## Inverse Problems and Optimal Design in Electricity and MagnetismIn the last thirty years optimization theory has been extensively applied to the optimal design of mechanical structures and, in general, to the solution of inverse problems in structural mechanics. In electromagnetism, however, the impact of optimization methods is much more recent. The present book is the first one on the subject of inverse problems and optimal design in electricity and magnetism. Filling this gap in the literature was the primary goal of the authors. The secondary one was to provide a comprehensive reference book offering a broad view of the subject ranging from theory to computer implementations. Having this in mind, the authors tried to write a book which might serve as a textbook for graduate students in electrical engineering as well as a reference for applied mathematicians and researchers. Possible applications pertain to a great many different areas: electrical machines, high voltage engineering, nuclear magnetic resonance spectrography, electron optics, plasma techniques, etc. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

Mathematical preliminaries | 3 |

Numerical methods for systems of equations | 76 |

Unconstrained optimization | 89 |

Constrained optimization | 137 |

Linear leastsquares | 161 |

Nonlinear leastsquares | 172 |

Introduction | 191 |

Potential equations in electricity and magnetism | 198 |

Synthesis of boundary conditions | 259 |

Synthesis of material properties | 269 |

Optimal shape synthesis | 276 |

Remarks on inverse and design problems | 298 |

Artificial neural networks ANNs for inverse electromagnetic | 309 |

designsensitivity and shape design procedures | 315 |

Finiteelement designsensitivity analysis | 325 |

Subroutine libraries | 339 |

Numerical methods in electromagnetism | 210 |

Inverse problems and optimal design | 229 |

Synthesis of sources | 237 |

Author index | 355 |

### Common terms and phrases

algorithm analysis applied approximation automatic differentiation boundary conditions boundary-value problems constrained optimization controlled subregion convergence current density defined denotes derivatives design variables design vector differential Dirichlet discrete domain Q electricity and magnetism electromagnetic fields evolution strategies example Figure finite element method finite-element finite-element method formulation given gradient Hessian matrix IEEE Trans ill-posed problems initial integral equations inverse problems iteration Laplace's equation least-squares problem line search Lipschitz magnetic field Math mathematical Maxwell's equations mesh minimum move limits Neittaanmaki neural network nodes nonlinear norm objective function obtained optimal design optimal shape design optimization problem permittivity positive definite potential quadratic region regularization parameter Rmxn Savini scalar search direction Section SIAM simulated annealing singular values singular-value decomposition solenoid solution solving Step steplength stochastic subroutine synthesis problems techniques Theorem Tikhonov regularization tion triangulation unconstrained xk+i

### References to this book

Optimization and Inverse Problems in Electromagnetism Marek Rudnicki,Slawomir Wiak Limited preview - 2003 |

Essays and Surveys in Global Optimization Charles Audet,Pierre Hansen,Giles Savard Limited preview - 2005 |