Introduction to the Finite Element Method in Electromagnetics

by Polycarpou, Anastasis

• ISBN13: 9781598290462
• ISBN10: 1598290460
• Format: Paperback
• Copyright: 2006-10-30
• Publisher: Morgan & Claypool

Summary

This lecture is written primarily for the non-expert 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 designed for research engineers who have knowledge of other numerical techniques and want to familiarize themselves with the finite element method.Finite element method is a numerical method used to solve boundary-value problems characterized by a partial differential equation and a set of boundary conditions. Author Anastasis Polycarpou provides the reader with all information necessary to successfully apply the finite element method to one- and two-dimensional boundary-value problems in electromagnetics.The book is accompanied by a number of codes written by the author in Matlab. These are the finite element codes that were used to generate most of the graphs presented in this book. Specifically, there are three Matlab codes for the one-dimensional case (Chapter 1) and two Matlab codes for the two-dimensional case (Chapter 2). The reader may execute these codes, modify certain parameters such as mesh size or object dimensions, and visualize the results. The codes are available on the Morgan & Claypool Web site at http://www.morganclaypool.com.

Table of Contents

One-Dimensional Boundary-Value Problems	1	(50)
Introduction	1	(1)
Electrostatic BVP and the Analytical Solution	1	(2)
The Finite Element Method	3	(2)
Domain Discretization	5	(1)
Interpolation Functions	5	(2)
The Method of Weighted Residual: The Galerkin Approach	7	(6)
Assembly of Elements	13	(6)
Imposition of Boundary Conditions	19	(3)
Dirichlet Boundary Conditions	19	(3)
Mixed Boundary Conditions	22	(1)
Finite Element Solution of the Electrostatic Boundary-Value Problem	22	(7)
One-Dimensional Higher Order Interpolation Functions	29	(7)
Quadratic Elements	30	(3)
Cubic Elements	33	(3)
Element Matrix and Right-Hand-Side Vector Using Quadratic Elements	36	(3)
Element Matrix and Right-Hand-Side Vector Using Cubic Elements	39	(1)
Postprocessing of the Solution: Quadratic Elements	39	(8)
Postprocessing of the Solution: Cubic Elements	47	(1)
Software	48	(3)
Two-Dimensional Boundary-Value Problems	51	(60)
Introduction	51	(1)
Domain Discretization	52	(2)
Interpolation Functions	54	(7)
Linear Triangular Element	54	(5)
Bilinear Quadrilateral Element	59	(2)
The Method of Weighted Residual: The Galerkin Approach	61	(5)
Evaluation of Element Matrices and Vectors	66	(20)
Linear Triangular Elements	67	(8)
Bilinear Quadrilateral Elements	75	(11)
Assembly of the Global Matrix System	86	(4)
Imposition of Boundary Conditions	90	(1)
Solution of the Global Matrix System	90	(1)
Postprocessing of the Results	91	(1)
Application Problems	92	(13)
Electrostatic Boundary-Value Problem	92	(5)
Two-Dimensional Scattering Problem	97	(8)
Higher Order Elements	105	(6)
A Nine-Node Quadratic Quadrilateral Element	106	(2)
A Six-Node Quadratic Triangular Element	108	(2)
A Ten-Node Cubic Triangular Element	110	(1)
Software	111