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The finite element analysis of high frequency vibrations of quartz crystalplates is a necessary process required in the design of quartz crystalresonators of precision types for applications in filters and sensors. Theanisotropic materials and extremely high frequency in radiofrequency range ofresonators determine that vibration frequency spectra are complicated withstrong couplings of large number of different vibration modes representingdeformations which do not appear in usual structural problems. For instance,the higher-order thickness-shear vibrations usually representing the sharpdeformation of thin plates in the thickness direction, expecting the analysisis to be done with refined meshing schemes along the relatively small thicknessand consequently the large plane area. To be able to represent the precisevibration mode shapes, a very large number of elements are needed in the finiteelement analysis with either the three-dimensional theory or the higher-orderplate theory, although considerable reduction of numbers of degree-of-freedom(DOF) are expected for the two-dimensional analysis without scarifying theaccuracy. In this paper, we reviewed the software architecture for the analysisand demonstrated the evaluation and tuning of parameters for the improvement ofthe analysis with problems of elements with a large number of DOF in each node,or a problem with unusually large bandwidth of the banded stiffness and massmatrices in comparison with conventional finite element formulation. Such aproblem can be used as an example for the optimization and tuning of problemsfrom multi-physics analysis which are increasingly important in applicationswith excessive large number of DOF and bandwidth in engineering.

Tuning and Optimizing the Finite Element Analysis with Elements of Large Nodal DOF on a Linux Cluster