Eigenvalue analysis for 2-D piezoelectric problems by the time-harmonic BEM

We present the direct formulation of the time-harmonic Boundary Element Method (BEM) for two-dimensional piezoelectric solids that uses the fundamental generalized displacement solution obtained by the Radon transform. We apply the BEM to the eigenválue analysis for piezoelectric materials. In the eigenvalue problem we encounter full non-symmetric complex-valued matrices whose components depend nonlinearly on the frequency. We test two algorithms, the QZ algorithm and the implicitly restarted Arnoldi method (IRAM), as the nonlinear eigenvalue solvers to recommend the IRAM which is faster and has more control over the solution procedure than the QZ algorithm.