; and Cray/2. The implementation of the algorithm is discussed in relation to these architectures and measures of the performance on each machine are given. The basic comparison is among SIMD instruction parallelism on the MPP, MIMD process parallelism on the Flex/32, and vectorization of a serial code on the Cray/2. Simple performance models are used to describe the performance. These models highlight the bottlenecks and limiting factors for this algorithm on these architectures. Finally, conclusions are presented.