Mathematical Models for Eddy Currents and Magnetostatics
Mathematical Models for Eddy Currents and Magnetostatics

Author: Rachid Touzani

Publisher: Springer

Published: 2013-10-15

Total Pages: 0

ISBN-13: 9789400702011

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This monograph addresses fundamental aspects of mathematical modeling and numerical solution methods of electromagnetic problems involving low frequencies, i.e. magnetostatic and eddy current problems which are rarely presented in the applied mathematics literature. In the first part, the authors introduce the mathematical models in a realistic context in view of their use for industrial applications. Several geometric configurations of electric conductors leading to different mathematical models are carefully derived and analyzed, and numerical methods for the solution of the obtained problems are given. Related issues such as convergence of the approximations and error estimates are discussed. The second part of the monograph presents various coupled problems that involve eddy current or magnetostatic problems, in particular magneto-hydrodynamic problems and magnetic shaping problems concerning the melt flow of electrically conducting metals, induction heating processes, inductively coupled plasmas and ferromagnetic screening modeling. The presentation of each model comes with numerical illustration from industrial applications.

Mathematical Models for Eddy Currents and Magnetostatics
Mathematical Models for Eddy Currents and Magnetostatics

Author: Rachid Touzani

Publisher: Springer Science & Business Media

Published: 2013-10-01

Total Pages: 309

ISBN-13: 9400702027

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This monograph addresses fundamental aspects of mathematical modeling and numerical solution methods of electromagnetic problems involving low frequencies, i.e. magnetostatic and eddy current problems which are rarely presented in the applied mathematics literature. In the first part, the authors introduce the mathematical models in a realistic context in view of their use for industrial applications. Several geometric configurations of electric conductors leading to different mathematical models are carefully derived and analyzed, and numerical methods for the solution of the obtained problems are given. Related issues such as convergence of the approximations and error estimates are discussed. The second part of the monograph presents various coupled problems that involve eddy current or magnetostatic problems, in particular magneto-hydrodynamic problems and magnetic shaping problems concerning the melt flow of electrically conducting metals, induction heating processes, inductively coupled plasmas and ferromagnetic screening modeling. The presentation of each model comes with numerical illustration from industrial applications.

Mathematical Models and Numerical Simulation in Electromagnetism
Mathematical Models and Numerical Simulation in Electromagnetism

Author: Alfredo Bermúdez de Castro

Publisher: Springer

Published: 2014-07-22

Total Pages: 440

ISBN-13: 3319029495

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The book represents a basic support for a master course in electromagnetism oriented to numerical simulation. The main goal of the book is that the reader knows the boundary-value problems of partial differential equations that should be solved in order to perform computer simulation of electromagnetic processes. Moreover it includes a part devoted to electric circuit theory based on ordinary differential equations. The book is mainly oriented to electric engineering applications, going from the general to the specific, namely, from the full Maxwell’s equations to the particular cases of electrostatics, direct current, magnetostatics and eddy currents models. Apart from standard exercises related to analytical calculus, the book includes some others oriented to real-life applications solved with MaxFEM free simulation software.

Proceedings of the Third European Conference on Mathematics in Industry
Proceedings of the Third European Conference on Mathematics in Industry

Author: J. Manley

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 544

ISBN-13: 9400906293

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The European Consortium for Mathematics in Industry (ECMI) was founded, largely due to the driving energy of Michiel Hazewinkel on the 14th April, 1986 in Neustadt-Mussbach in West Germany. The founder signatories were A. Bensoussan (INRIA, Paris), A. Fasano (University of Florence), M. Hazewinkel (CWI, Amsterdam), M. Heilio (Lappeenranta University, Finland), F. Hodnett (University of Limerick, Ireland), H. Martens (Norwegian Institute of Technology, Trondheim), S. McKee (University of Strathclyde, Scotland), H. NeURzert (University of Kaiserslautern, Germany), D. Sundstrom (The Swedish Institute of Applied Mathematics, Stockholm), A. Tayler (University of Oxford, England) and Hj. Wacker (University of Linz, Austria). The European Consortium for Mathematics in Industry is dedicated to: (a) promote the use of mathematical models in Industry (b) educate industrial mathematicians to meet the growing demand for such experts (c) operate on a European scale. ECMI is still a young organisation but its membership is growing fast. Although it has still to persuade more industrialists to join, ECMI certainly operates on a European scale and a flourishing postgraduate programme with student exchange has been underway for some time. It is perhaps fitting that the first open meeting of ECMI was held at the University of Strathclyde in Glasgow. Glasgow is and was the industrial capital of Scotland and was, and arguably still is, Britain's second city after London; when this volume appears it will have rightly donned the mantle of the cultural capital of Europe.

Magnetic Components
Magnetic Components

Author: Peter Zacharias

Publisher: Springer Nature

Published: 2022-12-09

Total Pages: 817

ISBN-13: 3658372060

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The book deals with methods for the description and design of electromagnetic components. Both linear and nonlinear components are covered. For electrical simulations the necessary equivalent circuit diagrams are derived and a general methodology is developed. Possible influences on properties via material selection, winding design and premagnetisation of sections are treated. Measurement characterization, modeling, possible errors and model limits are dealt with extensively. In the last chapter examples are discussed.

Eddy Current Approximation of Maxwell Equations
Eddy Current Approximation of Maxwell Equations

Author: Ana Alonso Rodriguez

Publisher: Springer Science & Business Media

Published: 2010-11-22

Total Pages: 355

ISBN-13: 8847015065

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This book deals with the mathematical analysis and the numerical approximation of eddy current problems in the time-harmonic case. It takes into account all the most used formulations, placing the problem in a rigorous functional framework.

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016
Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016

Author: Marco L. Bittencourt

Publisher: Springer

Published: 2017-11-07

Total Pages: 681

ISBN-13: 3319658700

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This book features a selection of high-quality papers chosen from the best presentations at the International Conference on Spectral and High-Order Methods (2016), offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions.

Numerical Approximation of the Magnetoquasistatic Model with Uncertainties
Numerical Approximation of the Magnetoquasistatic Model with Uncertainties

Author: Ulrich Römer

Publisher: Springer

Published: 2016-07-27

Total Pages: 128

ISBN-13: 3319412949

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This book presents a comprehensive mathematical approach for solving stochastic magnetic field problems. It discusses variability in material properties and geometry, with an emphasis on the preservation of structural physical and mathematical properties. It especially addresses uncertainties in the computer simulation of magnetic fields originating from the manufacturing process. Uncertainties are quantified by approximating a stochastic reformulation of the governing partial differential equation, demonstrating how statistics of physical quantities of interest, such as Fourier harmonics in accelerator magnets, can be used to achieve robust designs. The book covers a number of key methods and results such as: a stochastic model of the geometry and material properties of magnetic devices based on measurement data; a detailed description of numerical algorithms based on sensitivities or on a higher-order collocation; an analysis of convergence and efficiency; and the application of the developed model and algorithms to uncertainty quantification in the complex magnet systems used in particle accelerators.

Mathematical Models for the Design of Electrical Machines
Mathematical Models for the Design of Electrical Machines

Author: Frédéric Dubas

Publisher: MDPI

Published: 2021-03-15

Total Pages: 252

ISBN-13: 3036503986

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This book is a comprehensive set of articles reflecting the latest advances and developments in mathematical modeling and the design of electrical machines for different applications. The main models discussed are based on the: i) Maxwell–Fourier method (i.e., the formal resolution of Maxwell’s equations by using the separation of variables method and the Fourier’s series in 2-D or 3-D with a quasi-Cartesian or polar coordinate system); ii) electrical, thermal and magnetic equivalent circuit; iii) hybrid model. In these different papers, the numerical method and the experimental tests have been used as comparisons or validations.

Principles of Magnetostatics
Principles of Magnetostatics

Author: Richard C. Fernow

Publisher: Cambridge University Press

Published: 2023-01-31

Total Pages: 315

ISBN-13: 1009291149

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This 2016 book, now OA, explains the mathematical theory behind the forces and fields resulting from the steady electrical currents.