A new storage scheme for the Lanczos solution of large scale finite element models of piezoelectric resonators

A storage algorithm for solving a large piezoelectric eigenvalue problem is presented. The storage algorithm could reduce memory requirements and computational time by more than an order of magnitude over a current storage scheme, which separates the mechanical stiffness matrix elements from the dielectric matrix elements in the finite element matrix equations. Details of the proposed algorithm is presented with regards to using a Lanczos eigenvalue solver. Finite element solutions for the free vibrations of a piezoelectric cube and bar are shown to illustrate the economy of the proposed storage scheme. Graphs of memory usage and computational time versus the size of the finite element model are presented to compare the results of the current storage scheme with those of the proposed storage scheme