A Mindlin plate theory based parallel 2D finite element analysis of quartz crystal resonators

Since resonators are climbing to higher frequency and shrinking to smaller size, the software needs to be parallelized with new algorithms and libraries for large size problems. The 2D program is implemented with the higher-order Mindlin plate theory and integrating thermal and piezoelectric effect into the analysis. The standard finite element formulation and procedure is demonstrated, but we highlight the distributed parallel algorithms, which include the eigensolver combined with PARPACK, SuperLU_DIST, Aztec and ParMetis, and the linear equation solver only couple with SuperLU_DIST and ParMetis. We tested our software on a Linux cluster with 16 processors. 2D and 3D FEM analyses based on our own development and commercial software have their own advantages and draw backs, but it is always desirable to reduce the problem size for limited computing power.