Title
Parallel Multigrid Waveform Relaxation for Parabolic Problems (Teubner Skripten zur Numerik) (German Edition),Used
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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 1011, juli 1991. The numerical solution of a parabolic partial differential equation is usually calcu lated by using a timestepping method. This precludes the efficient use of parallelism and vectorization, unless the problem to be solved at each timelevel 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 timelevels, or along a continuous timewindow 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 timeperiodic parabolic problems. We analyse in this book theoretical and practical aspects of the multigrid waveform relaxation algorithm. Its implementation on a distributed memory messagepassing 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 timeperiodic solvers.
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This warranty strictly does not cover damages that arose from negligence, misuse, wear and tear, or not in accordance with product instructions (dropping the product, etc.).
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