1,532 research outputs found
A Simple Optimum-Time FSSP Algorithm for Multi-Dimensional Cellular Automata
The firing squad synchronization problem (FSSP) on cellular automata has been
studied extensively for more than forty years, and a rich variety of
synchronization algorithms have been proposed for not only one-dimensional
arrays but two-dimensional arrays. In the present paper, we propose a simple
recursive-halving based optimum-time synchronization algorithm that can
synchronize any rectangle arrays of size m*n with a general at one corner in
m+n+max(m, n)-3 steps. The algorithm is a natural expansion of the well-known
FSSP algorithm proposed by Balzer [1967], Gerken [1987], and Waksman [1966] and
it can be easily expanded to three-dimensional arrays, even to
multi-dimensional arrays with a general at any position of the array.Comment: In Proceedings AUTOMATA&JAC 2012, arXiv:1208.249
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
Rectilinear partitioning of irregular data parallel computations
New mapping algorithms for domain oriented data-parallel computations, where the workload is distributed irregularly throughout the domain, but exhibits localized communication patterns are described. Researchers consider the problem of partitioning the domain for parallel processing in such a way that the workload on the most heavily loaded processor is minimized, subject to the constraint that the partition be perfectly rectilinear. Rectilinear partitions are useful on architectures that have a fast local mesh network. Discussed here is an improved algorithm for finding the optimal partitioning in one dimension, new algorithms for partitioning in two dimensions, and optimal partitioning in three dimensions. The application of these algorithms to real problems are discussed
Transport efficiency of metachronal waves in 3d cilia arrays immersed in a two-phase flow
The present work reports the formation and the characterization of
antipleptic and symplectic metachronal waves in 3D cilia arrays immersed in a
two-fluid environment, with a viscosity ratio of 20. A coupled
lattice-Boltzmann-Immersed-Boundary solver is used. The periciliary layer is
confined between the epithelial surface and the mucus. Its thickness is chosen
such that the tips of the cilia can penetrate the mucus. A purely
hydrodynamical feedback of the fluid is taken into account and a coupling
parameter is introduced allowing the tuning of both the direction of
the wave propagation, and the strength of the fluid feedback. A comparative
study of both antipleptic and symplectic waves, mapping a cilia inter-spacing
ranging from 1.67 up to 5 cilia length, is performed by imposing the
metachrony. Antipleptic waves are found to systematically outperform sympletic
waves. They are shown to be more efficient for transporting and mixing the
fluids, while spending less energy than symplectic, random, or synchronized
motions
On relations between arrays of processing elements of different dimensionality
We are examining the power of -dimensional arrays of
processing elements in view of a special kind of structural
complexity. In particular simulation techniques are shown, which
allow to reduce the dimension at an increased cost of time
only. Conversely, it is not possible to regain the speed by
increasing the dimension. Moreover, we demonstrate that increasing
the computation time (just by a constant factor) can have a more
favorable effect than increasing the dimension (arbitrari
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