Simple Fields of Physics by Finite Element Analysis

Simple Fields of Physics by Finite Element Analysis PDF (Adobe DRM)

by: Gunnar Backstrom

Have you Ever Solved a Partial Differential Equation? The laws of physics may be transformed mathematically into second-order partial differential equations (PDEs). The simplest one of this type is known as the Laplace equation. This governs the distribution of gravitation in free space. Other PDEs, for the electric and magnetic fields etc., are somewhat similar but more complicated. Partial Differential Equations (PDEs) predict how fields vary in space and time, and they are hence of critical importance in physics and engineering. In spite of this central role, PDEs have not yet received the attention they deserve in college curricula. This is because very few exact solutions exist, and numerical solutions are cumbersome, to the extent that the latter are taught within separate academic disciplines, such as Applied Mathematics, Numerical Analysis, and Computation. These disciplines focus on numerical methods rather than actual solutions and are accordingly of little practical value to scientists and engineers. The last decade brought convenient software for solving PDEs with various boundary conditions. One such program (the Student Version of FlexPDE®) may be downloaded for free on the web, and the user only needs superficial knowledge of how solutions are generated internally. It is a finite-element program that solves PDEs in seconds on a simple PC. Parameters may easily be changed using the built-in editor. The program constitutes a powerful tool for learning about classical fields, which are notoriously difficult parts of the physics curriculum. Electro- and magnetostatics are examples of fields that are now easily accessible. Heat transfer, electromagnetic waves, wave mechanics, elastic deformation and vibration, and viscous liquid flow are other examples. The present book is unique in its approach. It is not another volume on conceivable algorithms of finite element analysis. Its main purpose is to exploit a free web program for dealing with PDEs occurring in physics. The FlexPDE software is exploited in this self-instructional treatise. This program solves a typical example in seconds and promptly presents the results graphically by a variety of plots. Sample chapters of this book are available for free on www.LearnByComputing.com. The main topics treated are the following. Plotting Functions Laplace and Poisson PDEs Electricity Magnetism Heat Problems in 3D Space Electromagnetic Waves Wave Mechanics Fluid Dynamics