Improvements in 2D FEM modeling software for crystal resonators

Improvements to our 2D FEM modeling software for crystal resonators are described, including a capability for modal analysis and a skyline storage scheme, accounting for the characteristic sparsity structure of the mass matrix. A variant of the Lanczos algorithm-as implemented in the numerical ARPACK library-is employed in the solution of the piezoelectric eigenproblem, giving eigenpairs within a specified frequency range of interest. The method retains the band structure of the stiffness matrix, resulting in an effective solution. Thereafter, the modal constants, which measure the strengths of the resonances, are computed, allowing for an identification of the unwanted spurious modes. The improvements newly introduced have strongly decreased the computing time and significantly reduced the memory requirements. To demonstrate the performance of our modeling program, results for a composite resonator structures reported in the literature are presented.