2-D time-harmonic BEM for general anisotropy applied to eigenvalue analysis of quartz resonators

The two-dimensional time-harmonic Boundary Element Method (BEM) for the general anisotropy is presented and applied to the eigen frequency analysis of quartz resonators. The use of the time-harmonic fundamental solution provides a clean boundary only formulation of the BEM without domain integrals. The resulting eigenvalue problem, given by a full matrix with each element depending nonlinearly on the frequency, is reduced to a generalized linear eigenvalue problem, which is solved by the QZ algorithm. Numerical results are presented for eigenvalue analysis of quartz and compared with existing FEM and analytical solutions. The proposed BEM equals or surpasses the performance of the FEM in its accuracy.