| Parallel Multigrid Waveform Relaxation for Parabolic Problems 1993 Edition Contributor(s): Vandewalle, Stefan (With) |
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ISBN: 3519027178 ISBN-13: 9783519027171 Publisher: Vieweg+teubner Verlag OUR PRICE: $42.74 Product Type: Paperback Language: German Published: January 1993 |
| Additional Information |
| BISAC Categories: - Technology & Engineering | Engineering (general) |
| Dewey: 620 |
| LCCN: 95151377 |
| Series: Quellen Und Studien Zur Geschichte Des Ostlichen Europa |
| Physical Information: 0.55" H x 6.14" W x 9.21" (0.81 lbs) 247 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |
