The values of the model entities (the lumped elements) are not straightforward to determine in all cases. This can be due to the fact that an element represents a phenomenon which can not be localised intuitively, that it represents a non-linear effect or that it is difficult to be represented in a single element. Examples are cases where all the vibrational modes of a plate have to be considered, when the shape of a structure is very complicated or when there is no analytical solution to a certain non-linear differential equation. In that case modelling must be based on the motional differential equations directly.
The Finite Element Method (FEM) is based on spatial segmentation of a structure where each segment is described by its coupled differential equations. Software packages like ANSYS, COMSOL, CoventorWare and FEMLAB are available for numerical evaluations and provide graphical representations of the results.
However, this method has several drawbacks. The finite element method is a low-level interpretation of the physical behaviour. To combine them into macroscopic overviews of device characteristics, large capacity with respect to memory and calculation speed is required. It is very hard to maintain the systems overview since the links between physical domains have become invisible. In many cases, the designer has to limit himself to a FEM analysis of only a part, one or two domains, of the problem to limit the complexity of the problem. To understand the relation between design parameters and performance in FEM analysis it has become the skill of the scientist, rather than the power of the tool as we have seen with the lumped element method.
These are the chapters for the Sensor Technology course: