Finite Element Method to Model Electromagnetic Systems in Low Frequency (eBook, PDF)

Redaktion: Piriou, Francis; Clenet, Stephane

• Format: PDF

Produktbeschreibung

Numerical modeling now plays a central role in the design and study of electromagnetic systems. In the field of devices operating in low frequency, it is the finite element method that has come to the fore in recent decades. Today, it is widely used by engineers and researchers in industry, as well as in research centers. This book describes in detail all the steps required to discretize Maxwell's equations using the finite element method. This involves progressing from the basic equations in the continuous domain to equations in the discrete domain that are solved by a computer. This approach is carried out with a constant focus on maintaining a link between physics, i.e. the properties of electromagnetic fields, and numerical analysis. Numerous academic examples, which are used throughout the various stages of model construction, help to clarify the developments.

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Produktdetails

• Verlag: John Wiley & Sons
• Seitenzahl: 320
• Erscheinungstermin: 13. Februar 2024
• Englisch
• ISBN-13: 9781394276462
• Artikelnr.: 69998631

Autorenporträt

Francis Piriou is former Director of the research group L2EP and Professor Emeritus at the University of Lille, France. His research focuses on computational electromagnetics. Stéphane Clénet is Professor at ENSAM and researcher at the group L2EP in the field of computational electromagnetics in France.

Inhaltsangabe

Introduction ix Chapter 1 Equations of Electromagnetism 1 1.1 Maxwell's
equations 1 1.2 Behavior laws of materials 2 1.2.1 General case 2 1.2.2
Simplified forms 3 1.3 Interface between two media and boundary conditions
8 1.3.1 Continuity conditions between two media 9 1.3.2 Boundary conditions
12 1.4 Integral forms: fundamental theorems 13 1.4.1 Faraday's law 13 1.4.2
Ampère's law 14 1.4.3 Law of conservation of the magnetic flux 15 1.4.4
Gauss' law 16 1.5 Various forms of Maxwell's equations 17 1.5.1
Electrostatics 17 1.5.2 Electrokinetics 19 1.5.3 Magnetostatics 20 1.5.4
Magnetodynamics 22 Chapter 2 Function Spaces 25 2.1 Introduction 25 2.2
Spaces of differential operators 25 2.2.1 Definitions 25 2.2.2 Function
spaces of grad, curl, div 26 2.2.3 Kernel of vector operators 27 2.2.4
Image spaces of operators 27 2.3 Studied topologies 29 2.3.1 Connected and
disconnected domain 29 2.3.2 Simply connected and not simply connected
domain 29 2.3.3 Contractible and non-contractible domain 30 2.3.4
Properties of function spaces 31 2.4 Relations between vector subspaces 31
2.4.1 Orthogonality of function spaces 31 2.4.2 Analysis of function
subspaces 33 2.4.3 Organization of function spaces 39 2.5 Vector fields
defined by a vector operator 40 2.5.1 Infinite number of solutions 41 2.5.2
Gauge conditions 42 2.6 Structure of function spaces 44 2.6.1 Adjoint
operators 44 2.6.2 Tonti diagram 46 Chapter 3 Maxwell's Equations:
Potential Formulations 49 3.1 Introduction 49 3.2 Consideration of source
terms 49 3.2.1 Global source quantities imposed on the boundaries 50 3.2.2
Source quantities inside the domain 58 3.2.3 Examples of the calculation of
support fields 62 3.3 Electrostatics 69 3.3.1 Source terms imposed on the
boundary of the domain 69 3.3.2 Internal electrode 80 3.3.3 Tonti diagram
90 3.4 Electrokinetics 91 3.4.1 Elementary geometry 91 3.4.2 Multisource
case 102 3.4.3 Tonti diagram 107 3.5 Magnetostatics 107 3.5.1 Studied
problems 107 3.5.2 Scalar potential Phi formulation 108 3.5.3 Vector
potential A formulation 121 3.5.4 Summarizing tables 129 3.5.5 Tonti
diagram 131 3.6 Magnetodynamics 131 3.6.1 Imposed electric quantities 134
3.6.2 Imposed magnetic quantities 148 3.6.3 Summarizing tables 162 3.6.4
Tonti diagram 166 Chapter 4 Formulations in the Discrete Domain 169 4.1
Introduction 169 4.2 Weighted residual method: weak form of Maxwell's
equations 170 4.2.1 Methodology 170 4.2.2 Weak form of the equations of
electrostatics 173 4.2.3 Weak form of the equations of electrokinetics 179
4.2.4 Weak form of the equations of magnetostatics 183 4.2.5 Weak form of
the equations of magnetodynamics 188 4.2.6 Synthesis of results 200 4.3
Finite element discretization 201 4.3.1 The need for discretization 201
4.3.2 Approximation functions 203 4.3.3 Discretization of vector operators
211 4.3.4 Discretization of physical quantities and associated fields 226
4.3.5 Taking into account homogeneous boundary conditions 228 4.3.6 Gauge
conditions in the discrete domain 231 4.3.7 Discretization of support
fields and associated potentials 240 4.4 Discretization of weak
formulations 244 4.4.1 Notations 244 4.4.2 Ritz-Galerkin method 245 4.4.3
Electrostatics 248 4.4.4 Electrokinetics 260 4.4.5 Magnetostatics 269 4.4.6
Magnetodynamics 281 References 295 Index 297