Preconditioning and Boundary Conditions (Classic Reprint)
Language: English
Published by Forgotten Books, 2022
- Softcover
- New
Seller: Forgotten Books, London, United KingdomForgotten Books
AbeBooks seller since June 2, 2021
Condition: New
US$ 17.65
Quantity: Over 20 available
Add to basketItem description from seller
Print on Demand. This book provides a thorough examination of the role of preconditioners in enhancing the efficiency of solving linear equations stemming from the discretization of second-order elliptic boundary value problems. Preconditioners are mathematical tools employed to accelerate the convergence of iterative methods used in solving these equations. The author presents a detailed analysis of the impact of boundary conditions on the effectiveness of preconditioners, demonstrating how boundary conditions influence the condition number of the preconditioned system. The book also delves into the concept of H1 norm equivalence and its relationship to the choice of preconditioners. By exploring both the theoretical foundations and practical implications, this book offers valuable insights into the design and implementation of preconditioners for elliptic problems with diverse boundary conditions. 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.…
Seller Inventory # 9781332180547_0
- Title
- Preconditioning and Boundary Conditions (Classic Reprint)
- Author
- Thomas A. Manteuffel
- Publisher
- Forgotten Books
- Publication year
- 2022
- Condition
- New
- Book Type
- print-on-demand item
- Binding
- Paperback
- Language
- English
- ISBN 10
- 133218054X
- ISBN 13
- 9781332180547
- Seller catalogs
- Calculus
This deep dive explains how to make solving elliptic equations faster and more reliable through preconditioning and careful handling of boundary conditions.
In this work, you’ll learn how numerical methods tackle elliptic operators and why the way you precondition can shape solver performance. The author compares left- versus right-preconditioning, highlights the role of boundary conditions, and explains how different norms affect stability and accuracy. The discussion blends theory with finite-element intuition to clarify when certain approaches help and when they don’t.
Readers will gain a framework for understanding condition numbers, norm equivalence, and the influence of domain geometry on discretized problems. The book also surveys classic results and situates them in the context of modern iterative methods, offering guidance for choosing effective preconditioners in realistic problems.
- How preconditioning changes the condition number and what that means for solver speed
- The impact of boundary conditions on operator equivalence and discretization
- Different norms (L2 and Hi) and when each is most relevant
- Connections between continuous operators and their finite-element approximations
Ideal for readers of advanced numerical analysis and computational science who want a rigorous, practical view of preconditioning and boundary conditions.
"Synopsis" may belong to another edition of this title.
Forgotten Books
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Forgotten Books’ Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings. Careful attention has been made to accurately preserve the original format of each page whilst digitally enhancing the quality of the aged text.
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