Distributed Finite Element Analysis Using a Transputer Network

The principal objective of this research effort was to demonstrate the extraordinarily cost effective acceleration of finite element structural analysis problems using a transputer-based parallel processing network. This objective was accomplished in the form of a commercially viable parallel processing workstation. The workstation is a desktop size, low-maintenance computing unit capable of supercomputer performance yet costs two orders of magnitude less. To achieve the principal research objective, a transputer based structural analysis workstation termed XPFEM was implemented with linear static structural analysis capabilities resembling commercially available NASTRAN. Finite element model files, generated using the on-line preprocessing module or external preprocessing packages, are downloaded to a network of 32 transputers for accelerated solution. The system currently executes at about one third Cray X-MP24 speed but additional acceleration appears likely. For the NASA selected demonstration problem of a Space Shuttle main engine turbine blade model with about 1500 nodes and 4500 independent degrees of freedom, the Cray X-MP24 required 23.9 seconds to obtain a solution while the transputer network, operated from an IBM PC-AT compatible host computer, required 71.7 seconds. Consequently, the $80,000 transputer network demonstrated a cost-performance ratio about 60 times better than the$15,000,000 Cray X-MP24 system

Computer algebra and transputers applied to the finite element method

Recent developments in computing technology have opened new prospects for computationally intensive numerical methods such as the finite element method. More complex and refined problems can be solved, for example increased number and order of the elements improving accuracy. The power of Computer Algebra systems and parallel processing techniques is expected to bring significant improvement in such methods. The main objective of this work has been to assess the use of these techniques in the finite element method. The generation of interpolation functions and element matrices has been investigated using Computer Algebra. Symbolic expressions were obtained automatically and efficiently converted into FORTRAN routines. Shape functions based on Lagrange polynomials and mapping functions for infinite elements were considered. One and two dimensional element matrices for bending problems based on Hermite polynomials were also derived. Parallel solvers for systems of linear equations have been developed since such systems often arise in numerical methods. Both symmetric and asymmetric solvers have been considered. The implementation was on Transputer-based machines. The speed-ups obtained are good. An analysis by finite element method of a free surface flow over a spillway has been carried out. Computer Algebra was used to derive the integrand of the element matrices and their numerical evaluation was done in parallel on a Transputer-based machine. A graphical interface was developed to enable the visualisation of the free surface and the influence of the parameters. The speed- ups obtained were good. Convergence of the iterative solution method used was good for gated spillways. Some problems experienced with the non-gated spillways have lead to a discussion and tests of the potential factors of instability

Numerical simulation of non-Newtonian fluid flow in mixing geometries

In this thesis, a theoretical investigation is undertaken into fluid and mixing flows generated by various geometries for Newtonian and non-Newtonian fluids, on both sequential and parallel computer systems. The thesis begins by giving the necessary background to the mixing process and a summary of the fundamental characteristics of parallel architecture machines. This is followed by a literature review which covers accomplished work in mixing flows, numerical methods employed to simulate fluid mechanics problems and also a review of relevant parallel algorithms. Next, an overview is given of the numerical methods that have been reviewed, discussing the advantages and disadvantages of the different methods. In the first section of the work the implementation of the primitive variable finite element method to solve a simple two dimensional fluid flow problem is studied. For the same geometry colour band mixing is also investigated. Further investigational work is undertaken into the flows generated by various rotors for both Newtonian and non-Newtonian fluids. An extended version of the primitive variable formulation is employed, colour band mixing is also carried out on two of these geometries. The latter work is carried out on a parallel architecture machine. The design specifications of a parallel algorithm for a MIMD system are discussed, with particular emphasis placed on frontal and multifrontal methods. This is followed by an explanation of the implementation of the proposed parallel algorithm, applied to the same fluid flow problems as considered earlier and a discussion of the efficiency of the system is given. Finally, a discussion of the conclusions of the entire accomplished work is presented. A number of suggestions for future work are also given. Three published papers relating to the work carried out on the transputer networks are included in the appendices

A Massively Parallel Algorithm for the Approximate Calculation of Inverse p-th Roots of Large Sparse Matrices

We present the submatrix method, a highly parallelizable method for the approximate calculation of inverse p-th roots of large sparse symmetric matrices which are required in different scientific applications. We follow the idea of Approximate Computing, allowing imprecision in the final result in order to be able to utilize the sparsity of the input matrix and to allow massively parallel execution. For an n x n matrix, the proposed algorithm allows to distribute the calculations over n nodes with only little communication overhead. The approximate result matrix exhibits the same sparsity pattern as the input matrix, allowing for efficient reuse of allocated data structures. We evaluate the algorithm with respect to the error that it introduces into calculated results, as well as its performance and scalability. We demonstrate that the error is relatively limited for well-conditioned matrices and that results are still valuable for error-resilient applications like preconditioning even for ill-conditioned matrices. We discuss the execution time and scaling of the algorithm on a theoretical level and present a distributed implementation of the algorithm using MPI and OpenMP. We demonstrate the scalability of this implementation by running it on a high-performance compute cluster comprised of 1024 CPU cores, showing a speedup of 665x compared to single-threaded execution

Parallel algorithms for the solution of elliptic and parabolic problems on transputer networks

This thesis is a study of the implementation of parallel algorithms for solving elliptic and parabolic partial differential equations on a network of transputers. The thesis commences with a general introduction to parallel processing. Here a discussion of the various ways of introducing parallelism in computer systems and the classification of parallel architectures is presented. In chapter 2, the transputer architecture and the associated language OCCAM are described. The transputer development system (TDS) is also described as well as a short account of other transputer programming languages. Also, a brief description of the methodologies for programming transputer networks is given. The chapter is concluded by a detailed description of the hardware used for the research. [Continues.

Lewis Structures Technology, 1988. Volume 1: Structural Dynamics

The specific purpose of the symposium was to familiarize the engineering structures community with the depth and range of research performed by the Structures Division of the Lewis Research Center and its academic and industrial partners. Sessions covered vibration control, fracture mechanics, ceramic component reliability, parallel computing, nondestructive testing, dynamical systems, fatigue and damage, wind turbines, hot section technology, structural mechanics codes, computational methods for dynamics, structural optimization, and applications of structural dynamics

Probabilistic structural mechanics research for parallel processing computers

Aerospace structures and spacecraft are a complex assemblage of structural components that are subjected to a variety of complex, cyclic, and transient loading conditions. Significant modeling uncertainties are present in these structures, in addition to the inherent randomness of material properties and loads. To properly account for these uncertainties in evaluating and assessing the reliability of these components and structures, probabilistic structural mechanics (PSM) procedures must be used. Much research has focused on basic theory development and the development of approximate analytic solution methods in random vibrations and structural reliability. Practical application of PSM methods was hampered by their computationally intense nature. Solution of PSM problems requires repeated analyses of structures that are often large, and exhibit nonlinear and/or dynamic response behavior. These methods are all inherently parallel and ideally suited to implementation on parallel processing computers. New hardware architectures and innovative control software and solution methodologies are needed to make solution of large scale PSM problems practical

The application of parallel computer technology to the dynamic analysis of suspension bridges

This research is concerned with the application of distributed computer technology to the solution of non-linear structural dynamic problems, in particular the onset of aerodynamic instabilities in long span suspension bridge structures, such as flutter which is a catastrophic aeroelastic phenomena. The thesis is set out in two distinct parts:- Part I, presents the theoretical background of the main forms of aerodynamic instabilities, presenting in detail the main solution techniques used to solve the flutter problem. The previously written analysis package ANSUSP is presented which has been specifically developed to predict numerically the onset of flutter instability. The various solution techniques which were employed to predict the onset of flutter for the Severn Bridge are discussed. All the results presented in Part I were obtained using a 486DX2 66MHz serial personal computer. Part II, examines the main solution techniques in detail and goes on to apply them to a large distributed supercomputer, which allows the solution of the problem to be achieved considerably faster than is possible using the serial computer system. The solutions presented in Part II are represented as Performance Indices (PI) which quote the ratio of time to performing a specific calculation using a serial algorithm compared to a parallel algorithm running on the same computer system

The Laplace transform boundary element method for diffusion-type problems

Diffusion-type problems are described by parabolic partial differential equations; they are defined on a domain involving both time and space. The usual method of solution is to use a finite difference time-stepping process which leads to an elliptic equation in the space variable. The major drawback with the finite difference method in time is the possibility of severe stability restrictions. An alternative process is to use the Laplace transform. The transformed problem can be solved using a suitable partial differential equation solver and the solution is transformed back into the time domain using a suitable inversion process. In all practical situations a numerical inversion is required. For problems with discontinuous or periodic boundary conditions, the numerical inversion is not straightforward and we show how to overcome these difficulties. The boundary element method is a well-established technique for solving elliptic problems. One of the procedures required is the evaluation of singular integrals which arise in the solution process and a new formulation is developed to handle these integrals. For the solution of non-homogeneous equations an additional technique is required and the dual reciprocity method used in conjunction with the boundary element method provides a way forward. The Laplace transform is a linear operator and as such cannot handle non-linear terms. We address this problem by a linearisation process together with a suitable iterative scheme. We apply such a procedure to a non-linear coupled electromagnetic heating problem with electrical and thermal properties exhibiting temperature dependencies