EAN: 9783519027171

TEUBNER SKRIPTEN ZUR NUMERIK PARALLEL MULTIGR...

Wetenschap is meer dan het object dat zij bestudeert. Wetenschap is ook de weg naar de
ontdekking  en bovendien  wetenschap is ook het verhaaJ van de ontdekkingsreis. -Po Thielen
Focus research  Nr 10-11  juli 1991. The numerical solution of a parabolic partial differential
equation is usually calcu lated by using a time-stepping method. This precludes the efficient
use of parallelism and vectorization  unless the problem to be solved at each time-level is
very large. This monograph investigates the use of an algorithm that overcomes the limitations
of the standard schemes by calculating the solution at many time-levels  or along a continuous
time-window simultaneously. The algorithm is based on waveform relazation  a highly parallel
technique for solving very large systems of ordinary differential equations  and multigrid  a
very fast method for solving elliptic partial differential equations. The resulting multigrid
waveform relazation method is applicable to both initial boundary value and time-periodic
parabolic problems. We analyse in this book theoretical and practical aspects of the multigrid
waveform relaxation algorithm. Its implementation on a distributed memory message-passing
computer and its computational complexity (arithmetic complexity  communication complexity and
potential for vectorization) are studied. The method has been im plemented and extensively
tested on a hypercube multiprocessor with vector nodes. Results of numerical experiments are
given  which illustrate a severalfold performance gain when compared to parallel
implementations of a variety of standard initial bound ary value and time-periodic solvers.

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