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Excerpt from Iterative Substructuring Methods: The General Elliptic Case
In section 3, we establish, by using elementary arguments, that the performance of iterative substructuring methods must decline in the absence of a mechanism for global transportation of information. In that section, we also consider the simplest case of problems with intersecting cuts, namely second order problems in planar regions approximated by piecewise linear elements. By introducing an idea from multigrid methods, we derive an algorithm which turns out to be identical to one recently introduced by Bramble, Pasciak and Schatz An alternative algorithm, see Dryja [17] and Dryja, Proskurowski and Widlund is also described and estimates are given of the rate of convergence of these two algorithms.
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Paperback. Condizione: New. Print on Demand. Delve into the world of iterative substructuring methods for elliptic finite element problems in this illuminating book by the author. A groundbreaking domain decomposition technique, these methods have gained immense popularity in solving large-scale elliptic problems in the engineering and scientific domains. The book commences with a comprehensive introduction that traces the intriguing history of the subject and places it within the broader context of numerical analysis. The author meticulously describes the fundamental concepts and algorithms, empowering readers with a thorough understanding of the subject. The central theme revolves around the notion of optimality and the delicate balance between computational efficiency and accuracy. The book explores a variety of topics, including preconditioners and convergence analysis, providing valuable insights into the intricacies of these methods. Ultimately, the book underscores the significance of iterative substructuring methods in tackling complex problems, making it an essential resource for researchers, engineers, and postgraduate students in the fields of computational mechanics and applied mathematics. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Codice articolo 9781332090396_0
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