Learning About Fields by Finite Element Analysis

Abstract

The partial differential equations of physics have remained notoriously obscure elements of the academic curriculum, not because they should be difficult to derive or understand but because so few exact solutions can be obtained in closed form. To those who have considered the field equations impressive but virtually useless, the news that they can now be easily solved on a PC should be welcome. Several commercial programs are now available which permit us to exploit the power of finite element analysis without writing complicated code. Any student who is familiar with the differential form of classical field theory can write a short problem descriptor, specifying the equation, and the shape and functional conditions at the boundary. The problem is then solved automatically and the result appears in the form of plots as requested. The short time spent to learn the syntax is offset by the usefulness of the software, which extends from vector analysis, via electric and thermal conduction, electro-and magnetostatics, elasticity, fluid flow, and vibrations, to electromagnetic waves and quantum mechanics.