Download or read book On the Numerical Solution of Helmholtz s Equation by the Capacitance Matrix Method written by Olof Widlund and published by . This book was released on 1975 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book On the Numerical Solution of Helmholtz s Equation by the Capacitance Matrix Method Classic Reprint written by Olof Widlund and published by Forgotten Books. This book was released on 2017-12-21 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from On the Numerical Solution of Helmholtz's Equation by the Capacitance Matrix Method These fast methods can also be used for elliptic problems on regions, or With boundary conditions, which do not allow for separation of variables, provided that the differential operator allows for separation of variables on a different region or With different boundary conditions, see Buzbee, Dorr, George and Golub Buzbee and Dorr [es] and Hockney This last condition amounts to a requirement that the differential operator can be split into the sum of commuting operators, each of which contains derivatives With respect to only one variable. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com 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.

Download or read book Numerical Solution of Helmholtz s Equation by the Capacitance Matrix Method In FORTRAN for IBM 360 75 Computer written by and published by . This book was released on 1975 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The computer solution of the Helmholtz equation is discussed. Problems can be treated on bounded regions which do not allow for separation of variables. The topics treated in the report are as follows: certain results from classical potential theory, the imbedding of discrete Poisson problems, a capacitance matrix method for the Dirichlet case, a capacitance matrix method for the Neumann case, the Fourier--Toeplitz method and the fast generation of the capacitance matrix, the conjugate gradient method, previous work on capacitance matrix methods, numeral experiments, and outline of a computer program for the numerical solution of the interior Helmholtz equation in two variables with the Dirichlet and Neumann boundary conditions by finite difference methods. 3 figures, 8 tables. (RWR).

Download or read book On the Numerical Solution of Helmholtzs Equation by the Capacitance Matrix Method Part I written by and published by . This book was released on 1976 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book On the Numerical Solution of Helmholtz s Equation by the Capacitance Matrix Method 1 written by Wlodzimierz Proskurowski and published by . This book was released on 1976 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book On the Numerical Solution of Helmholtz s Equation and the Eigenvalue Problem of the Laplace Operator by the Capacitance Matrix Method written by Wlodzimierz Proskurowski and published by . This book was released on 1976 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Capacitance Matrix Methods for the Helmholtz Equation on General Three Dimensional Regions Classic Reprint written by Dianne P. O'Leary and published by Forgotten Books. This book was released on 2016-08-30 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com 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.

Download or read book Applied Iterative Methods written by Louis A. Hageman and published by Elsevier. This book was released on 2014-06-28 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: Applied Iterative Methods

Download or read book On the Numerical Solution of Helmholtz s Equation by the Capacitance Matrix Method written by Wlodzimierz Proskurowski and published by . This book was released on 1975 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations written by Tarek Mathew and published by Springer Science & Business Media. This book was released on 2008-06-25 with total page 775 pages. Available in PDF, EPUB and Kindle. Book excerpt: Domain decomposition methods are divide and conquer computational methods for the parallel solution of partial differential equations of elliptic or parabolic type. The methodology includes iterative algorithms, and techniques for non-matching grid discretizations and heterogeneous approximations. This book serves as a matrix oriented introduction to domain decomposition methodology. A wide range of topics are discussed include hybrid formulations, Schwarz, and many more.

Download or read book Mathematical Analysis and Numerical Methods for Science and Technology written by Robert Dautray and published by Springer Science & Business Media. This book was released on 1999-11-23 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: These 6 volumes - the result of a 10 year collaboration between the authors, two of France's leading scientists and both distinguished international figures - compile the mathematical knowledge required by researchers in mechanics, physics, engineering, chemistry and other branches of application of mathematics for the theoretical and numerical resolution of physical models on computers. Since the publication in 1924 of the "Methoden der mathematischen Physik" by Courant and Hilbert, there has been no other comprehensive and up-to-date publication presenting the mathematical tools needed in applications of mathematics in directly implementable form. The advent of large computers has in the meantime revolutionised methods of computation and made this gap in the literature intolerable: the objective of the present work is to fill just this gap. Many phenomena in physical mathematics may be modeled by a system of partial differential equations in distributed systems: a model here means a set of equations, which together with given boundary data and, if the phenomenon is evolving in time, initial data, defines the system. The advent of high-speed computers has made it possible for the first time to calculate values from models accurately and rapidly. Researchers and engineers thus have a crucial means of using numerical results to modify and adapt arguments and experiments along the way. Every facet of technical and industrial activity has been affected by these developments. Modeling by distributed systems now also supports work in many areas of physics (plasmas, new materials, astrophysics, geophysics), chemistry and mechanics and is finding increasing use in the life sciences.

Download or read book Matrix Preconditioning Techniques and Applications written by Ke Chen and published by Cambridge University Press. This book was released on 2005-07-14 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introduction to preconditioning techniques, now an essential part of successful and efficient iterative solutions of matrices.

Download or read book Handbook of Numerical Analysis written by Philippe G. Ciarlet and published by Gulf Professional Publishing. This book was released on 1990 with total page 1187 pages. Available in PDF, EPUB and Kindle. Book excerpt: Includes following subjects: Solution of equations in Rn, Finite difference methods, Finite element methods, Techniques of scientific computing, Optimization theory and systems science, Numerical methods for fluids, Numerical methods for solids, Specific applications

Download or read book A Theoretical Introduction to Numerical Analysis written by Victor S. Ryaben'kii and published by CRC Press. This book was released on 2006-11-02 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Theoretical Introduction to Numerical Analysis presents the general methodology and principles of numerical analysis, illustrating these concepts using numerical methods from real analysis, linear algebra, and differential equations. The book focuses on how to efficiently represent mathematical models for computer-based study. An accessible yet rigorous mathematical introduction, this book provides a pedagogical account of the fundamentals of numerical analysis. The authors thoroughly explain basic concepts, such as discretization, error, efficiency, complexity, numerical stability, consistency, and convergence. The text also addresses more complex topics like intrinsic error limits and the effect of smoothness on the accuracy of approximation in the context of Chebyshev interpolation, Gaussian quadratures, and spectral methods for differential equations. Another advanced subject discussed, the method of difference potentials, employs discrete analogues of Calderon’s potentials and boundary projection operators. The authors often delineate various techniques through exercises that require further theoretical study or computer implementation. By lucidly presenting the central mathematical concepts of numerical methods, A Theoretical Introduction to Numerical Analysis provides a foundational link to more specialized computational work in fluid dynamics, acoustics, and electromagnetism.

Download or read book Mathematical and Numerical Aspects of Wave Propagation WAVES 2003 written by Gary Cohen and published by Springer Science & Business Media. This book was released on 2003-06-17 with total page 896 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings include articles of the Sixth International Conference on Mathematical and Numerical Aspects of Wave Propagation (WAVES 2003), held in Jyviiskylii, Finland, from June 30 to July 4, 2003. As in the previous five conferences in this series, its program covered a broad range of topics related to the mathematical modeling and numerical simulation of wave phenomena. Topics of specific interest included various areas of acoustics, electromagnetics, elasticity, and related optimization and inverse problems. In addition to the nine invited presentations, we selected for this confer ence 152 high-level papers from over 20 countries, especially from Europe. Most of them are contained in this book. They provide an extensive overview on the recent developments in the theoretical and applied wave propagation. The conference was organized by the University of Jyviiskylii and the Institut National de Recherche en Informatique et en Automatique (INRIA) in cooperation with Jyviiskylii Congresses. The editors would like to thank the organizing institutions and the in ternational scientific committee for their efforts in the preparation of this conference. We are also grateful to all the authors of the papers for their contributions to these proceedings. Special acknowledgment is due to Ms. Dominique Potherat, to Ms. Helene Chanut and to Ms. Marja-Leena Ranta lainen for their valuable assistance in the preparation of this proceedings volume. Jyviiskylii, Gary C. Cohen February 2003 Erkki H eikkola Patrick loly Pekka Neittaanmiiki Contents Part I Invited Presentations Dispersive Properties of High Order Finite Elements Mark Ainsworth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . . . . . . . . . . . . . ."

Download or read book Introduction to Numerical Analysis written by J. Stoer and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on a one-year introductory course on numerical analysis given by the authors at several universities in Germany and the United States. The authors concentrate on methods which can be worked out on a digital computer. For important topics, algorithmic descriptions (given more or less formally in ALGOL 60), as well as thorough but concise treatments of their theoretical founda tions, are provided. Where several methods for solving a problem are presented, comparisons of their applicability and limitations are offered. Each comparison is based on operation counts, theoretical properties such as convergence rates, and, more importantly, the intrinsic numerical properties that account for the reliability or unreliability of an algorithm. Within this context, the introductory chapter on error analysis plays a special role because it precisely describes basic concepts, such as the numerical stability of algorithms, that are indispensable in the thorough treatment of numerical questions. The remaining seven chapters are devoted to describing numerical methods in various contexts. In addition to covering standard topics, these chapters encom pass some special subjects not usually found in introductions to numerical analysis. Chapter 2, which discusses interpolation, gives an account of modem fast Fourier transform methods. In Chapter 3, extrapolation techniques for spe~d ing up the convergence of discretization methods in connection with Romberg integration are explained at length.

Download or read book Numerical Treatment of Differential Equations written by R. Bulirsch and published by Springer. This book was released on 2006-11-15 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: