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In this paper the implementation of a parallel O (Log N) algorithm for computation of rigid multibody dynamics on a Hypercube MIMD parallel architecture is presented.
Class of parallel and parallel/pipeline algorithms presented for more efficient computation of manipulator inertia matrix. Essential for implementing advanced dynamic control schemes as well as dynamic simulation of manipulator motion.
We describe a parallel genetic algorithm (GA) that automatically generates circuit designs using evolutionary search. A circuit-construction programming language is introduced and we show how evolution can generate practical analog circuit designs. Our system allows circuit size (number of devices), circuit topology, and device values to be evolved. We present experimental results as applied to analog filter and amplifier design tasks.
The fact that conventional line-drawing algorithms, when applied directly on parallel machines, can lead to very inefficient codes is addressed. It is suggested that instead of modifying an existing algorithm for a parallel machine, a more efficient implementation can be produced by going back to the invariants in the definition. Popular line-drawing algorithms are compared with two alternatives; distance to a line (a point is on the line if sufficiently close to it) and intersection with a line (a point on the line if an intersection point). For massively parallel single-instruction-multiple-data (SIMD) machines (with thousands of processors and up), the alternatives provide viable line-drawing algorithms. Because of the pixel-per-processor mapping, their performance is independent of the line length and orientation.
This paper describes two models of the cost of data movement in parallel numerical algorithms. One model is a generalization of an approach due to Hockney, and is suitable for shared memory multiprocessors where each processor has vector capabilities. The other model is applicable to highly parallel nonshared memory MIMD systems. In the second model, algorithm performance is characterized in terms of the communication network design. Techniques used in VLSI complexity theory are also brought in, and algorithm independent upper bounds on system performance are derived for several problems that are important to scientific computation.
A completely parallel algorithm for the symmetric eigenproblem AX = Lambda BX is outlined. The algorithm is parallel in the sense that the numerical operations do not occur in a fixed sequence. Therefore, a large number of operations can be programmed to be performed concurrently on a computer with multiple central processing units. The standard symmetric eigenvalue problem AX = Lambda X has the property that the n eigenvalues of the principal submatrix of A of order n are separated by the (n-1) eignvalues of the principal submatrix of order (n-1). The separation property delineated n intervals containing one eigenvalue. Each eigenvalue and corresponding eigenvector can be computed independently. The n eigenproblem calculations can be divided among multiple processing units.
The parallel diagonal dominant (PDD) algorithm is an efficient tridiagonal solver. This paper presents for study a variation of the PDD algorithm, the reduced PDD algorithm. The new algorithm maintains the minimum communication provided by the PDD algorithm, but has a reduced operation count. The PDD algorithm also has a smaller operation count than the conventional sequential algorithm for many applications. Accuracy analysis is provided for the reduced PDD algorithm for symmetric Toeplitz tridiagonal (STT) systems. Implementation results on Langley's Intel Paragon and IBM SP2 show that both the PDD and reduced PDD algorithms are efficient and scalable.
The convergence rate of standard multigrid algorithms degenerates on problems with stretched grids or anisotropic operators. The usual cure for this is the use of line or plane relaxation. However, multigrid algorithms based on line and plane relaxation have limited and awkward parallelism and are quite difficult to map effectively to highly parallel architectures. Newer multigrid algorithms that overcome anisotropy through the use of multiple coarse grids rather than relaxation are better suited to massively parallel architectures because they require only simple point-relaxation smoothers. In this paper, we look at the parallel implementation of a V-cycle multiple semicoarsened grid (MSG) algorithm on distributed-memory architectures such as the Intel iPSC/860 and Paragon computers. The MSG algorithms provide two levels of parallelism: parallelism within the relaxation or interpolation on each grid and across the grids on each multigrid level. Both levels of parallelism must be exploited to map these algorithms effectively to parallel architectures. This paper describes a mapping of an MSG algorithm to distributed-memory architectures that demonstrates how both levels of parallelism can be exploited. The result is a robust and effective multigrid algorithm for distributed-memory machines.
The convergence rate of standard multigrid algorithms degenerates on problems with stretched grids or anisotropic operators. The usual cure for this is the use of line or plane relaxation. However, multigrid algorithms based on line and plane relaxation have limited and awkward parallelism and are quite difficult to map effectively to highly parallel architectures. Newer multigrid algorithms that overcome anisotropy through the use of multiple coarse grids rather than line relaxation are better suited to massively parallel architectures because they require only simple point-relaxation smoothers. The parallel implementation of a V-cycle multiple semi-coarsened grid (MSG) algorithm or distributed-memory architectures such as the Intel iPSC/860 and Paragon computers is addressed. The MSG algorithms provide two levels of parallelism: parallelism within the relaxation or interpolation on each grid and across the grids on each multigrid level. Both levels of parallelism must be exploited to map these algorithms effectively to parallel architectures. A mapping of an MSG algorithm to distributed-memory architectures that demonstrate how both levels of parallelism can be exploited is described. The results is a robust and effective multigrid algorithm for distributed-memory machines.
The Advisory Group for Aerospace Research and Development (AGARD) has requested my participation in the lecture series entitled Parallel Computing in Computational Fluid Dynamics to be held at the von Karman Institute in Brussels, Belgium on May 15-19, 1995. In addition, a request has been made from the US Coordinator for AGARD at the Pentagon for NASA Ames to hold a repetition of the lecture series on October 16-20, 1995. I have been asked to be a local coordinator for the Ames event. All AGARD lecture series events have attendance limited to NATO allied countries. A brief of the lecture series is provided in the attached enclosure. Specifically, I have been asked to give two lectures of approximately 75 minutes each on the subject of parallel solution techniques for the fluid flow equations on unstructured meshes. The title of my lectures is "Parallel CFD Algorithms for Aerodynamical Flow Solvers on Unstructured Meshes" (Parts I-II). The contents of these lectures will be largely review in nature and will draw upon previously published work in this area. Topics of my lectures will include: (1) Mesh partitioning algorithms. Recursive techniques based on coordinate bisection, Cuthill-McKee level structures, and spectral bisection. (2) Newton's method for large scale CFD problems. Size and complexity estimates for Newton's method, modifications for insuring global convergence. (3) Techniques for constructing the Jacobian matrix. Analytic and numerical techniques for Jacobian matrix-vector products, constructing the transposed matrix, extensions to optimization and homotopy theories. (4) Iterative solution algorithms. Practical experience with GIVIRES and BICG-STAB matrix solvers. (5) Parallel matrix preconditioning. Incomplete Lower-Upper (ILU) factorization, domain-decomposed ILU, approximate Schur complement strategies.
Architectures, algorithms, and applications for systolic processors are described with attention to the realization of parallel algorithms on various optical systolic array processors. Systolic processors for matrices with special structure and matrices of general structure, and the realization of matrix-vector, matrix-matrix, and triple-matrix products and such architectures are described. Parallel algorithms for direct and indirect solutions to systems of linear algebraic equations and their implementation on optical systolic processors are detailed with attention to the pipelining and flow of data and operations. Parallel algorithms and their optical realization for LU and QR matrix decomposition are specifically detailed. These represent the fundamental operations necessary in the implementation of least squares, eigenvalue, and SVD solutions. Specific applications (e.g., the solution of partial differential equations, adaptive noise cancellation, and optimal control) are described to typify the use of matrix processors in modern advanced signal processing.
A new hybrid preconditioning algorithm will be presented which combines the favorable attributes of incomplete lower-upper (ILU) factorization with the favorable attributes of the approximate inverse method recently advocated by numerous researchers. The quality of the preconditioner is adjustable and can be increased at the cost of additional computation while at the same time the storage required is roughly constant and approximately equal to the storage required for the original matrix. In addition, the preconditioning algorithm suggests an efficient and natural parallel implementation with reduced communication. Sample calculations will be presented for the numerical solution of multi-dimensional advection-diffusion equations. The matrix solver has also been embedded into a Newton algorithm for solving the nonlinear Euler and Navier-Stokes equations governing compressible flow. The full paper will show numerous examples in CFD to demonstrate the efficiency and robustness of the method.
Symbolic state-space generators are notoriously hard to parallelize. However, the Saturation algorithm implemented in the SMART verification tool differs from other sequential symbolic state-space generators in that it exploits the locality of ring events in asynchronous system models. This paper explores whether event locality can be utilized to efficiently parallelize Saturation on shared-memory architectures. Conceptually, we propose to parallelize the ring of events within a decision diagram node, which is technically realized via a thread pool. We discuss the challenges involved in our parallel design and conduct experimental studies on its prototypical implementation. On a dual-processor dual core PC, our studies show speed-ups for several example models, e.g., of up to 50% for a Kanban model, when compared to running our algorithm only on a single core.
Applications such as animation and scientific visualization demand high performance rendering of complex three dimensional scenes. To deliver the necessary rendering rates, highly parallel hardware architectures are required. The challenge is then to design algorithms and software which effectively use the hardware parallelism. A rendering algorithm targeted to distributed memory MIMD architectures is described. For maximum performance, the algorithm exploits both object-level and pixel-level parallelism. The behavior of the algorithm is examined both analytically and experimentally. Its performance for large numbers of processors is found to be limited primarily by communication overheads. An experimental implementation for the Intel iPSC/860 shows increasing performance from 1 to 128 processors across a wide range of scene complexities. It is shown that minimal modifications to the algorithm will adapt it for use on shared memory architectures as well.
The problem of allocating nodes of a program graph to processors in a parallel processing architecture is considered. The algorithm is based on critical path analysis, some allocation heuristics, and the execution granularity of nodes in a program graph. These factors, and the structure of interprocessor communication network, influence the allocation. To achieve realistic estimations of the executive durations of allocations, the algorithm considers the fact that nodes in a program graph have to communicate through varying numbers of tokens. Coarse and fine granularities have been implemented, with interprocessor token-communication duration, varying from zero up to values comparable to the execution durations of individual nodes. The effect on allocation of communication network structures is demonstrated by performing allocations for crossbar (non-blocking) and star (blocking) networks. The algorithm assumes the availability of as many processors as it needs for the optimal allocation of any program graph. Hence, the focus of allocation has been on varying token-communication durations rather than varying the number of processors. The algorithm always utilizes as many processors as necessary for the optimal allocation of any program graph, depending upon granularity and characteristics of the interprocessor communication network.
As a Guest Computational Investigator under the NASA administered component of the High Performance Computing and Communication Program, we implemented a massively parallel genetic algorithm on the MasPar SIMD computer. Experiments were conducted using Earth Science data in the domains of meteorology and oceanography. Results obtained in these domains are competitive with, and in most cases better than, similar problems solved using other methods. In the meteorological domain, we chose to identify clouds using AVHRR spectral data. Four cloud speciations were used although most researchers settle for three. Results were remarkedly consistent across all tests (91% accuracy). Refinements of this method may lead to more timely and complete information for Global Circulation Models (GCMS) that are prevalent in weather forecasting and global environment studies. In the oceanographic domain, we chose to identify ocean currents from a spectrometer having similar characteristics to AVHRR. Here the results were mixed (60% to 80% accuracy). Given that one is willing to run the experiment several times (say 10), then it is acceptable to claim the higher accuracy rating. This problem has never been successfully automated. Therefore, these results are encouraging even though less impressive than the cloud experiment. Successful conclusion of an automated ocean current detection system would impact coastal fishing, naval tactics, and the study of micro-climates. Finally we contributed to the basic knowledge of GA (genetic algorithm) behavior in parallel environments. We developed better knowledge of the use of subpopulations in the context of shared breeding pools and the migration of individuals. Rigorous experiments were conducted based on quantifiable performance criteria. While much of the work confirmed current wisdom, for the first time we were able to submit conclusive evidence. The software developed under this grant was placed in the public domain. An extensive user's manual was written and distributed nationwide to scientists whose work might benefit from its availability. Several papers, including two journal articles, were produced.
A current thread in parallel computation is the use of cluster computers created by networking a few to thousands of commodity general-purpose workstation-level commuters using the Linux operating system. For example on the Medusa cluster at NASA/GSFC, this provides for super computing performance, 130 G(sub flops) (Linpack Benchmark) at moderate cost, $370K. However, to be useful for scientific computing in the area of Earth science, issues of ease of programming, access to existing scientific libraries, and portability of existing code need to be considered. In this paper, I address these issues in the context of tools for rendering earth science remote sensing data into useful products. In particular, I focus on a problem that can be decomposed into a set of independent tasks, which on a serial computer would be performed sequentially, but with a cluster computer can be performed in parallel, giving an obvious speedup. To make the ideas concrete, I consider the problem of classifying hyperspectral imagery where some ground truth is available to train the classifier. In particular I will use the Support Vector Machine (SVM) approach as applied to hyperspectral imagery. The approach will be to introduce notions about parallel computation and then to restrict the development to the SVM problem. Pseudocode (an outline of the computation) will be described and then details specific to the implementation will be given. Then timing results will be reported to show what speedups are possible using parallel computation. The paper will close with a discussion of the results.
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.