## Mathematical Models and Numerical Simulation in ElectromagnetismThe 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

3 | |

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 |

### Other editions - View all

Mathematical Models and Numerical Simulation in Electromagnetism Alfredo Bermúdez de Castro,Dolores Gómez,Pilar Salgado No preview available - 2014 |

Mathematical Models and Numerical Simulation in Electromagnetism Alfredo Bermúdez de Castro,Dolores Gómez,Pilar Salgado No preview available - 2013 |

### Common terms and phrases

affine space Ampère's law Bermúdez boundary condition capacitor charge density coil computational domain conducting domain conductor constant coordinates core corresponding curl H current density current intensity curve cylinder deduce defined dielectric dipole direct current distribution eddy currents eddy currents model edge electric field electric permittivity electric potential electrostatics finite element frequency function Gauss geometry given grad graph Green’s formula H(curl Hence hysteresis induction inductor infinite integral ISBN Let us consider Let us denote linear magnetic field magnetic flux magnetic permeability magnetostatic material Mathematical Models matrix MaxFEM Maxwell’s equations modulus Moreover nodes notice null Numerical Simulation obtain parameters plane Preisach problem radius Relative magnetic permeability resistance respectively RLC circuit Salgado Sect Simulation in Electromagnetism ſº solve source voltage surface symmetry tensor theorem UNITEXT vector field wave weak formulation x3-axis