A review of parallel finite element methods on the DAP

AbstractThis paper reviews the research work that has been done to implement the finite element method for solving partial differential equations on the ICL distributed array processor (DAP). A brief outline of the principle features of the method is given, followed by details of the novel techniques required for implementation on the highly parallel architecture. Various methods of solution of the finite element equations are discussed; both direct and iterative techniques are included. The current state-of-the-art favours the use of the preconditioned conjugate gradient method. Some suggestions for future research work on parallel finite element methods are made

Lattice gauge theories dynamical fermions and parallel computation

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Adapting a Navier-Stokes code to the ICL-DAP

The results of an experiment are reported, i.c., to adapt a Navier-Stokes code, originally developed on a serial computer, to concurrent processing on the CL Distributed Array Processor (DAP). The algorithm used in solving the Navier-Stokes equations is briefly described. The architecture of the DAP and DAP FORTRAN are also described. The modifications of the algorithm so as to fit the DAP are given and discussed. Finally, performance results are given and conclusions are drawn

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

Solution of partial differential equations on vector and parallel computers

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

Survey of new vector computers: The CRAY 1S from CRAY research; the CYBER 205 from CDC and the parallel computer from ICL - architecture and programming

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

Particle simulation of plasmas on the massively parallel processor

Particle simulations, in which collective phenomena in plasmas are studied by following the self consistent motions of many discrete particles, involve several highly repetitive sets of calculations that are readily adaptable to SIMD parallel processing. A fully electromagnetic, relativistic plasma simulation for the massively parallel processor is described. The particle motions are followed in 2 1/2 dimensions on a 128 x 128 grid, with periodic boundary conditions. The two dimensional simulation space is mapped directly onto the processor network; a Fast Fourier Transform is used to solve the field equations. Particle data are stored according to an Eulerian scheme, i.e., the information associated with each particle is moved from one local memory to another as the particle moves across the spatial grid. The method is applied to the study of the nonlinear development of the whistler instability in a magnetospheric plasma model, with an anisotropic electron temperature. The wave distribution function is included as a new diagnostic to allow simulation results to be compared with satellite observations

Parallel algorithm for large scale electronic structure calculations

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Solving the Cauchy-Riemann equations on parallel computers

Discussed is the implementation of a single algorithm on three parallel-vector computers. The algorithm is a relaxation scheme for the solution of the Cauchy-Riemann equations; a set of coupled first order partial differential equations. The computers were chosen so as to encompass a variety of architectures. They are: the MPP, and SIMD machine with 16K bit serial processors; FLEX/32, an MIMD machine with 20 processors; and CRAY/2, an MIMD machine with four vector processors. The machine architectures are briefly described. The implementation of the algorithm is discussed in relation to these architectures and measures of the performance on each machine are given. Simple performance models are used to describe the performance. These models highlight the bottlenecks and limiting factors for this algorithm on these architectures. Conclusions are presented