TY - GEN A1 - Huang, Tsung-Ming A1 - Lin, Wen-Wei A1 - Mehrmann, Volker T1 - A Newton-Type Method with Non-equivalence Deflation for Nonlinear Eigenvalue Problems Arising in Photonic Crystal Modeling N2 - The numerical simulation of the band structure of three-dimensional dispersive metallic photonic crystals with face-centered cubic lattices leads to large-scale nonlinear eigenvalue problems, which are very challenging due to a high dimensional subspace associated with the eigenvalue zero and the fact that the desired eigenvalues (with smallest real part) cluster near the zero eigenvalues. For the solution of the eigenvalue problem, a Newton-type iterative method is proposed and the nullspace-free method is applied to exclude the zero eigenvalues from the associated generalized eigenvalue problem. To find the successive eigenvalue/eigenvector pairs, we propose a new non-equivalence deflation method to transform converged eigenvalues to infinity, while all other eigenvalues remain unchanged. The deflated problem is then solved by the same Newton-type method, which uses a hybrid method that combines the Jacobi-Davidson, the shift-invert residual Arnoldi and nonlinear Arnoldi methods to compute the clustered eigenvalues. Numerical results illustrate that the method is robust even for the case of computing many eigenvalues in very large problems. KW - Maxwell equation KW - dispersive metallic photonic crystals KW - nonlinear eigenvalue problem KW - non-equivalence deflation Y1 - 2015 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/1334 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-13344 ER -