Types of Solutions and Degrees of Freedom (DOFs)

Solving an electromagnetic field problem is always based on solving Maxwell's equations. However, the process of obtaining the solution is typically based on solving a second-order consequence of Maxwell's equations with the consideration of applicable constitutive equations. At the same time – as a rule – a subset of complete Maxwell’s equations is considered according to characteristic aspects of the application. Thus for reasons of efficiency of the solution, applications are classified as electrostatic, magnetostatic, frequency domain or time domain and as a consequence a specific type of solver is used in each case. This allows the users to obtain the solution with the desired accuracy but always within the limits of the fundamental assumptions made when the application was classified along the lines of the above mentioned criteria. The guidelines that can be used to correctly identify the type of solution to use are detailed in the topics that follow. The unknowns for each type of solution can be different, depending on the formulation.