This volume deals with problems of modern effective algorithms for
the numerical solution of the most frequently occurring elliptic
partial differential equations. From the point of view of
implementation, attention is paid to algorithms for both classical
sequential and parallel computer systems. The first two chapters
are devoted to fast algorithms for solving the Poisson and
biharmonic equation. In the third chapter, parallel algorithms for
model parallel computer systems of the SIMD and MIMD types are
described. The implementation aspects of parallel algorithms for
solving model elliptic boundary value problems are outlined for
systems with matrix, pipeline and multiprocessor parallel computer
architectures. A modern and popular multigrid computational
principle which offers a good opportunity for a parallel
realization is described in the next chapter. More parallel
variants based in this idea are presented, whereby methods and
assignments strategies for hypercube systems are treated in more
detail. The last chapter presents VLSI designs for solving special
tridiagonal linear systems of equations arising from
finite-difference approximations of elliptic problems. For
researchers interested in the development and application of fast
algorithms for solving elliptic partial differential equations
using advanced computer systems.
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