Excerpt from Towards an Unified Theory of Domain Decomposition Algorithms for Elliptic Problems
The paper is organized as follows. After introducing two elliptic model problems and certain finite element methods in Section 2, we begin Section 3 by reviewing Schwarz's alternating algorithm in its classical setting. Following Sobolev [50] and P. L. Lions we indicate how this algorithm can be expressed in a variational form. Since this formulation is very convenient for the analysis of finite element problems, we work in this Hilbert space setting throughout the paper.
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Paperback. Zustand: New. Print on Demand. This book provides an innovative and accessible exploration of the fascinating world of domain decomposition algorithms for elliptic partial differential equations, offering a unified theoretical framework for analyzing and developing these algorithms. The author, an expert in the field, presents a comprehensive overview of the latest research on the subject, providing valuable insights into the effectiveness and limitations of different approaches. Throughout the book, the author demonstrates how domain decomposition algorithms can be tailored to specific problems, making them a versatile tool for solving complex scientific and engineering challenges. The book delves into the mathematical foundations of these algorithms, offering a deep understanding of their convergence properties and computational complexity. By providing a unified framework for understanding domain decomposition algorithms, this book empowers readers to make informed decisions when selecting and applying these techniques to their own research or practical applications. Ultimately, the book's insights advance the comprehension and utilization of domain decomposition algorithms, contributing to advancements in computational science and engineering. 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. Bestandsnummer des Verkäufers 9781334016790_0
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