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Capacitance Matrix Methods for the Helmholtz Equation on General Three-Dimensional Regions (Classic Reprint) - Brossura
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Excerpt from Capacitance Matrix Methods for the Helmholtz Equation on General Three-Dimensional Regions
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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Capacitance Matrix Methods for the Helmholtz Equation on General
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Paperback. Condizione: New. 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. print-on-demand item. Codice articolo 9781333415372_0
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Capacitance Matrix Methods for the Helmholtz Equation on General Three-Dimensional Regions (Classic Reprint)
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PAP. Condizione: New. New Book. Shipped from UK. Established seller since 2000. Codice articolo LW-9781333415372
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