ABSTRACT
This chapter utilizes Finite Element Method to two-dimensional (2-D) boundary value problems in electromagnetics. Most of the electromagnetic problems in 2-D are typically governed by a scalar second-order partial differential equation. The chapter directly starts from the weak form and focuses on its finite element solution. While combining the element matrices, the sum of line integrals of two neighboring elements cancels out. Mesh generation is the process of representing the domain of interest as a collection of elements. In 2-D problems, the two most commonly-used elements are triangular and quadrilateral elements. Triangular elements are preferred due to their simplicity and the possibility of developing algorithms for automatic triangulation of the computational domain. There is another straightforward approach that can be applied to quadrilateral or Lagrangian type elements using Lagrange polynomial functions. Since quadrilateral element is a type of Lagrangian element, the shape functions can also be derived from the Lagrange polynomials.
