The scheduling of sparse matrix-vector multiplication on a massively parallel dap computer

An efficient data structure is presented which supports general unstructured sparse matrix-vector multiplications on a Distributed Array of Processors (DAP). This approach seeks to reduce the inter-processor data movements and organises the operations in batches of massively parallel steps by a heuristic scheduling procedure performed on the host computer. The resulting data structure is of particular relevance to iterative schemes for solving linear systems. Performance results for matrices taken from well known Linear Programming (LP) test problems are presented and analysed

Solution of large linear systems of equations on the massively parallel processor

The Massively Parallel Processor (MPP) was designed as a special machine for specific applications in image processing. As a parallel machine, with a large number of processors that can be reconfigured in different combinations it is also applicable to other problems that require a large number of processors. The solution of linear systems of equations on the MPP is investigated. The solution times achieved are compared to those obtained with a serial machine and the performance of the MPP is discussed

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

Lanczos eigensolution method for high-performance computers

The theory, computational analysis, and applications are presented of a Lanczos algorithm on high performance computers. The computationally intensive steps of the algorithm are identified as: the matrix factorization, the forward/backward equation solution, and the matrix vector multiples. These computational steps are optimized to exploit the vector and parallel capabilities of high performance computers. The savings in computational time from applying optimization techniques such as: variable band and sparse data storage and access, loop unrolling, use of local memory, and compiler directives are presented. Two large scale structural analysis applications are described: the buckling of a composite blade stiffened panel with a cutout, and the vibration analysis of a high speed civil transport. The sequential computational time for the panel problem executed on a CONVEX computer of 181.6 seconds was decreased to 14.1 seconds with the optimized vector algorithm. The best computational time of 23 seconds for the transport problem with 17,000 degs of freedom was on the the Cray-YMP using an average of 3.63 processors

Computational methods and software systems for dynamics and control of large space structures

Two key areas of crucial importance to the computer-based simulation of large space structures are discussed. The first area involves multibody dynamics (MBD) of flexible space structures, with applications directed to deployment, construction, and maneuvering. The second area deals with advanced software systems, with emphasis on parallel processing. The latest research thrust in the second area involves massively parallel computers

Algorithmic considerations of integrated design for CSI on a hypercube architecture

An approach is presented to the integrated design problem for actively controlled large, flexible mechanical systems for which Control Structure Interaction (CSI) problems are of concern. The two coupled design problems were identified as the optimal Structural Design problem the optimal Controller Design problem. These two problems can be addressed within a decision making loop that would consider each separately, and then sequentially analyze the effects of one on the other. Embedded in such a loop would be the simulation and coordination tasks as part of the decision tools required in a total (software) package. All of the above are compute-intensive tasks. In any such task, possible decompositions and gains due to the inherent parallelism have to be exploited. The problems under consideration, as applied to large flexible mechanical structures, are particularly suited to be mapped onto multicomputer systems in a hypercube topology

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

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

ELSI: A Unified Software Interface for Kohn-Sham Electronic Structure Solvers

Solving the electronic structure from a generalized or standard eigenproblem is often the bottleneck in large scale calculations based on Kohn-Sham density-functional theory. This problem must be addressed by essentially all current electronic structure codes, based on similar matrix expressions, and by high-performance computation. We here present a unified software interface, ELSI, to access different strategies that address the Kohn-Sham eigenvalue problem. Currently supported algorithms include the dense generalized eigensolver library ELPA, the orbital minimization method implemented in libOMM, and the pole expansion and selected inversion (PEXSI) approach with lower computational complexity for semilocal density functionals. The ELSI interface aims to simplify the implementation and optimal use of the different strategies, by offering (a) a unified software framework designed for the electronic structure solvers in Kohn-Sham density-functional theory; (b) reasonable default parameters for a chosen solver; (c) automatic conversion between input and internal working matrix formats, and in the future (d) recommendation of the optimal solver depending on the specific problem. Comparative benchmarks are shown for system sizes up to 11,520 atoms (172,800 basis functions) on distributed memory supercomputing architectures.Comment: 55 pages, 14 figures, 2 table