2.1. INTRODUCTION

The temperature profile inside the different layers is calculated by Finite Element Approximations. Besides Finite Element Analysis (FEA), there are other methods for solving Partial Differential Equations (PDEs). Monte Carlo Method is one of these. But there are others, the so-called spectral and variational methods, for example. However, FEA is often preferred by practitioners in e.g. solid mechanics or structural engineering, because these methods allow considerable ‘freedom’ in putting computational elements where they want them. This is important when dealing with high irregular geometries or when dealing with complex decomposition reactions. Spectral methods are sometimes preferred for very regular geometries and smooth functions; they might converge more rapidly than (FEA), but they sometimes do not work well for problems with discontinuities.



Fig. 2.1: FEA is the application of the Finite Element Methods. In it, the object or system is represented by a geometrically similar model consisting of multiple, linked, simplified representations of discrete regions i.e., finite elements. The analysis is therefore done by modeling an object into thousands of small pieces (finite elements). The finite elements are used for solving partial differential equations (PDE) approximately.




Fig. 2.2: Finite Element Analysis is written as a set of communicating elements (Organization of an object in a virtual mesh and grid generation in time and in space)