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 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 1976 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 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 The Computer Implementation of an Amplicit Capacitance Matrix Method for the Numerical Solution of Helmholtz s Equation Over General Bounded Planar Domains written by Ionel Michael Navon and published by . This book was released on 1980 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 ERDA Energy Research Abstracts written by United States. Energy Research and Development Administration and published by . This book was released on 1976 with total page 772 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Domain Decomposition Methods in Science and Engineering XXI written by Jocelyne Erhel and published by Springer. This book was released on 2014-10-10 with total page 931 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a selection of papers presented at the 21st international conference on domain decomposition methods in science and engineering held in Rennes, France, June 25-29, 2012. Domain decomposition is an active and interdisciplinary research discipline, focusing on the development, analysis and implementation of numerical methods for massively parallel computers. Domain decomposition methods are among the most efficient solvers for large scale applications in science and engineering. They are based on a solid theoretical foundation and shown to be scalable for many important applications. Domain decomposition techniques can also naturally take into account multiscale phenomena. This book contains the most recent results in this important field of research, both mathematically and algorithmically and allows the reader to get an overview of this exciting branch of numerical analysis and scientific computing.

Download or read book Energy Research Abstracts written by and published by . This book was released on 1989 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Optimization Optimal Control and Partial Differential Equations written by V. Barbu and published by Birkhäuser. This book was released on 2013-03-07 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects research papers presented in the First Franco Romanian Conference on Optimization, Optimal Control and Partial Differential Equations held at lasi on 7-11 september 1992. The aim and the underlying idea of this conference was to take advantage of the new SOCial developments in East Europe and in particular in Romania to stimulate the scientific contacts and cooperation between French and Romanian mathematicians and teams working in the field of optimization and partial differential equations. This volume covers a large spectrum of problems and result developments in this field in which most of the participants have brought notable contributions. The following topics are discussed in the contributions presented in this volume. 1 -Variational methods in mechanics and physical models Here we mention the contributions of D. Cioranescu. P. Donato and H.I. Ene (fluid flows in dielectric porous media). R. Stavre (the impact of a jet with two fluids on a porous wall). C. Lefter and D. Motreanu (nonlinear eigenvalue problems with discontinuities). I. Rus (maximum principles for elliptic systems). and on asymptotic XII properties of solutions of evolution equations (R Latcu and M. Megan. R Luca and R Morozanu. R Faure). 2 -The controllabillty of Inflnlte dimensional and distributed parameter systems with the contribution of P. Grisvard (singularities and exact controllability for hyperbolic systems). G. Geymonat. P. Loreti and V. Valente (exact controllability of a shallow shell model). C.

Download or read book Recent Developments in Numerical Methods and Software for ODEs DAEs PDEs written by George D. Byrne and published by World Scientific. This book was released on 1992 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ordinary differential equations (ODEs), differential-algebraic equations (DAEs) and partial differential equations (PDEs) are among the forms of mathematics most widely used in science and engineering. Each of these equation types is a focal point for international collaboration and research. This book contains papers by recognized numerical analysts who have made important contributions to the solution of differential systems in the context of realistic applications, and who now report the latest results of their work in numerical methods and software for ODEs/DAEs/PDEs. The papers address parallelization and vectorization of numerical methods, the numerical solution of ODEs/DAEs/PDEs, and the use of these numerical methods in realistic scientific and engineering applications.

Download or read book Selected Papers from the Second Conference on Parallel Processing for Scientific Computing written by Charles William Gear and published by SIAM. This book was released on 1987-01-01 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings -- Parallel Computing.

Download or read book Computational Magnetics written by J. Sykulski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book fills the gap between theory, available computational techniques and engineering practice in the design of electrical and electromechanical machines. The theory underlying all currently recommended computational and experimental methods is covered comprehensively, including field analysis and synthesis, magnetic fields coupled to stress and thermal fields. The book is very practically oriented and includes many examples of actual solutions to real devices.

Download or read book ERDA Research Abstracts written by United States. Energy Research and Development Administration and published by . This book was released on 1976 with total page 716 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book ERDA Energy Research Abstracts written by United States. Energy Research and Development Administration. Technical Information Center and published by . This book was released on 1976 with total page 724 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Applied Numerical Linear Algebra written by William W. Hager and published by SIAM. This book was released on 2022-01-21 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces numerical issues that arise in linear algebra and its applications. It touches on a wide range of techniques, including direct and iterative methods, orthogonal factorizations, least squares, eigenproblems, and nonlinear equations. Detailed explanations on a wide range of topics from condition numbers to singular value decomposition are provided, as well as material on nonlinear and linear systems. Numerical examples, often based on discretizations of boundary-value problems, are used to illustrate concepts. Exercises with detailed solutions are provided at the end of the book, and supplementary material and updates are available online. This Classics edition is appropriate for junior and senior undergraduate students and beginning graduate students in courses such as advanced numerical analysis, special topics on numerical analysis, topics on data science, topics on numerical optimization, and topics on approximation theory.