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Electromagnetic problem solutions are based on the macroscopic theory of the continuous model for the electromagnetic field (EMF). It is described by a system of integral or partial differential equations for five vector quantities, namely, electric field strength, electric flux density, current density, magnetic field strength, and magnetic flux density. This article describes the behavior of the EMF by Maxwell's equations in integral or differential forms. It discusses the definition of potentials; methods of mathematical modeling; boundary conditions; and energy, power density, and electromagnetic forces.

Temperature is a typical parameter characterizing the heating level of any particle belonging to a heated body. The basic problem of heat transfer computation is associated with appropriate determination of heat transfer coefficients. This article provides a discussion on the basic equations, initial and boundary conditions, and multiple reflection phenomena of mathematical modeling. These boundary conditions include the Dirichlet, Neumann, and Henkel conditions.

Induction heating computations deal with a multiphysics problem containing analysis of several coupled physical fields such as electromagnetic, temperature, mechanical, and metallurgical. In order to solve coupled electromagnetic-temperature field problems, it is necessary to develop suitable algorithms and numerical procedures, which make it possible to deal with these nonlinear coupled problems. This article focuses on the most common approaches to coupled electromagnetic and heat transfer problems, namely, weak-, quasi-, and hard-coupled formulations.