380 research outputs found
Efficient spares matrix multiplication scheme for the CYBER 203
This work has been directed toward the development of an efficient algorithm for performing this computation on the CYBER-203. The desire to provide software which gives the user the choice between the often conflicting goals of minimizing central processing (CPU) time or storage requirements has led to a diagonal-based algorithm in which one of three types of storage is selected for each diagonal. For each storage type, an initialization sub-routine estimates the CPU and storage requirements based upon results from previously performed numerical experimentation. These requirements are adjusted by weights provided by the user which reflect the relative importance the user places on the resources. The three storage types employed were chosen to be efficient on the CYBER-203 for diagonals which are sparse, moderately sparse, or dense; however, for many densities, no diagonal type is most efficient with respect to both resource requirements. The user-supplied weights dictate the choice
Effect of virtual memory on efficient solution of two model problems
Computers with virtual memory architecture allow programs to be written as if they were small enough to be contained in memory. Two types of problems are investigated to show that this luxury can lead to quite an inefficient performance if the programmer does not interact strongly with the characteristics of the operating system when developing the program. The two problems considered are the simultaneous solutions of a large linear system of equations by Gaussian elimination and a model three-dimensional finite-difference problem. The Control Data STAR-100 computer runs are made to demonstrate the inefficiencies of programming the problems in the manner one would naturally do if the problems were indeed, small enough to be contained in memory. Program redesigns are presented which achieve large improvements in performance through changes in the computational procedure and the data base arrangement
An alternating direction implicit method for the Control Data STAR-100 vector computer
An implementation of the alternating direction implicit (ADI) method for the Control Data STAR-100 computer is presented and analyzed. Two parallel algorithms, both of which are most efficient when used to solve many independent tridiagonal systems of equations, are discussed relative to their usefulness in an ADI implementation on the STAR-100 computer. It is shown that it may be desirable to alternate between the parallel algorithms as the direction of implicitness is alternated in order to eliminate the data rearrangement which would otherwise be required. The applicability of the two parallel tridiagonal solvers to several other numerical algorithms is also discussed
An efficient sparse matrix multiplication scheme for the CYBER 205 computer
This paper describes the development of an efficient algorithm for computing the product of a matrix and vector on a CYBER 205 vector computer. The desire to provide software which allows the user to choose between the often conflicting goals of minimizing central processing unit (CPU) time or storage requirements has led to a diagonal-based algorithm in which one of four types of storage is selected for each diagonal. The candidate storage types employed were chosen to be efficient on the CYBER 205 for diagonals which have nonzero structure which is dense, moderately sparse, very sparse and short, or very sparse and long; however, for many densities, no diagonal type is most efficient with respect to both resource requirements, and a trade-off must be made. For each diagonal, an initialization subroutine estimates the CPU time and storage required for each storage type based on results from previously performed numerical experimentation. These requirements are adjusted by weights provided by the user which reflect the relative importance the user places on the two resources. The adjusted resource requirements are then compared to select the most efficient storage and computational scheme
Vectorization on the star computer of several numerical methods for a fluid flow problem
A reexamination of some numerical methods is considered in light of the new class of computers which use vector streaming to achieve high computation rates. A study has been made of the effect on the relative efficiency of several numerical methods applied to a particular fluid flow problem when they are implemented on a vector computer. The method of Brailovskaya, the alternating direction implicit method, a fully implicit method, and a new method called partial implicitization have been applied to the problem of determining the steady state solution of the two-dimensional flow of a viscous imcompressible fluid in a square cavity driven by a sliding wall. Results are obtained for three mesh sizes and a comparison is made of the methods for serial computation
Star adaptation for two-algorithms used on serial computers
Two representative algorithms used on a serial computer and presently executed on the Control Data Corporation 6000 computer were adapted to execute efficiently on the Control Data STAR-100 computer. Gaussian elimination for the solution of simultaneous linear equations and the Gauss-Legendre quadrature formula for the approximation of an integral are the two algorithms discussed. A description is given of how the programs were adapted for STAR and why these adaptations were necessary to obtain an efficient STAR program. Some points to consider when adapting an algorithm for STAR are discussed. Program listings of the 6000 version coded in 6000 FORTRAN, the adapted STAR version coded in 6000 FORTRAN, and the STAR version coded in STAR FORTRAN are presented in the appendices
Majority Model on a network with communities
We focus on the majority model in a topology consisting of two coupled
fully-connected networks, thereby mimicking the existence of communities in
social networks. We show that a transition takes place at a value of the
inter-connectivity parameter. Above this value, only symmetric solutions
prevail, where both communities agree with each other and reach consensus.
Below this value, in contrast, the communities can reach opposite opinions and
an asymmetric state is attained. The importance of the interface between the
sub-networks is shown.Comment: 4 page
From particle segregation to the granular clock
Recently several authors studied the segregation of particles for a system
composed of mono-dispersed inelastic spheres contained in a box divided by a
wall in the middle. The system exhibited a symmetry breaking leading to an
overpopulation of particles in one side of the box. Here we study the
segregation of a mixture of particles composed of inelastic hard spheres and
fluidized by a vibrating wall. Our numerical simulations show a rich
phenomenology: horizontal segregation and periodic behavior. We also propose an
empirical system of ODEs representing the proportion of each type of particles
and the segregation flux of particles. These equations reproduce the major
features observed by the simulations.Comment: 10 page
Laplacian Dynamics and Multiscale Modular Structure in Networks
Most methods proposed to uncover communities in complex networks rely on
their structural properties. Here we introduce the stability of a network
partition, a measure of its quality defined in terms of the statistical
properties of a dynamical process taking place on the graph. The time-scale of
the process acts as an intrinsic parameter that uncovers community structures
at different resolutions. The stability extends and unifies standard notions
for community detection: modularity and spectral partitioning can be seen as
limiting cases of our dynamic measure. Similarly, recently proposed
multi-resolution methods correspond to linearisations of the stability at short
times. The connection between community detection and Laplacian dynamics
enables us to establish dynamically motivated stability measures linked to
distinct null models. We apply our method to find multi-scale partitions for
different networks and show that the stability can be computed efficiently for
large networks with extended versions of current algorithms.Comment: New discussions on the selection of the most significant scales and
the generalisation of stability to directed network
A vectorization of the Jameson-Caughey NYU transonic swept-wing computer program FLO-22-V1 for the STAR-100 computer
The computer program FLO-22 for analyzing inviscid transonic flow past 3-D swept-wing configurations was modified to use vector operations and run on the STAR-100 computer. The vectorized version described herein was called FLO-22-V1. Vector operations were incorporated into Successive Line Over-Relaxation in the transformed horizontal direction. Vector relational operations and control vectors were used to implement upwind differencing at supersonic points. A high speed of computation and extended grid domain were characteristics of FLO-22-V1. The new program was not the optimal vectorization of Successive Line Over-Relaxation applied to transonic flow; however, it proved that vector operations can readily be implemented to increase the computation rate of the algorithm
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