Maxwell’s Equations, Finite and Boundary Element Methods

Abstract

What are the essential needs of modern life? One can say without any hesita- tion, electric lighting, heating and cooling, telephones, electric motors and genera- tors, radio, television, X-ray machine, ECG machine, radars and weather forecasting system equipment, etc. In fact, the invention of electromagnetism embracing electricity and magnetism completely revolutionized our way of life. Every day, some new tools, techniques and equipment are being developed based on the concepts of the electromagnetism theory. The backbone of modern electromagnetism is a system or a set of four equations established by the Scottish Scientist James Clark Maxwell, a professor at the University of Cambridge, around 1872. This system is now known as the system of Maxwell’s equations. In the last three decades, two powerful methods, namely, the finite element and the boundary element, have been invented to find out solutions of physical phenomena represented by differential equations.