This talk will focus on computing the complex band structure of three-dimensional photonic crystals (dispersive or non-dispersive) from the structured quadratic eigenvalue problem (QEP) perspective. We reformulate this gyroscopic-structured QEP as a ⊤-palindromic QEP, which is further transformed into a structured generalized eigenvalue problem. Furthermore, we have built a structure-preserving shift-invert Arnoldi algorithm. In our numerical experiments, we propose an efficient preconditioner that implements fast Fourier transforms to speed up the internal iterations of the shift-invert Arnoldi algorithm. Finally, we discuss the advantages of the proposed method in detail and are corroborated by several numerical results.

WebEx Link

https://nationaltaiwanuniversity-ksz.my.webex.com/nationaltaiwanuniversity-ksz.my/j.php?MTID=mcef553f4cd487cc88bc7e311c4ec2452