Mathematical Models and Numerical Simulation in Electromagnetism

Front Cover
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.
 

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Contents

1 The harmonic oscillator
3
2 The series RLC circuit
21
3 Linear electrical circuits
33
Part II Distributed Parameter Models
50
4 Maxwells equations in free space
52
5 Some solutions of Maxwells equations in free space
67
6 Maxwells equations in material regions
76
7 Electrostatics
115
13 Electrostatics with MaxFEM
266
14 Direct current with MaxFEM
299
15 Magnetostatics with MaxFEM
307
16 Eddy currents with MaxFEM
324
Appendix A Elements of graph theory
347
Appendix B Vector calculus
354
Appendix C Function spaces for electromagnetism
387
average values
405

8 Direct current
138
9 Magnetostatics
151
10 The eddy currents model
183
11 An introduction to nonlinear magnetics Hysteresis
217
Part III Numerical Solution of Maxwells Equations
241
12 Electrical circuits with MaxFEM
243
Appendix E Linear nodal and edge finite elements
407
Appendix F Maxwells equations in Lagrangian coordinates
412
References
421
Index
427
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