Numerical Conformal Mapping

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Numerical Conformal Mapping

Author : Nicolas Papamichael
Publisher : World Scientific
ISBN 13 : 9814289531
Total Pages : 242 pages
Book Rating : 4.8/5 (142 download)

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Book Synopsis Numerical Conformal Mapping by : Nicolas Papamichael

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.

Numerical Conformal Mapping

Author : Lloyd Nicholas Trefethen
Publisher : North Holland
ISBN 13 :
Total Pages : 288 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Numerical Conformal Mapping by : Lloyd Nicholas Trefethen

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:

Boundary Behaviour of Conformal Maps

Author : Christian Pommerenke
Publisher : Springer Science & Business Media
ISBN 13 : 3662027704
Total Pages : 307 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Boundary Behaviour of Conformal Maps by : Christian Pommerenke

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.

Conformal Mapping

Author : Roland Schinzinger
Publisher : Courier Corporation
ISBN 13 : 0486150747
Total Pages : 628 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Conformal Mapping by : Roland Schinzinger

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.

Handbook of Conformal Mappings and Applications

Author : Prem K. Kythe
Publisher : CRC Press
ISBN 13 : 1351718738
Total Pages : 943 pages
Book Rating : 4.3/5 (517 download)

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Book Synopsis Handbook of Conformal Mappings and Applications by : Prem K. Kythe

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.

A Numerical Conformal Mapping

Author : M. Javad Sorouri
Publisher :
ISBN 13 :
Total Pages : 250 pages
Book Rating : 4.:/5 (362 download)

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Book Synopsis A Numerical Conformal Mapping by : M. Javad Sorouri

Download or read book A Numerical Conformal Mapping written by M. Javad Sorouri and published by . This book was released on 1996 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Conformal Mapping

Author : Zeev Nehari
Publisher : Courier Corporation
ISBN 13 : 0486145034
Total Pages : 418 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Conformal Mapping by : Zeev Nehari

Download or read book Conformal Mapping written by Zeev Nehari and published by Courier Corporation. This book was released on 2012-05-23 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conformal mapping is a field in which pure and applied mathematics are both involved. This book tries to bridge the gulf that many times divides these two disciplines by combining the theoretical and practical approaches to the subject. It will interest the pure mathematician, engineer, physicist, and applied mathematician. The potential theory and complex function theory necessary for a full treatment of conformal mapping are developed in the first four chapters, so the reader needs no other text on complex variables. These chapters cover harmonic functions, analytic functions, the complex integral calculus, and families of analytic functions. Included here are discussions of Green's formula, the Poisson formula, the Cauchy-Riemann equations, Cauchy's theorem, the Laurent series, and the Residue theorem. The final three chapters consider in detail conformal mapping of simply-connected domains, mapping properties of special functions, and conformal mapping of multiply-connected domains. The coverage here includes such topics as the Schwarz lemma, the Riemann mapping theorem, the Schwarz-Christoffel formula, univalent functions, the kernel function, elliptic functions, univalent functions, the kernel function, elliptic functions, the Schwarzian s-functions, canonical domains, and bounded functions. There are many problems and exercises, making the book useful for both self-study and classroom use. The author, former professor of mathematics at Carnegie-Mellon University, has designed the book as a semester's introduction to functions of a complex variable followed by a one-year graduate course in conformal mapping. The material is presented simply and clearly, and the only prerequisite is a good working knowledge of advanced calculus.

Computational Conformal Mapping

Author : Prem Kythe
Publisher : Springer Science & Business Media
ISBN 13 : 1461220025
Total Pages : 479 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Computational Conformal Mapping by : Prem Kythe

Download or read book Computational Conformal Mapping written by Prem Kythe and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book evolved out of a graduate course given at the University of New Orleans in 1997. The class consisted of students from applied mathematics andengineering. Theyhadthebackgroundofatleastafirstcourseincomplex analysiswithemphasisonconformalmappingandSchwarz-Christoffeltrans formation, a firstcourse in numerical analysis, and good to excellent working knowledgeofMathematica* withadditionalknowledgeofsomeprogramming languages. Sincetheclasshad nobackground inIntegralEquations, thechap tersinvolvingintegralequationformulations werenotcoveredindetail, except for Symm's integral equation which appealed to a subsetofstudents who had some training in boundary element methods. Mathematica was mostly used for computations. In fact, it simplified numerical integration and other oper ations very significantly, which would have otherwise involved programming inFortran, C, orotherlanguageofchoice, ifclassical numericalmethods were attempted. Overview Exact solutions of boundary value problems for simple regions, such as cir cles, squares or annuli, can be determined with relative ease even where the boundaryconditionsarerathercomplicated. Green'sfunctionsforsuchsimple regions are known. However, for regions with complex structure the solution ofa boundary value problem often becomes more difficult, even for a simple problemsuchastheDirichletproblem. Oneapproachtosolvingthesedifficult problems is to conformally transform a given multiply connected region onto *Mathematica is a registered trade mark of Wolfram Research, Inc. ix x PREFACE simpler canonical regions. This will, however, result in change not only in the region and the associated boundary conditions but also in the governing differential equation. As compared to the simply connected regions, confor mal mapping ofmultiply connected regions suffers from severe limitations, one of which is the fact that equal connectivity ofregions is not a sufficient condition to effect a reciprocally connected map ofone region onto another.

Numerical Conformal Mapping

Author : Mien-Hsan Niu
Publisher :
ISBN 13 :
Total Pages : 94 pages
Book Rating : 4.:/5 (179 download)

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Book Synopsis Numerical Conformal Mapping by : Mien-Hsan Niu

Download or read book Numerical Conformal Mapping written by Mien-Hsan Niu and published by . This book was released on 1987 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Kernel Function and Conformal Mapping

Author : Stefan Bergman
Publisher : American Mathematical Soc.
ISBN 13 : 0821815059
Total Pages : 269 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Kernel Function and Conformal Mapping by : Stefan Bergman

Download or read book The Kernel Function and Conformal Mapping written by Stefan Bergman and published by American Mathematical Soc.. This book was released on 1950-03 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Kernel Function and Conformal Mapping by Stefan Bergman is a revised edition of ""The Kernel Function"". The author has made extensive changes in the original volume. The present book will be of interest not only to mathematicians, but also to engineers, physicists, and computer scientists. The applications of orthogonal functions in solving boundary value problems and conformal mappings onto canonical domains are discussed; and publications are indicated where programs for carrying out numerical work using high-speed computers can be found.The unification of methods in the theory of functions of one and several complex variables is one of the purposes of introducing the kernel function and the domains with a distinguished boundary. This approach has been extensively developed during the last two decades. This second edition of Professor Bergman's book reviews this branch of the theory including recent developments not dealt with in the first edition. The presentation of the topics is simple and presupposes only knowledge of an elementary course in the theory of analytic functions of one variable.

Numerical Conformal Mapping in Two-dimensional Hydrodynamics & Related Problems of Electrodynamics and Elasticity Theory

Author : Boris Isaakovich Rabinovich
Publisher :
ISBN 13 : 9785856920337
Total Pages : 312 pages
Book Rating : 4.9/5 (23 download)

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Book Synopsis Numerical Conformal Mapping in Two-dimensional Hydrodynamics & Related Problems of Electrodynamics and Elasticity Theory by : Boris Isaakovich Rabinovich

Download or read book Numerical Conformal Mapping in Two-dimensional Hydrodynamics & Related Problems of Electrodynamics and Elasticity Theory written by Boris Isaakovich Rabinovich and published by . This book was released on 2000 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Construction and Applications of Conformal Maps

Author : Institute for Numerical Analysis (U.S.)
Publisher :
ISBN 13 :
Total Pages : 296 pages
Book Rating : 4.:/5 (31 download)

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Book Synopsis Construction and Applications of Conformal Maps by : Institute for Numerical Analysis (U.S.)

Download or read book Construction and Applications of Conformal Maps written by Institute for Numerical Analysis (U.S.) and published by . This book was released on 1952 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Numerical Conformal Mapping of Long, Slender Regions

Author : Hans-Jürgen F. Sladeczek
Publisher :
ISBN 13 :
Total Pages : 178 pages
Book Rating : 4.:/5 (295 download)

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Book Synopsis Numerical Conformal Mapping of Long, Slender Regions by : Hans-Jürgen F. Sladeczek

Download or read book Numerical Conformal Mapping of Long, Slender Regions written by Hans-Jürgen F. Sladeczek and published by . This book was released on 1993 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Handbook of Conformal Mapping with Computer-Aided Visualization

Author : Valentin I. Ivanov
Publisher : CRC Press
ISBN 13 : 9780849389368
Total Pages : 372 pages
Book Rating : 4.3/5 (893 download)

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Book Synopsis Handbook of Conformal Mapping with Computer-Aided Visualization by : Valentin I. Ivanov

Download or read book Handbook of Conformal Mapping with Computer-Aided Visualization written by Valentin I. Ivanov and published by CRC Press. This book was released on 1994-12-16 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a guide on conformal mappings, their applications in physics and technology, and their computer-aided visualization. Conformal mapping (CM) is a classical part of complex analysis having numerous applications to mathematical physics. This modern handbook on CM includes recent results such as the classification of all triangles and quadrangles that can be mapped by elementary functions, mappings realized by elliptic integrals and Jacobian elliptic functions, and mappings of doubly connected domains. This handbook considers a wide array of applications, among which are the construction of a Green function for various boundary-value problems, streaming around airfoils, the impact of a cylinder on the surface of a liquid, and filtration under a dam. With more than 160 domains included in the catalog of mapping, Handbook of Conformal Mapping with Computer-Aided Visualization is more complete and useful than any previous volume covering this important topic. The authors have developed an interactive ready-to-use software program for constructing conformal mappings and visualizing plane harmonic vector fields. The book includes a floppy disk for IBM-compatible computers that contains the CONFORM program.

Handbook of Conformal Mappings and Applications

Author : Prem K. Kythe
Publisher : CRC Press
ISBN 13 : 135171872X
Total Pages : 663 pages
Book Rating : 4.3/5 (517 download)

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Book Synopsis Handbook of Conformal Mappings and Applications by : Prem K. Kythe

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 663 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.

The Cauchy Transform, Potential Theory and Conformal Mapping

Author : Steven R. Bell
Publisher : CRC Press
ISBN 13 : 1498727212
Total Pages : 221 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis The Cauchy Transform, Potential Theory and Conformal Mapping by : Steven R. Bell

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

Numerical Conformal Mapping Using Cross-ratios and Delaunay Triangulation

Author : Tobin A. Driscoll
Publisher :
ISBN 13 :
Total Pages : 38 pages
Book Rating : 4.:/5 (317 download)

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Book Synopsis Numerical Conformal Mapping Using Cross-ratios and Delaunay Triangulation by : Tobin A. Driscoll

Download or read book Numerical Conformal Mapping Using Cross-ratios and Delaunay Triangulation written by Tobin A. Driscoll and published by . This book was released on 1996 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "We propose a new algorithm for computing the Riemann mapping of the unit disk to a polygon, also known as the Schwarz-Christoffel transformation. The new algorithm, CRDT, is based on cross-ratios of the prevertices, and also on cross-ratios of quadrilaterals in a Delaunay triangulation of the polygon. The CRDT algorithm produces an accurate representation of the Riemann mapping even in the presence of arbitrary long, thin regions in the polygon, unlike any previous conformal mapping algorithm. We believe that CRDT can never fail to converge to the correct Riemann mapping, but the correctness and convergence proof depend on conjectures that we have so far not been able to prove. We demonstrate convergence with computational experiments. The Riemann mapping has applications to problems in two-dimensional potential theory and to finite-difference mesh generation. We use CRDT to produce a mapping and solve a boundary value problem on long, thin regions for which no other algorithm can solve these problems."