P3H-4 The Finite Element Analysis of Quartz Crystal Resonators with Mindlin Plate Theory and Parallel Computing Techniques on Computer Clusters

The accurate analysis of high frequency vibrations of quartz crystal resonators are increasingly critical in product design and development because the miniaturization has signified effects of complications such as electrodes, beveling, and mountings, which affect the resonator performance through key indicators like the frequency-temperature characteristics and quality factor. The practical solutions are available from finite element analysis based on the implementation of three- dimensional piezoelectricity equations and Mindlin plate theory with proven success. On the other hand, the strong demand on computing resource and software has discouraged applications and further development efforts in industry. In order to advance the design technology through the utilization of advanced computer clusters based on the open source Linux operating system and software components, we need to integrate the latest technology with cost-effective hardware to achieve industrial strength performance. With these objectives, we have rewritten our proven Mindlin plate theory based finite element analysis program with public domain software for the parallel implementation, eigenvalue extraction, and sparse matrix handling to improve the computing efficiency with scaleable clusters. Our research results on Mindlin plate theory have also been incorporated into the program to improve the accuracy in frequency calculation. The improved software has increased the performance in comparison with the earlier sequential program for single processor machines, and core software components also make the completed software more affordable to industrial users. Our results show that through aggressive parallelization and utilization of sparse matrix techniques, computing efficiency in terms of time can be reduced significantly, and it is a great improvement from our record a few years ago. Further improvements are being implemented for the adoption of computing technology for the reduction of computing time and memory requirement, and latest features of Mindlin plate theory and quartz crystal resonator model will also be added to meet actual design needs. The software will be validated through our joint efforts in the design process integration, and further optimization and tuning will be performed based on design cycles.