AUTOMATIC ORDER REDUCTION FOR FINITE ELEMENT MODELS

In the process of physical modelling of microsystems operating on various energy domains, the engineer is used to apply Finite Element techniques for the discrete representation of the functionality of the device under investigation in a simulation environment. There are many commercial products that help the engineer in performing this task. The common feature of all these simulation tools is that the discrete representation consists of a system of ordinary differential equations. The dimension of this system is directly connected to the number of degrees of freedom for the respective problem. For a spatial displacement field, e.g., the degrees of freedom are three times the number of discretization nodes. The higher the requirements for precision of the simulation results, the more discretization nodes are usually introduced. Nevertheless, the results the engineer will use are in most cases of low dimensional order. In other words, the characteristic features of the required functionality of the device under developement are well represented in low dimensional subspace of the entire solution space of a very fine Finite Element model. Moreover, the requirement for system behaviour simulation makes it impossible to couple large-scale