This series lecture is an introduction to the finite element method with applications in
electromagnetics. The finite element method is a numerical method that is used to solve
boundary-value problems characterized by a partial differential equation and a set of boundary
conditions. The geometrical domain of a boundary-value problem is discretized using sub-domain
elements called the finite elements and the differential equation is applied to a single
element after it is brought to a weak integro-differential form. A set of shape functions is
used to represent the primary unknown variable in the element domain. A set of linear equations
is obtained for each element in the discretized domain. A global matrix system is formed after
the assembly of all elements. This lecture is divided into two chapters. Chapter 1 describes
one-dimensional boundary-value problems with applications to electrostatic problems described
by the Poisson's equation. The accuracy of the finite element methodis evaluated for linear and
higher order elements by computing the numerical error based on two different definitions.
Chapter 2 describes two-dimensional boundary-value problems in the areas of electrostatics and
electrodynamics (time-harmonic problems). For the second category an absorbing boundary
condition was imposed at the exterior boundary to simulate undisturbed wave propagation toward
infinity. Computations of the numerical error were performed in order to evaluate the accuracy
and effectiveness of the method in solving electromagnetic problems. Both chapters are
accompanied by a number of Matlab codes which can be used by the reader to solve one- and
two-dimensional boundary-value problems. These codes can be downloaded from the publisher's
URL: www.morganclaypool.com page polycarpou This lecture is written primarily for the nonexpert
engineer or the undergraduate or graduate student who wants to learn for the first time the
finite element method with applications to electromagnetics. It is also targeted for research
engineers who have knowledge of other numerical techniques and want to familiarize themselves
with the finite element method. The lecture begins with the basics of the method including
formulating a boundary-value problem using a weighted-residual method and the Galerkin approach
and continues with imposing all three types of boundary conditions including absorbing boundary
conditions. Another important topic of emphasis is the development of shape functions including
those of higher order. In simple words this series lecture provides the reader with all
information necessary for someone to apply successfully the finite element method to one- and
two-dimensional boundary-value problems in electromagnetics. It is suitable for newcomers in
the field of finite elements in electromagnetics.
