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At least 163 records · Page 9

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NASA NTRS1985

Finite elements and the method of conjugate gradients on a concurrent processor

An algorithm for the iterative solution of finite element problems on a concurrent processor is presented. The method of conjugate gradients is used to solve the system of matrix equations, which is distributed among the processors of a MIMD computer according to an element-based spatial decomposition. This algorithm is implemented in a two-dimensional elastostatics program on the Caltech Hypercube concurrent processor. The results of tests on up to 32 processors show nearly linear concurrent speedup, with efficiencies over 90 percent for sufficiently large problems.

Lyzenga, G. A.↗

NASA NTRS1987

Parallel Algorithm Solves Coupled Differential Equations

Numerical methods adapted to concurrent processing. Algorithm solves set of coupled partial differential equations by numerical integration. Adapted to run on hypercube computer, algorithm separates problem into smaller problems solved concurrently. Increase in computing speed with concurrent processing over that achievable with conventional sequential processing appreciable, especially for large problems.

Hayashi, A.↗

NASA NTRS1987

Algorithm implementation on the Navier-Stokes computer

The Navier-Stokes Computer is a multi-purpose parallel-processing supercomputer which is currently under development at Princeton University. It consists of multiple local memory parallel processors, called Nodes, which are interconnected in a hypercube network. Details of the procedures involved in implementing an algorithm on the Navier-Stokes computer are presented. The particular finite difference algorithm considered in this analysis was developed for simulation of laminar-turbulent transition in wall bounded shear flows. Projected timing results for implementing this algorithm indicate that operation rates in excess of 42 GFLOPS are feasible on a 128 Node machine.

Krist, Steven E.↗

NASA NTRS1987

Analysis of a parallelized nonlinear elliptic boundary value problem solver with application to reacting flows

A parallelized finite difference code based on the Newton method for systems of nonlinear elliptic boundary value problems in two dimensions is analyzed in terms of computational complexity and parallel efficiency. An approximate cost function depending on 15 dimensionless parameters is derived for algorithms based on stripwise and boxwise decompositions of the domain and a one-to-one assignment of the strip or box subdomains to processors. The sensitivity of the cost functions to the parameters is explored in regions of parameter space corresponding to model small-order systems with inexpensive function evaluations and also a coupled system of nineteen equations with very expensive function evaluations. The algorithm was implemented on the Intel Hypercube, and some experimental results for the model problems with stripwise decompositions are presented and compared with the theory. In the context of computational combustion problems, multiprocessors of either message-passing or shared-memory type may be employed with stripwise decompositions to realize speedup of O(n), where n is mesh resolution in one direction, for reasonable n.

Keyes, David E.↗

NASA NTRS1986

Two-dimensional nonsteady viscous flow simulation on the Navier-Stokes computer miniNode

The needs of large-scale scientific computation are outpacing the growth in performance of mainframe supercomputers. In particular, problems in fluid mechanics involving complex flow simulations require far more speed and capacity than that provided by current and proposed Class VI supercomputers. To address this concern, the Navier-Stokes Computer (NSC) was developed. The NSC is a parallel-processing machine, comprised of individual Nodes, each comparable in performance to current supercomputers. The global architecture is that of a hypercube, and a 128-Node NSC has been designed. New architectural features, such as a reconfigurable many-function ALU pipeline and a multifunction memory-ALU switch, have provided the capability to efficiently implement a wide range of algorithms. Efficient algorithms typically involve numerically intensive tasks, which often include conditional operations. These operations may be efficiently implemented on the NSC without, in general, sacrificing vector-processing speed. To illustrate the architecture, programming, and several of the capabilities of the NSC, the simulation of two-dimensional, nonsteady viscous flows on a prototype Node, called the miniNode, is presented.

Nosenchuck, Daniel M.↗

NASA NTRS1987

A partitioning strategy for nonuniform problems on multiprocessors

The partitioning of a problem on a domain with unequal work estimates in different subdomains is considered in a way that balances the work load across multiple processors. Such a problem arises for example in solving partial differential equations using an adaptive method that places extra grid points in certain subregions of the domain. A binary decomposition of the domain is used to partition it into rectangles requiring equal computational effort. The communication costs of mapping this partitioning onto different microprocessors: a mesh-connected array, a tree machine and a hypercube is then studied. The communication cost expressions can be used to determine the optimal depth of the above partitioning.

Berger, Marsha J.↗

NASA NTRS1987

Simulations of transition and turbulence on the Navier-Stokes computer

The Navier-Stokes Computer (NSC) consists of multiple local memory parallel processors interconnected in a hypercube network. Efficient implementation of algorithms on the NSC thus requires the effective utilization of both the coarse and fine grain paralelism inherent in the architectural design. The basic approach to implementing an algorithm on the NSC is presented herein. The particular finite-difference algorithm considered was developed for performing transition and turbulence simulations by direct solution of the time-dependent incompressible Navier-Stokes equations. The suitability of this algorithm for performing simulations of the isotropic turbulence problem is verified from computations performed on a Cray 2. Projected timing results for the algorithm on the NSC itself are presented for both the isotropic turbulence and laminar turbulent transition problems.

Krist, S. E.↗

NASA NTRS1988

Experiences with serial and parallel algorithms for channel routing using simulated annealing

Two algorithms for channel routing using simulated annealing are presented. Simulated annealing is an optimization methodology which allows the solution process to back up out of local minima that may be encountered by inappropriate selections. By properly controlling the annealing process, it is very likely that the optimal solution to an NP-complete problem such as channel routing may be found. The algorithm presented proposes very relaxed restrictions on the types of allowable transformations, including overlapping nets. By freeing that restriction and controlling overlap situations with an appropriate cost function, the algorithm becomes very flexible and can be applied to many extensions of channel routing. The selection of the transformation utilizes a number of heuristics, still retaining the pseudorandom nature of simulated annealing. The algorithm was implemented as a serial program for a workstation, and a parallel program designed for a hypercube computer. The details of the serial implementation are presented, including many of the heuristics used and some of the resulting solutions.

Brouwer, Randall Jay↗

NASA NTRS1988

Networking and AI systems: Requirements and benefits

The price performance benefits of network systems is well documented. The ability to share expensive resources sold timesharing for mainframes, department clusters of minicomputers, and now local area networks of workstations and servers. In the process, other fundamental system requirements emerged. These have now been generalized with open system requirements for hardware, software, applications and tools. The ability to interconnect a variety of vendor products has led to a specification of interfaces that allow new techniques to extend existing systems for new and exciting applications. As an example of the message passing system, local area networks provide a testbed for many of the issues addressed by future concurrent architectures: synchronization, load balancing, fault tolerance and scalability. Gold Hill has been working with a number of vendors on distributed architectures that range from a network of workstations to a hypercube of microprocessors with distributed memory. Results from early applications are promising both for performance and scalability.

Source record↗

NASA NTRS1988

Hypercluster - Parallel processing for computational mechanics

An account is given of the development status, performance capabilities and implications for further development of NASA-Lewis' testbed 'hypercluster' parallel computer network, in which multiple processors communicate through a shared memory. Processors have local as well as shared memory; the hypercluster is expanded in the same manner as the hypercube, with processor clusters replacing the normal single processor node. The NASA-Lewis machine has three nodes with a vector personality and one node with a scalar personality. Each of the vector nodes uses four board-level vector processors, while the scalar node uses four general-purpose microcomputer boards.

Blech, Richard A.↗

NASA NTRS1988

Design and implementation of parallel multigrid algorithms

Techniques for mapping multigrid algorithms to solve elliptic PDEs on hypercube parallel computers are described and demonstrated. The need for proper data mapping to minimize communication distances is stressed, and an execution-time model is developed to show how algorithm efficiency is affected by changes in the machine and algorithm parameters. Particular attention is then given to the case of coarse computational grids, which can lead to idle processors, load imbalances, and inefficient performance. It is shown that convergence can be improved by using idle processors to solve a new problem concurrently on the fine grid defined by a splitting.

Chan, Tony F.↗

NASA NTRS1988

On multigrid methods for the Navier-Stokes Computer

The overall architecture of the multipurpose parallel-processing Navier-Stokes Computer (NSC) being developed by Princeton and NASA Langley (Nosenchuck et al., 1986) is described and illustrated with extensive diagrams, and the NSC implementation of an elementary multigrid algorithm for simulating isotropic turbulence (based on solution of the incompressible time-dependent Navier-Stokes equations with constant viscosity) is characterized in detail. The present NSC design concept calls for 64 nodes, each with the performance of a class VI supercomputer, linked together by a fiber-optic hypercube network and joined to a front-end computer by a global bus. In this configuration, the NSC would have a storage capacity of over 32 Gword and a peak speed of over 40 Gflops. The multigrid Navier-Stokes code discussed would give sustained operation rates of about 25 Gflops.

Nosenchuck, D. M.↗

NASA NTRS1987

Solving finite element equations on concurrent computers

This paper discusses the development of a concurrent algorithm for the solution of systems of equations arising in finite element applications. The approach is based on a hybrid of direct elimination method and preconditioned conjugate iteration. Two different preconditioners are used; diagonal scaling and a concurrent implementation of incomplete LU factorization. First, an automatic procedure is used to partition the finite element mesh into sub-structures. The particular mesh partition is chosen to minimize an estimate of the cost for evaluating the solution using this algorithm on a concurrent computer. These procedures are implemented in a finite element program on the JPL/CalTech MARK III hypercube computer. An overview of the structure of this program is presented. The performance of the solution method is demonstrated with the aid of a number of numerical test runs, and its advantages for concurrent implementations are discussed. Efficiency and speed-up factors over sequential machines for the numerical examples are highlighted.

Nour-Omid, B.↗

NASA NTRS1987

Optimal mapping of irregular finite element domains to parallel processors

Mapping the solution domain of n-finite elements into N-subdomains that may be processed in parallel by N-processors is an optimal one if the subdomain decomposition results in a well-balanced workload distribution among the processors. The problem is discussed in the context of irregular finite element domains as an important aspect of the efficient utilization of the capabilities of emerging multiprocessor computers. Finding the optimal mapping is an intractable combinatorial optimization problem, for which a satisfactory approximate solution is obtained here by analogy to a method used in statistical mechanics for simulating the annealing process in solids. The simulated annealing analogy and algorithm are described, and numerical results are given for mapping an irregular two-dimensional finite element domain containing a singularity onto the Hypercube computer.

Flower, J.↗

NASA NTRS1987

A parallelized elliptic solver for reacting flows

A modified Newton algorithm for the solution of nonlinear elliptic boundary value problems via finite discretization methods is presented. A serial implementation of this algorithm which has recently been applied successfully to the computation of an axisymmetric over-ventilated subsonic laminar methane-air jet diffusion flame is described. Parallel implementation issues and a complexity theory are presented. Included as well are actual performance data for model systems obtained on the Intel Hypercube and a discussion of its implications for modeling realistic systems.

Keyes, David E.↗

NASA NTRS1988

TRAPEDS: Producing traces for multicomputers via execution-driven simulation

Trace-driven simulation is an important aid in performance analysis of computer systems. Capturing address traces for these simulations is a difficult problem for single processors and particularly for multicomputers. Even when existing trace methods can be used on multicomputers, the amount of collected data typically grows with the number of processors, so I/O and trace storage costs increase. A new technique is presented which modifies the executable code to dynamically collect the address trace from the user code and analyzes this trace during the execution of the program. This method helps resolve the I/O and storage problems and facilitates parallel analysis of the address trace. If a trace stored on disk is desired, the generated trace information can also be written to files during execution, with a resultant drop in program execution speed. An initial implementation on the Intel iPSC/2 hypercube multicomputer is detailed, and sample simulation results are presented. The effect of this trace collection method on execution time is illustrated.

Stunkel, Craig B.↗

NASA NTRS1989

A message passing kernel for the hypercluster parallel processing test bed

A Message-Passing Kernel (MPK) for the Hypercluster parallel-processing test bed is described. The Hypercluster is being developed at the NASA Lewis Research Center to support investigations of parallel algorithms and architectures for computational fluid and structural mechanics applications. The Hypercluster resembles the hypercube architecture except that each node consists of multiple processors communicating through shared memory. The MPK efficiently routes information through the Hypercluster, using a message-passing protocol when necessary and faster shared-memory communication whenever possible. The MPK also interfaces all of the processors with the Hypercluster operating system (HYCLOPS), which runs on a Front-End Processor (FEP). This approach distributes many of the I/O tasks to the Hypercluster processors and eliminates the need for a separate I/O support program on the FEP.

Blech, Richard A.↗

NASA NTRS1988

Totally parallel multilevel algorithms

Four totally parallel algorithms for the solution of a sparse linear system have common characteristics which become quite apparent when they are implemented on a highly parallel hypercube such as the CM2. These four algorithms are Parallel Superconvergent Multigrid (PSMG) of Frederickson and McBryan, Robust Multigrid (RMG) of Hackbusch, the FFT based Spectral Algorithm, and Parallel Cyclic Reduction. In fact, all four can be formulated as particular cases of the same totally parallel multilevel algorithm, which are referred to as TPMA. In certain cases the spectral radius of TPMA is zero, and it is recognized to be a direct algorithm. In many other cases the spectral radius, although not zero, is small enough that a single iteration per timestep keeps the local error within the required tolerance.

Frederickson, Paul O.↗