Download or read book A Numerical Conformal Mapping Method for Simply Connected Domains written by Emmanuel Ricky Kamgnia and published by . This book was released on 1985 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Conformal Mapping written by Nicolas Papamichael and published by World Scientific. This book was released on 2010 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a unique monograph on numerical conformal mapping that gives a comprehensive account of the theoretical, computational and application aspects of the problems of determining conformal modules of quadrilaterals and of mapping conformally onto a rectangle. It contains a detailed study of the theory and application of a domain decomposition method for computing the modules and associated conformal mappings of elongated quadrilaterals, of the type that occur in engineering applications. The reader will find a highly useful and up-to-date survey of available numerical methods and associated computer software for conformal mapping. The book also highlights the crucial role that function theory plays in the development of numerical conformal mapping methods, and illustrates the theoretical insight that can be gained from the results of numerical experiments.This is a valuable resource for mathematicians, who are interested in numerical conformal mapping and wish to study some of the recent developments in the subject, and for engineers and scientists who use, or would like to use, conformal transformations and wish to find out more about the capabilities of modern numerical conformal mapping.
Download or read book Two Numerical Methods for the Conformal Mapping of Simply connected Domains written by N. Papamichael and published by . This book was released on 1980 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Boundary Behaviour of Conformal Maps written by Christian Pommerenke and published by Springer Science & Business Media. This book was released on 2013-04-09 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the boundary behaviour of a conformal map of the unit disk onto an arbitrary simply connected plane domain. A principal aim of the theory is to obtain a one-to-one correspondence between analytic properties of the function and geometrie properties of the domain. In the classical applications of conformal mapping, the domain is bounded by a piecewise smooth curve. In many recent applications however, the domain has a very bad boundary. It may have nowhere a tangent as is the case for Julia sets. Then the conformal map has many unexpected properties, for instance almost all the boundary is mapped onto almost nothing and vice versa. The book is meant for two groups of users. (1) Graduate students and others who, at various levels, want to learn about conformal mapping. Most sections contain exercises to test the understand ing. They tend to be fairly simple and only a few contain new material. Pre requisites are general real and complex analyis including the basic facts about conformal mapping (e.g. AhI66a). (2) Non-experts who want to get an idea of a particular aspect of confor mal mapping in order to find something useful for their work. Most chapters therefore begin with an overview that states some key results avoiding tech nicalities. The book is not meant as an exhaustive survey of conformal mapping. Several important aspects had to be omitted, e.g. numerical methods (see e.g.
Download or read book A Comparison of Some Numerical Conformal Mapping Methods for Simply and Multiply Connected Domains written by Mohamed Badreddine and published by . This book was released on 2016 with total page 63 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation compares several methods for computing conformal maps from sim-ply and multiply connected domains bounded by circles to target domains bounded by smooth curves and curves with corners. We discuss the use of explicit preliminary maps, including the osculation method of Grassmann to conformally map the target domain to a more nearly circular domain. The Fourier series method due to Fornberg and its generalizations to multiply connected domains are then applied to compute the maps to the nearly circular domains. The ?nal map is represented as a composition of the Fourier/Laurent series with the inverted explicit preliminary maps. A novel method for systematically re-moving corners with power maps is also implemented and composed with the Fornberg maps (which require smooth boundaries) and the level of error that can be expected when using Fourier series to treat domains with corners is illustrated. Some comparison to Wegmann's alternating projection method, which does not require smooth boundaries, is included. We also combine the Fornberg-like method with Karman-Tre?tz method for removing trailing edge corners in multi-element airfoils. The use of explicit maps has been suggested often in the past, but has rarely been carefully studied especially for the multiply connected case. A key contribution of this dissertation is the development of Matlab code for testing existing and new combinations of these various methods, in order to provide a tool for future applications, such as solving potential theory problems in general, multiply connected domains in the plane.
Download or read book Conformal Mapping written by Roland Schinzinger and published by Courier Corporation. This book was released on 2012-04-30 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: Beginning with a brief survey of some basic mathematical concepts, this graduate-level text proceeds to discussions of a selection of mapping functions, numerical methods and mathematical models, nonplanar fields and nonuniform media, static fields in electricity and magnetism, and transmission lines and waveguides. Other topics include vibrating membranes and acoustics, transverse vibrations and buckling of plates, stresses and strains in an elastic medium, steady state heat conduction in doubly connected regions, transient heat transfer in isotropic and anisotropic media, and fluid flow. Revision of 1991 ed. 247 figures. 38 tables. Appendices.
Download or read book Handbook of Conformal Mappings and Applications written by Prem K. Kythe and published by CRC Press. This book was released on 2019-03-04 with total page 943 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of conformal mappings is a major part of geometric function theory that gained prominence after the publication of the Riemann mapping theorem — for every simply connected domain of the extended complex plane there is a univalent and meromorphic function that maps such a domain conformally onto the unit disk. The Handbook of Conformal Mappings and Applications is a compendium of at least all known conformal maps to date, with diagrams and description, and all possible applications in different scientific disciplines, such as: fluid flows, heat transfer, acoustics, electromagnetic fields as static fields in electricity and magnetism, various mathematical models and methods, including solutions of certain integral equations.
Download or read book Numerical Conformal Mapping written by Nicolas Papamichael and published by World Scientific. This book was released on 2010 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a unique monograph on numerical conformal mapping that gives a comprehensive account of the theoretical, computational and application aspects of the problems of determining conformal modules of quadrilaterals and of mapping conformally onto a rectangle. It contains a detailed study of the theory and application of a domain decomposition method for computing the modules and associated conformal mappings of elongated quadrilaterals, of the type that occur in engineering applications. The reader will find a highly useful and up-to-date survey of available numerical methods and associated computer software for conformal mapping. The book also highlights the crucial role that function theory plays in the development of numerical conformal mapping methods, and illustrates the theoretical insight that can be gained from the results of numerical experiments. This is a valuable resource for mathematicians, who are interested in numerical conformal mapping and wish to study some of the recent developments in the subject, and for engineers and scientists who use, or would like to use, conformal transformations and wish to find out more about the capabilities of modern numerical conformal mapping.
Download or read book Solving Problems in Multiply Connected Domains written by Darren Crowdy and published by SIAM. This book was released on 2020-04-20 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Whenever two or more objects or entities—be they bubbles, vortices, black holes, magnets, colloidal particles, microorganisms, swimming bacteria, Brownian random walkers, airfoils, turbine blades, electrified drops, magnetized particles, dislocations, cracks, or heterogeneities in an elastic solid—interact in some ambient medium, they make holes in that medium. Such holey regions with interacting entities are called multiply connected. This book describes a novel mathematical framework for solving problems in two-dimensional, multiply connected regions. The framework is built on a central theoretical concept: the prime function, whose significance for the applied sciences, especially for solving problems in multiply connected domains, has been missed until recent work by the author. This monograph is a one-of-a-kind treatise on the prime function associated with multiply connected domains and how to use it in applications. The book contains many results familiar in the simply connected, or single-entity, case that are generalized naturally to any number of entities, in many instances for the first time. Solving Problems in Multiply Connected Domains is aimed at applied and pure mathematicians, engineers, physicists, and other natural scientists; the framework it describes finds application in a diverse array of contexts. The book provides a rich source of project material for undergraduate and graduate courses in the applied sciences and could serve as a complement to standard texts on advanced calculus, potential theory, partial differential equations and complex analysis, and as a supplement to texts on applied mathematical methods in engineering and science.
Download or read book Numerical Conformal Mapping written by Lloyd Nicholas Trefethen and published by North Holland. This book was released on 1986 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Conformal Mapping of Simply connected Domains written by Colleen Frazer and published by . This book was released on 1962 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On Single step Conformal Mapping of Some Simply Connected Domains written by Maria Ewa Klonowska-Prosnak and published by . This book was released on 1991 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Numerical Conformal Mapping Method and the Poisson Equation on Irregular Domains written by Emmanuel Ricky Kamgnia and published by . This book was released on 1983 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bergman Kernel Methods for the Numerical Conformal Mapping of Simply and Doubly connected Domains written by M. K. Warby and published by . This book was released on 1984 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Cauchy Transform Potential Theory and Conformal Mapping written by Steven R. Bell and published by CRC Press. This book was released on 2015-11-04 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Cauchy Transform, Potential Theory and Conformal Mapping explores the most central result in all of classical function theory, the Cauchy integral formula, in a new and novel way based on an advance made by Kerzman and Stein in 1976.The book provides a fast track to understanding the Riemann Mapping Theorem. The Dirichlet and Neumann problems f
Download or read book A Fornberg like Method for the Numerical Conformal Mapping of Bounded Multiply Connected Domains written by Everett Kropf and published by . This book was released on 2009 with total page 55 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new Fornberg-like method is presented for computing conformal maps from the interior of the unit disk with m>1 circular holes to the interior of a smooth closed curve with m holes bounded by smooth curves. The method is a Newton-like method for computing the boundary correspondences and the conformal moduli (centers and radii of the circles). The inner linear systems are derived from conditions for analytic extension of functions defined on the circles to the interior domain. These systems are N-point trigonometric discretizations of the identity plus a compact operator and are solved efficiently with the conjugate gradient method at a cost of O(N2) per step.
Download or read book The Cauchy Transform Potential Theory and Conformal Mapping written by Steven R. Bell and published by CRC Press. This book was released on 1992-08-14 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Cauchy integral formula is the most central result in all of classical function theory. A recent discovery of Kerzman and Stein allows more theorems than ever to be deduced from simple facts about the Cauchy integral. In this book, the Riemann Mapping Theorem is deduced, the Dirichlet and Neumann problems for the Laplace operator are solved, the Poisson kernal is constructed, and the inhomogenous Cauchy-Reimann equations are solved concretely using formulas stemming from the Kerzman-Stein result. These explicit formulas yield new numerical methods for computing the classical objects of potential theory and conformal mapping, and the book provides succinct, complete explanations of these methods. The Cauchy Transform, Potential Theory, and Conformal Mapping is suitable for pure and applied math students taking a beginning graduate-level topics course on aspects of complex analysis. It will also be useful to physicists and engineers interested in a clear exposition on a fundamental topic of complex analysis, methods, and their application.
