Chapter 1 - Introduction

Abstract

Engineers, mathematicians, and those involved in natural sciences are generally interested in developing predictive capabilities for natural processes in order to establish causality relationships. Modeling and simulation are the tools generally used to this end. In this chapter, a brief introduction to the distinction between these two concepts is provided. The term model refers to developing a mathematical representation of a physical process that is observed in nature. The term simulation refers to solving the mathematical model and analyzing the results to gain insight into the cause–effects relationships. In this book, we deal with the initial value and boundary value problems. The emphasis is undoubtedly on the solution of these equations by using the finite element method. We emphasize that by learning the modeling process, we gain important access to the physics of the problem, and therefore all simulations should be accompanied by a good understanding of the underlying model.