Efficient determination of the left-eigenvectors for the Method ofLines

[摘要] The efficient determination of left eigenvectorsin the method of lines (MoL) is described in this paper.The electromagnetic fields are expanded into eigenmodesand the eigenmodes are determined from an explicit matrixeigenvector problem. To study complicated structures with a moderatenumerical effort, the analysis is done with a reduced set of these eigenmodes.The enforcements of the continuity of the transverse electric and magneticfields at interfaces leads to expressions with rectangular matrices.Now left eigenvectors can be considered as inverse of these rectangularmatrices. Until now, the left eigenvectorswere determined from a second explicit eigenvalue problem. Here, it is shown howthey can be determined with simple matrix products from previously determinedright eigenvectors. This is done by utilizingthe relation between the transverse electric and magnetic fields.The derived formulas hold for structures with Dirichlet, Neumannor periodic boundary conditionsand thematerials may be lossy.Open structures are modeled withperfectly matched layers (PML).To verify the expressions, various devices thatcontain suchPMLs andlossy metals were studied. In allcases, error measures show thatthe algorithm derived in this paper works very well.

[学科分类] 电子、光学、磁材料