{"product_id":"parallel-multigrid-waveform-relaxation-for-parabolic-problems-9783519027171","title":"Parallel Multigrid Waveform Relaxation for Parabolic Problems","description":"\u003cp\u003e • Author(s): Stefan Vandewalle\u003cbr\u003e • Publisher: Vieweg+teubner Verlag\u003cbr\u003e • Publisher Imprint: Vieweg+teubner Verlag\u003cbr\u003e • BISAC: Engineering (General)\u003c\/p\u003e\u003cp\u003eWetenschap 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.\u003c\/p\u003e","brand":"Vieweg+teubner Verlag","offers":[{"title":"Paperback","offer_id":46893546340503,"sku":"9783519027171","price":3089.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9783519027171.webp?v=1770317098","url":"https:\/\/atlanticbooks.com\/products\/parallel-multigrid-waveform-relaxation-for-parabolic-problems-9783519027171","provider":"Atlantic Books","version":"1.0","type":"link"}