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

Solving large sparse eigenvalue problems on supercomputers

An important problem in scientific computing consists in finding a few eigenvalues and corresponding eigenvectors of a very large and sparse matrix. The most popular methods to solve these problems are based on projection techniques on appropriate subspaces. The main attraction of these methods is that they only require the use of the matrix in the form of matrix by vector multiplications. The implementations on supercomputers of two such methods for symmetric matrices, namely Lanczos' method and Davidson's method are compared. Since one of the most important operations in these two methods is the multiplication of vectors by the sparse matrix, methods of performing this operation efficiently are discussed. The advantages and the disadvantages of each method are compared and implementation aspects are discussed. Numerical experiments on a one processor CRAY 2 and CRAY X-MP are reported. Possible parallel implementations are also discussed

Dynamic Systolization for Developing Multiprocessor Supercomputers

A dynamic network approach is introduced for developing reconfigurable, systolic arrays or wavefront processors; This allows one to design very powerful and flexible processors to be used in a general-purpose, reconfigurable, and fault-tolerant, multiprocessor computer system. The concepts of macro-dataflow and multitasking can be integrated to handle variable-resolution granularities in computationally intensive algorithms. A multiprocessor architecture, Remps, is proposed based on these design methodologies. The Remps architecture is generalized from the Cedar, HEP, Cray X- MP, Trac, NYU ultracomputer, S-l, Pumps, Chip, and SAM projects. Our goal is to provide a multiprocessor research model for developing design methodologies, multiprocessing and multitasking supports, dynamic systolic/wavefront array processors, interconnection networks, reconfiguration techniques, and performance analysis tools. These system design and operational techniques should be useful to those who are developing or evaluating multiprocessor supercomputers

On the parallel solution of parabolic equations

Parallel algorithms for the solution of linear parabolic problems are proposed. The first of these methods is based on using polynomial approximation to the exponential. It does not require solving any linear systems and is highly parallelizable. The two other methods proposed are based on Pade and Chebyshev approximations to the matrix exponential. The parallelization of these methods is achieved by using partial fraction decomposition techniques to solve the resulting systems and thus offers the potential for increased time parallelism in time dependent problems. Experimental results from the Alliant FX/8 and the Cray Y-MP/832 vector multiprocessors are also presented

Efficient solution of parabolic equations by Krylov approximation methods

Numerical techniques for solving parabolic equations by the method of lines is addressed. The main motivation for the proposed approach is the possibility of exploiting a high degree of parallelism in a simple manner. The basic idea of the method is to approximate the action of the evolution operator on a given state vector by means of a projection process onto a Krylov subspace. Thus, the resulting approximation consists of applying an evolution operator of a very small dimension to a known vector which is, in turn, computed accurately by exploiting well-known rational approximations to the exponential. Because the rational approximation is only applied to a small matrix, the only operations required with the original large matrix are matrix-by-vector multiplications, and as a result the algorithm can easily be parallelized and vectorized. Some relevant approximation and stability issues are discussed. We present some numerical experiments with the method and compare its performance with a few explicit and implicit algorithms

Algorithms in Lattice QCD

The enormous computing resources that large-scale simulations in Lattice QCD require will continue to test the limits of even the largest supercomputers into the foreseeable future. The efficiency of such simulations will therefore concern practitioners of lattice QCD for some time to come. I begin with an introduction to those aspects of lattice QCD essential to the remainder of the thesis, and follow with a description of the Wilson fermion matrix M, an object which is central to my theme. The principal bottleneck in Lattice QCD simulations is the solution of linear systems involving M, and this topic is treated in depth. I compare some of the more popular iterative methods, including Minimal Residual, Corij ugate Gradient on the Normal Equation, BI-Conjugate Gradient, QMR., BiCGSTAB and BiCGSTAB2, and then turn to a study of block algorithms, a special class of iterative solvers for systems with multiple right-hand sides. Included in this study are two block algorithms which had not previously been applied to lattice QCD. The next chapters are concerned with a generalised Hybrid Monte Carlo algorithm (OHM C) for QCD simulations involving dynamical quarks. I focus squarely on the efficient and robust implementation of GHMC, and describe some tricks to improve its performance. A limited set of results from HMC simulations at various parameter values is presented. A treatment of the non-hermitian Lanczos method and its application to the eigenvalue problem for M rounds off the theme of large-scale matrix computations

Evaluating linear recursive filters on clusters of workstations

The aim of this paper is to show that the recently developed high performance algorithm for solving linear recurrence systems with constant coefficients together with the new BLAS-based algorithm for narrow-banded triangular Toeplitz matrix-vector multiplication allow to evaluate linear recursive filters efficiently, even on clusters of workstations. The results of experiments performed on a cluster of twelve Linux workstations are also presented. The performance of the algorithm is comparable with the performance of two processors of Cray SV-1 for such kind of recursive problems