Contents Introduction
The finite element method (FEM) has long been employed to compute electromagnetic, thermal, and mechanical field problems [1], [2]. The FEM is based on finding a functional that is minimized or maximized by nature, such as the energy in the electric field. This functional is then extremized over discretized space to determine the approximate field. More precisely in the case of electric field problems, we divide space into elements which are small enough so that the potential at the elements can be interpolated with reasonable accuracy. We then formulate the energy as a function of the unknown nodal potentials. The nodal potentials that minimize the total energy in the electric field provide a good approximation to the correct potential distribution. Equating all the partial derivatives of the energy functional with respect to the node potential to zero results in a large set of simultaneous linear equations, which can be solved by matrix inversion.
