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

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

A methodology for exploiting parallelism in the finite element process

A methodology is described for developing a parallel system using a top down approach taking into account the requirements of the user. Substructuring, a popular technique in structural analysis, is used to illustrate this approach

A high-accuracy optical linear algebra processor for finite element applications

Optical linear processors are computationally efficient computers for solving matrix-matrix and matrix-vector oriented problems. Optical system errors limit their dynamic range to 30-40 dB, which limits their accuray to 9-12 bits. Large problems, such as the finite element problem in structural mechanics (with tens or hundreds of thousands of variables) which can exploit the speed of optical processors, require the 32 bit accuracy obtainable from digital machines. To obtain this required 32 bit accuracy with an optical processor, the data can be digitally encoded, thereby reducing the dynamic range requirements of the optical system (i.e., decreasing the effect of optical errors on the data) while providing increased accuracy. This report describes a new digitally encoded optical linear algebra processor architecture for solving finite element and banded matrix-vector problems. A linear static plate bending case study is described which quantities the processor requirements. Multiplication by digital convolution is explained, and the digitally encoded optical processor architecture is advanced

A New Method for Efficient Parallel Solution of Large Linear Systems on a SIMD Processor.

This dissertation proposes a new technique for efficient parallel solution of very large linear systems of equations on a SIMD processor. The model problem used to investigate both the efficiency and applicability of the technique was of a regular structure with semi-bandwidth $\beta,$ and resulted from approximation of a second order, two-dimensional elliptic equation on a regular domain under the Dirichlet and periodic boundary conditions. With only slight modifications, chiefly to properly account for the mathematical effects of varying bandwidths, the technique can be extended to encompass solution of any regular, banded systems. The computational model used was the MasPar MP-X (model 1208B), a massively parallel processor hostnamed hurricane and housed in the Concurrent Computing Laboratory of the Physics/Astronomy department, Louisiana State University. The maximum bandwidth which caused the problem\u27s size to fit the nyproc $\times$ nxproc machine array exactly, was determined. This as well as smaller sizes were used in four experiments to evaluate the efficiency of the new technique. Four benchmark algorithms, two direct--Gauss elimination (GE), Orthogonal factorization--and two iterative--symmetric over-relaxation (SOR) ($\omega$ = 2), the conjugate gradient method (CG)--were used to test the efficiency of the new approach based upon three evaluation metrics--deviations of results of computations, measured as average absolute errors, from the exact solution, the cpu times, and the mega flop rates of executions. All the benchmarks, except the GE, were implemented in parallel. In all evaluation categories, the new approach outperformed the benchmarks and very much so when N $\gg$ p, p being the number of processors and N the problem size. At the maximum system\u27s size, the new method was about 2.19 more accurate, and about 1.7 times faster than the benchmarks. But when the system size was a lot smaller than the machine\u27s size, the new approach\u27s performance deteriorated precipitously, and, in fact, in this circumstance, its performance was worse than that of GE, the serial code. Hence, this technique is recommended for solution of linear systems with regular structures on array processors when the problem\u27s size is large in relation to the processor\u27s size

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

Design and Implementation of a Low Complexity Multiuser Detector for Hybrid CDMA Systems

In hybrid CDMA systems, multiuser detection (MUD) algorithms are adopted at the base station to reduce both multiple access and inter symbol interference by exploiting space-time (ST) signal processing techniques. Linear ST-MUD algorithms solve a linear problem where the system matrix has a block-Toeplitz shape. While exact inversion techniques impose an intolerable computational load, reduced complexity algorithms may be efficiently employed even if they show suboptimal behavior introducing performance degradation and nearfar effects. The block-Fourier MUD algorithm is generally considered the most effective one. However, the block-Bareiss MUD algorithm, that has been recently reintroduced, shows also good performance and low computational complexity comparing favorably with the block Fourier one. In this paper, both MUD algorithms will be compared, along with other well known ones, in terms of complexity, performance figures, hardware feasibility and implementation issues. Finally a short hardware description of the block-Bareiss and block Fourier algorithms will be presented along with the FPGA (Field Programmable Gate Array) implementation of the block-Fourier using standard VHDL (VHSIC Hardware Description Language) design

Custom Integrated Circuits

Contains reports on twelve research projects.Analog Devices, Inc.International Business Machines, Inc.Joint Services Electronics Program (Contract DAAL03-86-K-0002)Joint Services Electronics Program (Contract DAAL03-89-C-0001)U.S. Air Force - Office of Scientific Research (Grant AFOSR 86-0164)Rockwell International CorporationOKI Semiconductor, Inc.U.S. Navy - Office of Naval Research (Contract N00014-81-K-0742)Charles Stark Draper LaboratoryNational Science Foundation (Grant MIP 84-07285)National Science Foundation (Grant MIP 87-14969)Battelle LaboratoriesNational Science Foundation (Grant MIP 88-14612)DuPont CorporationDefense Advanced Research Projects Agency/U.S. Navy - Office of Naval Research (Contract N00014-87-K-0825)American Telephone and TelegraphDigital Equipment CorporationNational Science Foundation (Grant MIP-88-58764