Overview of the Finite Element Method

Abstract

By using scalar and vector potentials, Maxwell's equations can be transformed into
partial differential equations. Generally, the partial differential equations can be solved by numerical methods. One of these numerical methods is the finite element method, which is based on the weak formulation of the partial differential equations. The basis of numerical techniques is to reduce the partial differential equations to algebraic ones whose
solution gives an approximation of the unknown potentials and electromagnetic field quantities. This reduction can be done by discretizing the partial differential equations in time if necessary and in space. The potential functions, the approximation method and the generated mesh distinguish the numerical field solvers. This paper summarize the finite element method as a CAD technique in electrical engineering to obtain the electromagnetic field quantities in the case of static magnetic field and eddy current field problems. Here, we show how to discretize the analyzed domain with finite elements, how to approximate potential functions with nodal and vector shape functions and how to build up the system of equations, which solution obtain the unknown potentials.