A tool-box approach to the simulation of multi-physics systems

Abstract

In many cases, modeling and simulation of multi-physics systems cannot be carried out with one simulator or one class of models. Typically, for complex heterogeneous systems a combination of different modeling approaches, sometimes combined with simulator coupling, is the most appropriate method. A tool-box containing different modeling tools and software for simulator coupling is presented which could be applied successfully in the simulation of MEMS. Keywords:MEMS, microsystems, modeling, simulation, multi-domain, order reduction, model generation Micro-electro-mechanical systems (MEMS) and other microsystems are often complex heterogeneous. Multi-domain description, coupled field problems, stiffness, nonlinearities, and an increasing role of electronic signal processing (analog and digital) are characteristic properties of such devices and systems. Therefore, modeling and simulation is a difficult task in the design process. Due to the complexity of MEMS, there is no commonly accepted modeling and simulation approach. We prefer a tool-box oriented approach to cover most of the different requirements: a collection of modeling, simulation, and optimization tools, together with a "canonical" description of the elements as the basis for libraries from which models of complex system may be build-up.In Fig. 1, the combination of • modeling by abstraction (from lower to higher modeling levels), • modeling by equivalence transformation between the different physical domains (e.g. to apply the most suitable system simulator), • simulator coupling for those problems which can not be modeled for a single simulator is shown. On the component or device level, FEM/FDM/BEM simulation [18], [2] is the most appropriate and widely used analysis method. But for the overall system simulation the underlying models are too complex. Therefore, the generation of more compact models (sometimes called "macromodels") is necessary. In Fig. 2, different approaches to construct compact models for system simulation are summarized [12].To support the physically-oriented approach, generalized KIRCHHOFFian networks [15], [10], [4] could be applied very successfully. Special attention has to be directed to the multi-port aspect to handle 3-dimensional translational and rotational effects, also in non-inertial systems [9], [14]. The analytical description of the basic elements may be based also on FEM formulas [7]. Geometrically complex or inhomogeneous systems may be composed of an appropriate number of parameterized elements (Fig. 3). It is a main advantage of this approach that also multi-domain problems (as arising e.g. in transducer modeling) can be handled and also some nonlinearities (as usual e.g. in electro-mechanical systems) may be included into the behavioral models. The elements have to model only the "local" behavior, while the "global" behavior is calculated numerically by the system simulator based on the interconnections of the elements and the elements' behavioral models.Another modeling approach uses the internal mode...