Computational challenges in MEMS

Small sensors and actuators made from materials like silicon, quartz or plastic are already parts of our everyday life. In cars there are often silicon sensors measuring acceleration, tyre pressure and car roll-over. There may be microfabricated mechanical components inside your light projector or in your ink-jet printer. In the future, microsystems are believed to be widespread, being used for environment monitoring, safety systems, medical care and biochemical analyses. The small mechanical elements are easily integrated in electrical circuits that control their behaviour, process their output signals or interconnect several active and passive elements in a control system. Behaviour of the mechanical elements is often governed by interacting elastic forces, electromagnetic forces and forces due to surrounding fluids. Computation of the behaviour is therefore complicated. Engineers working with macroscopic constructions like oil-platforms, where mechanical and fluid forces interact, face similar challenges. Experiences and research results from the macroscopic world are therefore of great importance for the design of microsystems. Microsystem elements usually involve micrometer sized features. The small scale introduces effects that are negligible on larger scales, such as strong surface forces. In addition, the continuum hypothesis may break down in some problems, excluding the use of partial differential equations describing the behaviour. There are also fundamental physical effects occurring on small scales that are not yet understood. An important task in microsystems design is to develop reduced-order macromodels that capture the essential behaviour of a mechanical microelement. The complicated electrical circuits controlling the mechanical elements need to be optimised, and this will be too time-consuming without simplified descriptions. We present examples of microsystems, outline current computational technology and some remaining challenges in these fields.