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ABSTRACT
This series lecture is an introduction to the finite element method with applications in electro-
magnetics.The finite elementmethod is a numericalmethod 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 method is 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 accompa-
nied 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 grad-
uate 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 impor-
tant 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.
Introduction_to_the_Finite_Element_Method_in_Electromagnetics: Introduction_to_the_Finite_Element_Method_in_Electromagnetics.rar
