Structure-preserving Arnoldi-type algorithm for solving eigenvalue problems in leaky surface wave propagation

摘要

We study the generalized eigenvalue problems (GEPs) that arise from modeling leaky surface wave propagation in an acoustic resonator with an infinite amount of periodically arranged interdigital transducers. The constitutive equations are discretized by finite element methods with mesh refinements along the electrode interfaces and corners. The nonzero eigenvalues of the resulting GEP appear in reciprocal pairs (λ,1/λ). We transform the GEP into a T-palindromic quadratic eigenvalue problem (TPQEP) to reveal the important reciprocal relationships of the eigenvalues. The TPQEP is then solved by a structure-preserving algorithm incorporating a generalized T-skew-Hamiltonian implicitly restarted Arnoldi method so that the reciprocal relationship of the eigenvalues may be automatically preserved. Compared with applying the Arnoldi method to solve the GEPs, our numerical results show that the eigenpairs produced by the proposed structure-preserving method not only preserve the reciprocal property but also possess high efficiency and accuracy.