Capacitance Matrix Methods for the Helmholtz Equation on General
Language: English
Published by Forgotten Books, 2017
- Softcover
- New
Seller: Forgotten Books, London, United KingdomForgotten Books
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Condition: New
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Print on Demand. This book by the author details advanced numerical techniques for solving Helmholtz's equation, a partial differential equation that arises in numerous scientific and engineering applications such as electromagnetics, acoustics, and fluid dynamics. The presented methods are applicable to problems defined on general three-dimensional regions and extend previously developed techniques for two-dimensional regions. The approach involves the use of capacitance matrices and fast Poisson solvers. Detailed discussions on the theoretical framework, algorithmic aspects, and implementation details provide a comprehensive guide for researchers and practitioners seeking efficient and reliable solutions to Helmholtz's equation in three dimensions. The significance of this work lies in its potential to enhance the accuracy and efficiency of numerical simulations in various scientific and engineering disciplines, leading to improved understanding and design of complex systems. 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 # 9781333415372_0
- Title
- Capacitance Matrix Methods for the Helmholtz Equation on General
- Author
- Dianne P. O'leary, Olof Widlund
- Publisher
- Forgotten Books
- Publication year
- 2017
- Condition
- New
- Book Type
- print-on-demand item
- Binding
- Paperback
- Language
- English
- ISBN 10
- 1333415370
- ISBN 13
- 9781333415372
- Seller catalogs
- Calculus
In the second section, we discuss the imbedding idea. Following a review of classical potential theory, we derive our capacitance matrix methods in Section 3. Section 4 focuses on algorithmic aspects which are of crucial importance in the develop ment of fast, reliable and modular computer code. We solve the capacitance matrix equations by conjugate gradient methods. These methods, originally used in a similar context by George are reviewed in that section. We also discuss how spectral information and approximate inverses of the capacitance matrices can be obtained and used at a moderate cost in computer time and storage. The fast Poisson solver which is used in our program is described in Section 5. It is numerically stable even for negative values of the coefficient c of the Helmholtz operator. Finally, we give details on the organization of our computer program and results from numerical experiments. These tests were designed to be quite severe and the method has proved efficient and reliable.
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This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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Forgotten Books publishes hundreds of thousands of rare and classic books.
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
This text has been digitally restored from a historical edition. Some errors may persist, however we consider it worth publishing due to the work's historical value.
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