Implementation of multigrid methods for solving Navier-Stokes equations on a multiprocessor system

Presented are schemes for implementing multigrid algorithms on message based MIMD multiprocessor systems. To address the various issues involved, a nontrivial problem of solving the 2-D incompressible Navier-Stokes equations is considered as the model problem. Three different multigrid algorithms are considered. Results from implementing these algorithms on an Intel iPSC are presented

A bibliography on parallel and vector numerical algorithms

This is a bibliography of numerical methods. It also includes a number of other references on machine architecture, programming language, and other topics of interest to scientific computing. Certain conference proceedings and anthologies which have been published in book form are listed also

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

Performance of a parallel code for the Euler equations on hypercube computers

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

Analysis of a parallel multigrid algorithm

The parallel multigrid algorithm of Frederickson and McBryan (1987) is considered. This algorithm uses multiple coarse-grid problems (instead of one problem) in the hope of accelerating convergence and is found to have a close relationship to traditional multigrid methods. Specifically, the parallel coarse-grid correction operator is identical to a traditional multigrid coarse-grid correction operator, except that the mixing of high and low frequencies caused by aliasing error is removed. Appropriate relaxation operators can be chosen to take advantage of this property. Comparisons between the standard multigrid and the new method are made

Development of a Navier-Stokes algorithm for parallel-processing supercomputers

An explicit flow solver, applicable to the hierarchy of model equations ranging from Euler to full Navier-Stokes, is combined with several techniques designed to reduce computational expense. The computational domain consists of local grid refinements embedded in a global coarse mesh, where the locations of these refinements are defined by the physics of the flow. Flow characteristics are also used to determine which set of model equations is appropriate for solution in each region, thereby reducing not only the number of grid points at which the solution must be obtained, but also the computational effort required to get that solution. Acceleration to steady-state is achieved by applying multigrid on each of the subgrids, regardless of the particular model equations being solved. Since each of these components is explicit, advantage can readily be taken of the vector- and parallel-processing capabilities of machines such as the Cray X-MP and Cray-2

Design and Analysis of Optical Interconnection Networks for Parallel Computation.

In this doctoral research, we propose several novel protocols and topologies for the interconnection of massively parallel processors. These new technologies achieve considerable improvements in system performance and structure simplicity. Currently, synchronous protocols are used in optical TDM buses. The major disadvantage of a synchronous protocol is the waste of packet slots. To offset this inherent drawback of synchronous TDM, a pipelined asynchronous TDM optical bus is proposed. The simulation results show that the performance of the proposed bus is significantly better than that of known pipelined synchronous TDM optical buses. Practically, the computation power of the plain TDM protocol is limited. Various extensions must be added to the system. In this research, a new pipelined optical TDM bus for implementing a linear array parallel computer architecture is proposed. The switches on the receiving segment of the bus can be dynamically controlled, which make the system highly reconfigurable. To build large and scalable systems, we need new network architectures that are suitable for optical interconnections. A new kind of reconfigurable bus called segmented bus is introduced to achieve reduced structure simplicity and increased concurrency. We show that parallel architectures based on segmented buses are versatile by showing that it can simulate parallel communication patterns supported by a wide variety of networks with small slowdown factors. New kinds of interconnection networks, the hypernetworks, have been proposed recently. Compared with point-to-point networks, they allow for increased resource-sharing and communication bandwidth utilization, and they are especially suitable for optical interconnects. One way to derive a hypernetwork is by finding the dual of a point-to-point network. Hypercube Q\sb{n}, where n is the dimension, is a very popular point-to-point network. It is interesting to construct hypernetworks from the dual Q\sbsp{n}{*} of hypercube of Q\sb{n}. In this research, the properties of Q\sbsp{n}{*} are investigated and a set of fundamental data communication algorithms for Q\sbsp{n}{*} are presented. The results indicate that the Q\sbsp{n}{*} hypernetwork is a useful and promising interconnection structure for high-performance parallel and distributed computing systems

Summary of research in applied mathematics, numerical analysis, and computer sciences

The major categories of current ICASE research programs addressed include: numerical methods, with particular emphasis on the development and analysis of basic numerical algorithms; control and parameter identification problems, with emphasis on effective numerical methods; computational problems in engineering and physical sciences, particularly fluid dynamics, acoustics, and structural analysis; and computer systems and software, especially vector and parallel computers