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Sinopsis
Learn a practical method for speeding up complex finite element calculations with the additive Schwarz approach, tailored for p-version elements.
This book presents how to apply the additive Schwarz method to a two- and three-dimensional model problem using square and brick-shaped elements. It explains the mathematical framework, including the discretization with high-degree polynomials and the construction of local subspaces that improve solver performance without sacrificing accuracy.
- See how subdomain projections are defined and used to split the problem into manageable pieces
- Understand error bounds and convergence results that hold uniformly as the polynomial degree increases
- Follow the step-by-step development from the two-dimensional case to three dimensions
- Explore the practical implications for preconditioning in p-version finite element methods
Ideal for engineers and researchers working on scalable solvers for high-order finite element problems who want a rigorous, implementable path to faster computations.
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Excerpt from An Additive Schwarz Method for the P-Version Finite Element Method
The following is the main result of this paper. The proof is first given for two dimensions and then extended to three in Section 4.
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An Additive Schwarz Method for the P-Version Finite Element Method
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Paperback. Condición: New. Print on Demand. This book explores a new method for solving large systems of linear equations in three dimensions by leveraging the finite element method. Said method, called the Schwarz method, focuses on increasing the accuracy of finding a solution by dividing the coefficient matrix of the system into submatrices, which it then solves iteratively. The book positions the Schwarz method within the broader context of numerical analysis, while presenting novel ways to extend its use to more complex situations. The work details a theoretical analysis of the method's convergence properties and finishes with encouraging numerical studies. This book is a valuable resource for students and professionals seeking an adept understanding of the Schwarz method and its assorted applications. 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. Nº de ref. del artículo: 9781334017568_0
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An Additive Schwarz Method for the PVersion Finite Element Method Classic Reprint
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An Additive Schwarz Method for the PVersion Finite Element Method Classic Reprint
Librería: PBShop.store UK, Fairford, GLOS, Reino Unido
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PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000. Nº de ref. del artículo: LW-9781334017568
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An Additive Schwarz Method for the P-Version Finite Element Method (Classic Reprint)
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Forgotten Books, 2016
ISBN 10: 1334017565
ISBN 13: 9781334017568
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Condición: Sehr gut. Zustand: Sehr gut | Sprache: Englisch | Produktart: Bücher | Keine Beschreibung verfügbar. Nº de ref. del artículo: 27939319/2
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