Solving Problems In Multiply Connected Domains

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Solving Problems In Multiply Connected Domains

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Author : Darren Crowdy
language : en
Publisher: SIAM
Release Date : 2020-04-20

Solving Problems In Multiply Connected Domains written by Darren Crowdy and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-20 with Mathematics categories.

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.

Computational Methods In Optimal Control

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Author : William H. Hager
language : en
Publisher: SIAM
Release Date : 2025-02-13

Computational Methods In Optimal Control written by William H. Hager and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-13 with Mathematics categories.

Using material from many different sources in a systematic and unified way, this self-contained book provides both rigorous mathematical theory and practical numerical insights while developing a framework for determining the convergence rate of discrete approximations to optimal control problems. Elements of the framework include the reference point, the truncation error, and a stability theory for the linearized first-order optimality conditions. Within this framework, the discretized control problem has a stationary point whose distance to the reference point is bounded in terms of the truncation error. The theory applies to a broad range of discretizations and provides completely new insights into the convergence theory for discrete approximations in optimal control, including the relationship between orthogonal collocation and Runge–Kutta methods. Throughout the book, derivatives associated with the discretized control problem are expressed in terms of a back-propagated costate. In particular, the objective derivative of a bang-bang or singular control problem with respect to a switch point of the control are obtained, which leads to the efficient solution of a class of nonsmooth control problems using a gradient-based optimizer. Computational Methods in Optimal Control: Theory and Practice is intended for numerical analysts and computational scientists. Users of the software package GPOPS may find the book useful since the theoretical basis for the GPOPS algorithm is developed within the book. It is appropriate for courses in variational analysis, numerical optimization, and the calculus of variations.

Menahem Max Schiffer Selected Papers Volume 2

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Author : Peter Duren
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-17

Menahem Max Schiffer Selected Papers Volume 2 written by Peter Duren and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-17 with Mathematics categories.

This two volume set presents over 50 of the most groundbreaking contributions of Menahem M Schiffer. All of the reprints of Schiffer’s works herein have extensive annotation and invited commentaries, giving new clarity and insight into the impact and legacy of Schiffer's work. A complete bibliography and brief biography make this a rounded and invaluable reference.

Applications Of Complex Variables

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Author : Foluso Ladeinde
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2024-05-06

Applications Of Complex Variables written by Foluso Ladeinde and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-06 with Mathematics categories.

The subject of applied complex variables is so fundamental that most of the other topics in advanced engineering mathematics (AEM) depend on it. The present book contains complete coverage of the subject, summarizing the more elementary aspects that you find in most AEM textbooks and delving into the more specialized topics that are less commonplace. The book represents a one-stop reference for complex variables in engineering analysis. The applications of conformal mapping in this book are significantly more extensive than in other AEM textbooks. The treatments of complex integral transforms enable a much larger class of functions that can be transformed, resulting in an expanded use of complex-transform techniques in engineering analysis. The inclusion of the asymptotics of complex integrals enables the analysis of models with irregular singular points. The book, which has more than 300 illustrations, is generous with realistic example problems.

Multiphysics Simulation By Design For Electrical Machines Power Electronics And Drives

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Author : Marius Rosu
language : en
Publisher: John Wiley & Sons
Release Date : 2017-11-10

Multiphysics Simulation By Design For Electrical Machines Power Electronics And Drives written by Marius Rosu and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-10 with Science categories.

Presents applied theory and advanced simulation techniques for electric machines and drives This book combines the knowledge of experts from both academia and the software industry to present theories of multiphysics simulation by design for electrical machines, power electronics, and drives. The comprehensive design approach described within supports new applications required by technologies sustaining high drive efficiency. The highlighted framework considers the electric machine at the heart of the entire electric drive. The book also emphasizes the simulation by design concept—a concept that frames the entire highlighted design methodology, which is described and illustrated by various advanced simulation technologies. Multiphysics Simulation by Design for Electrical Machines, Power Electronics and Drives begins with the basics of electrical machine design and manufacturing tolerances. It also discusses fundamental aspects of the state of the art design process and includes examples from industrial practice. It explains FEM-based analysis techniques for electrical machine design—providing details on how it can be employed in ANSYS Maxwell software. In addition, the book covers advanced magnetic material modeling capabilities employed in numerical computation; thermal analysis; automated optimization for electric machines; and power electronics and drive systems. This valuable resource: Delivers the multi-physics know-how based on practical electric machine design methodologies Provides an extensive overview of electric machine design optimization and its integration with power electronics and drives Incorporates case studies from industrial practice and research and development projects Multiphysics Simulation by Design for Electrical Machines, Power Electronics and Drives is an incredibly helpful book for design engineers, application and system engineers, and technical professionals. It will also benefit graduate engineering students with a strong interest in electric machines and drives.

Boundary Element Technology Vii

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Author : C.A. Brebbia
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Boundary Element Technology Vii written by C.A. Brebbia and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.

Seventh International Conference on Boundary Element Technology 'Betech 92', held at the University of New Mexico in Albuquerque, June 1992

Analysis Probability Applications And Computation

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Author : Karl‐Olof Lindahl
language : en
Publisher: Springer
Release Date : 2019-04-29

Analysis Probability Applications And Computation written by Karl‐Olof Lindahl and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-29 with Mathematics categories.

This book is a collection of short papers from the 11th International ISAAC Congress 2017 in Växjö, Sweden. The papers, written by the best international experts, are devoted to recent results in mathematics with a focus on analysis. The volume provides to both specialists and non-specialists an excellent source of information on the current research in mathematical analysis and its various interdisciplinary applications.

Advances In Discrete Differential Geometry

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Author : Alexander I. Bobenko
language : en
Publisher: Springer
Release Date : 2016-08-12

Advances In Discrete Differential Geometry written by Alexander I. Bobenko and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-12 with Mathematics categories.

This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, and on pure mathematics and its practical applications. The interaction of these facets is demonstrated by concrete examples, including discrete conformal mappings, discrete complex analysis, discrete curvatures and special surfaces, discrete integrable systems, conformal texture mappings in computer graphics, and free-form architecture. This richly illustrated book will convince readers that this new branch of mathematics is both beautiful and useful. It will appeal to graduate students and researchers in differential geometry, complex analysis, mathematical physics, numerical methods, discrete geometry, as well as computer graphics and geometry processing.

Modelling Ocean Climate Variability

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Author : Artem S. Sarkisyan
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-05-13

Modelling Ocean Climate Variability written by Artem S. Sarkisyan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-13 with Science categories.

In this wide-ranging and comprehensive review of the historical development and current status of ocean circulation models, the analysis extends from simple analytical approaches to the latest high-resolution numerical models with data assimilation. The authors, both of whom are pioneer scientists in ocean and shelf sea modelling, look back at the evolution of Western and Eastern modelling methodologies during the second half of the last century. They also present the very latest information on ocean climate modelling and offer examples for a number of oceans and shelf seas. The book includes a critical analysis of literature on ocean climate variability modelling, as well as assessing the strengths and weaknesses of the best-known modelling techniques. It also anticipates future developments in the field, focusing on models based on a synthesis of numerical simulation and field observation, and on nonlinear thermodynamic model data synthesis.

Block Method For Solving The Laplace Equation And For Constructing Conformal Mappings

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Author : Evgenii A. Volkov
language : en
Publisher: CRC Press
Release Date : 2017-07-28

Block Method For Solving The Laplace Equation And For Constructing Conformal Mappings written by Evgenii A. Volkov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-28 with Mathematics categories.

This book presents a new, efficient numerical-analytical method for solving the Laplace equation on an arbitrary polygon. This method, called the approximate block method, overcomes indicated difficulties and has qualitatively more rapid convergence than well-known difference and variational-difference methods. The block method also solves the complicated problem of approximate conformal mapping of multiply-connected polygons onto canonical domains with no preliminary information required. The high-precision results of calculations carried out on the computer are presented in an abundance of tables substantiating the exponential convergence of the block method and its strong stability concerning the rounding-off of errors.