Abstract
In this chapter we shall consider an effective method for solving inverse electromagnetic problems by applying Lagrange multipliers. In this chapter we shall also explore the properties and features of this method for practical use. In Section 4.1, we shall examine the application of Lagrange multipliers as continuous functions for electromagnetic optimization problems. When derived, the equations for field potentials and auxiliary adjoining functions can be used to show how to construct the boundary conditions for these functions and the algorithm for the numerical solution of optimization problems. Furthermore, in Section 4.2 we illustrate, through a number of examples, the procedure of finding field sources of the adjoining function, including the appropriate equations. The search for optimum distribution of a substance in a space can be carried out in various classes of media such as homogeneous, non-uniform, isotropic, nonlinear, etc. In Section 4.3, we shall also consider an algorithm for variations of the medium properties, allowing one to achieve local minima of the objective functional. Specific features of the method and its numerical realization will be considered by means of practical examples and application of benchmark problems in Section 4.4. Section 4.5 deals with the problems of computing values. In Section 4.6 some issues of the Lagrange method application for solution of optimization problems in non-stationary electromagnetic fields will be discussed.
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(2007). Solving Inverse Electromagnetic Problems by the Lagrange Method. In: Inverse Problems in Electric Circuits and Electromagnetics. Mathematical and Analytical Techniques with Applications to Engineering. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-46047-5_4
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DOI: https://doi.org/10.1007/978-0-387-46047-5_4
Publisher Name: Springer, Boston, MA
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