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Book synopsis

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.

Book details

Book category Books in English Mathematics & science Mathematics Calculus & mathematical analysis

• Full title: Parallel Multigrid Waveform Relaxation for Parabolic Problems
• Author: Stefan Vandewalle
• Language: English
• Binding: Paperback
• Number of pages: 247
• EAN: 9783519027171
• ISBN: 3519027178
• ID: 06801953
• Publisher: B.G.Teubner GmbH
• Weight: 404 g
• Dimensions: 236 × 156 × 19 mm
• Date of publishing: 01. December 1993

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