The use of eddy current devices is very common in several areas of Electrical Engineering such as non-destructive testing, electrical machines and induction heating. The latter, particularly, in the last decades, was widely applied to several fields, including heavy industry, chemical industry, electro-medical devices, domestic appliances. In fact this technique has a number of intrinsic advantages: such as a very quick response and a good efficiency. Induction heating also allows heating very locally, the heating speeds are extremely high because of the high power density and the heating process can be regulated precisely. The aim of this work was the development of numerical methods for analysis and design of induction devices. The analysis of these devices is usually tackled by means of numerical techniques and can be often very hard due to the necessity to deal with a three-dimensional electromagnetic field problem that extends to infinity. In the case of an induction heating devices the electromagnetic analysis is coupled with a non linear thermal one. The proposed approach minimizes the computational cost of analysis with no loss of accuracy. At first, a reduction of the number of numerical unknowns was obtained restrincting the FEM domain to conductors region by means of the new FEM-SDBCI method (Singular Dirichlet Boundary Condition Iteration), explained in Chapter I. The method is described for three-dimensional eddy current problems in which the electrical field is used as unknown in a mesh of edge elements. This method alleviates the major drawback of FEM-DBCI, that is, the insertion of some element layers between the integration and truncation surfaces and consequently allows the use of a common mesh for thermal analysis in coupled problems. The procedure couples a differential equation for the interior problem in terms of the electric field with an integral equation for the exterior one, which expresses the Dirichlet condition on the truncation boundary; note that, without the insertion of element layers between inner domain and truncation boundary, the integral equation becomes singular. The global algebraic system is efficiently solved in an iterative way. The use of an efficient mesh generator based on an artificial neural network which allows good-accuracy solutions with a lower computational effort is also described. In Chapter II a strategy to perform FEM solutions of coupled electromagnetic-thermal problems is described. In this kind of problems, the electromagnetic one needs the large part of computing time; it is possible to limit the number of electromagnetic solutions by means of a control on the variations of temperature-dependent electric parameters. The solution of the eddy current problem leads to the calculation of power density in each finite element. Starting from this power density, a transient thermal analysis employing nodal tetrahedral finite elements of a given order is carried out. The thermal conductivity and the specific heat are assumed to be temperature-dependent. To solve the transient non linear problem, a Crank-Nicolson scheme was implemented. In order to perform the design of induction devices the proposed analysis method was used as evaluation block into an optimization strategy particularly suitable to tackle this kind of problems, the PSALHE-EA algorithm, described in Chapter III. The PSALHE-EA has some new features that permit to considerably reduce the overall optimization time allowing to make full use of parallelization. Moreover, it is able to identify multiple optima by locating global as well as local optima; this aspect could be advantageous in industrial design, because the designer may want to see several design alternatives. The tests performed show that PSALHE-EA is a very efficient hybrid optimization method and in this work it was successfully applied to the design of an induction heater for conductor pieces.