Adapting the interior point method for the solution of LPs on serial, coarse grain parallel and massively parallel computers

In this paper we describe a unified scheme for implementing an interior point algorithm (IPM) over a range of computer architectures. In the inner iteration of the IPM a search direction is computed using Newton's method. Computationally this involves solving a sparse symmetric positive definite (SSPD) system of equations. The choice of direct and indirect methods for the solution of this system, and the design of data structures to take advantage of serial, coarse grain parallel and massively parallel computer architectures, are considered in detail. We put forward arguments as to why integration of the system within a sparse simplex solver is important and outline how the system is designed to achieve this integration

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

Group implicit concurrent algorithms in nonlinear structural dynamics

During the 70's and 80's, considerable effort was devoted to developing efficient and reliable time stepping procedures for transient structural analysis. Mathematically, the equations governing this type of problems are generally stiff, i.e., they exhibit a wide spectrum in the linear range. The algorithms best suited to this type of applications are those which accurately integrate the low frequency content of the response without necessitating the resolution of the high frequency modes. This means that the algorithms must be unconditionally stable, which in turn rules out explicit integration. The most exciting possibility in the algorithms development area in recent years has been the advent of parallel computers with multiprocessing capabilities. So, this work is mainly concerned with the development of parallel algorithms in the area of structural dynamics. A primary objective is to devise unconditionally stable and accurate time stepping procedures which lend themselves to an efficient implementation in concurrent machines. Some features of the new computer architecture are summarized. A brief survey of current efforts in the area is presented. A new class of concurrent procedures, or Group Implicit algorithms is introduced and analyzed. The numerical simulation shows that GI algorithms hold considerable promise for application in coarse grain as well as medium grain parallel computers

Analysis and design of parallel algorithms

The present state of electronic technology is such that factors affecting computation speed have almost been minimised; switching for instance is almost instantaneous. Electronic components are so good, in fact, that the time taken for a logic signal to travel between two points is now a significant factor of instruction times. Clearly, with the actual physical size of components being very small and the high circuit density, there is little scope for improving computation speech significantly by such means as even denser circuitry or still faster electronic components. Thus, development of faster computers will require a new approach that depends on the imaginative use of existing knowledge. One such approach is to increase computation speed through parallelism. Obviously, a parallel computer with p identical processors is potentially p times as fast as a single computer, although this limit can rarely be achieved

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

Towards developing robust algorithms for solving partial differential equations on MIMD machines

Methods for efficient computation of numerical algorithms on a wide variety of MIMD machines are proposed. These techniques reorganize the data dependency patterns to improve the processor utilization. The model problem finds the time-accurate solution to a parabolic partial differential equation discretized in space and implicitly marched forward in time. The algorithms are extensions of Jacobi and SOR. The extensions consist of iterating over a window of several timesteps, allowing efficient overlap of computation with communication. The methods increase the degree to which work can be performed while data are communicated between processors. The effect of the window size and of domain partitioning on the system performance is examined both by implementing the algorithm on a simulated multiprocessor system

Mapping numerical software onto distributed memory parallel systems

The aim of this thesis is to further the use of parallel computers, in particular distributed memory systems, by proving strategies for parallelisation and developing the core component of tools to aid scalar software porting. The ported code must not only efficiently exploit available parallel processing speed and distributed memory, but also enable existing users of the scalar code to use the parallel version with identical inputs and allow maintenance to be performed by the scalar code author in conjunction with the parallel code. The data partition strategy has been used to parallelise an in-house solidification modelling code where all requirements for the parallel software were successfully met. To confirm the success of this parallelisation strategy, a much sterner test was used, parallelising the HARWELL-FLOW3D fluid flow package. The performance results of the parallel version clearly vindicate the conclusions of the first example. Speedup efficiencies of around 80 percent have been achieved on fifty processors for sizable models. In both these tests, the alterations to the code were fairly minor, maintaining the structure and style of the original scalar code which can easily be recognised by its original author. The alterations made to these codes indicated the potential for parallelising tools since the alterations were fairly minor and usually mechanical in nature. The current generation of parallelising compilers rely heavily on heuristic guidance in parallel code generation and other decisions that may be better made by a human. As a result, the code they produce will almost certainly be inferior to manually produced code. Also, in order not to sacrifice parallel code quality when using tools, the scalar code analysis to identify inherent parallelism in a application code, as used in parallelising compilers, has been extended to eliminate dependencies conservatively assumed, since these dependencies can greatly inhibit parallelisation. Extra information has been extracted both from control flow and from processing symbolic information. The tests devised to utilise this information enable the non-existence of a significant number of previously assumed dependencies to be proved. In some cases, the number of true dependencies has been more than halved. The dependence graph produced is of sufficient quality to greatly aid the parallelisation, with user interaction and interpretation, parallelism detection and code transformation validity being less inhibited by assumed dependencies. The use of tools rather than the black box approach removes the handicaps associated with using heuristic methods, if any relevant heuristic methods exist