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- M. Südholt,
C. Piepenbrock, K. Obermayer, and P. Pepper. Solving Large Systems of
Differential Equations using Convolutions by Transformation.
.
In IFIP Working Conference on Algorithmic Languages and Calculi.
Chapman & Hall, 1997.
(FTP Gzipped PostScript, 28 pages, 99 kb)
The design and implementation of parallel algorithms for
distributed memory architectures is much harder than the development of
sequential algorithms. This is mainly due to the communication and
synchronization that is necessary to manage distributed data correctly. This
paper applies a methodology for the transformational derivation of parallel
programs using data distribution algebras that enable an abstract description
of data distribution issues. Algorithms are formulated using skeletons, that
is, specialized higher-order functions with particular parallel
implementations. The methodology is applied to a the solution of a system of
ordinary differential equations where convolutions can be computed using the
Fast Fourier transformation. The example illustrates the practical
optimization problems for a development model of the visual system that
involves large scale neural network simulations. Finally, this algorithm is
compared to an implementation of the same system of equations in the
programming language C* on a CM-5.
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