# Introduction to the Finite Element Method in Electromagnetics

Morgan & Claypool Publishers, 2006 - Technology & Engineering - 115 pages
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 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 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"

### What people are saying -Write a review

We haven't found any reviews in the usual places.

### Contents

 OneDimensional BoundaryValue Problems 1 13 THE FINITE ELEMENT METHOD 3 14 DOMAIN DISCRETIZATION 5 THE GALERKIN APPROACH 7 17 ASSEMBLY OF ELEMENTS 13 18 IMPOSITION OF BOUNDARY CONDITIONS 19 182 Mixed Boundary Conditions 22 110 ONEDIMENSIONAL HIGHER ORDER INTERPOLATION FUNCTIONS 29
 232 Bilinear Quadrilateral Element 59 THE GALERKIN APPROACH 61 25 EVALUATION OF ELEMENT MATRICES AND VECTORS 66 251 Linear Triangular Elements 67 252 Bilinear Quadrilateral Elements 75 26 ASSEMBLY OF THE GLOBAL MATRIX SYSTEM 86 27 IMPOSITION OF BOUNDARY CONDITIONS 90 29 POSTPROCESSING OF THE RESULTS 91

 1101 Quadratic Elements 30 1102 Cubic Elements 33 111 ELEMENT MATRIX AND RIGHTHANDSIDE VECTOR USING QUADRATIC ELEMENTS 36 112 ELEMENT MATRIX AND RIGHTHANDSIDE VECTOR USING CUBIC ELEMENTS 39 CUBIC ELEMENTS 47 115 SOFTWARE 48 TwoDimensional BoundaryValue Problems 51 22 DOMAIN DISCRETIZATION 52 23 INTERPOLATION FUNCTIONS 54
 210 APPLICATION PROBLEMS 92 2102 TwoDimensional Scattering Problem 97 211 HIGHER ORDER ELEMENTS 105 2111 A NineNode Quadratic Quadrilateral Element 106 2112 A SixNode Quadratic Triangular Element 108 2113 A TenNode Cubic Triangular Element 110 212 SOFTWARE 111 Copyright

### Popular passages

Page 112 - M. Abramowitz and IA Stegun, Handbook of Mathematical Functions, New York: Dover Publications, 1972, pp.