A novel approach for the symbolic calculation of polynomial integrals arising in 2D and 3D FEM applications

The rapid growth of the telecommunication and microelectronic industry has been pushing the performance limit of the passive and active electronic components and devices alike. Thereby, improved performance of the devices has become a necessity for operating frequencies moving into the MW region. Examples are Surface Acoustic Wave (SAW) and Bulk Acoustic Wave (BAW) Devices which are miniaturized microelectronic devices with a wide range of applications in signal processing, forming and sensing. Computation of electroacoustic field distribution in these structures needs to be accurate, efficient and rigorous. However, the amount of data required for preand post-processing is immensely large, and the processing and handling of data are extremely time consuming. In this paper we propose a conceptually novel method for significantly reducing the computational time and thus enhancing efficiency by pre-calculating relevant data, storing, and subsequently retrieving them whenever they are required for device analysis and simulation. We propose a method for symbolically and conveniently calculating two- or three dimensional integrals over the surface of an arbitrary triangle or within the volume of an arbitrary tetrahedral. The results we have obtained are universal in that their application is not limited to microacoustic devices. © 2008 SPIE.