EAN: 9783519027171

Bilder-Quelle: discount24.de - Sport-Freizeit

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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