Dielectric channel waveguide problems arise in many integrated circuit applications. Finite difference discretization of the governing Helmholtz equation for the magnetic field H,

,

leads to the nonsymmetric eigenvalue problem of the form

where C_{11} and C_{22} are penta- or tri-diagonal matrices, C_{12} and C_{21} are (tri-)diagonal matrices, and B_{11} and B_{22} are nonsingular diagonal matrices. This generalized eigenvalue problem is reduced to a standard eigenvalue problem, , where , since B is diagonal.

The computational task is to determine the right most eigenvalues and their corresponding eigenvectors. In some cases, there are eigenvalues with a negative real part several orders of magnitude larger than the desired eigenvalues with positive real part. This problem presents a challenge to existing numerical methods.

Note that DWA512 and DWB512 are matrices of the same order which correspond to different parameter values.

Matrices in this set:

DW2048 (real unsymmetric, 2048 by 2048, 10114 entries)

DW8192 (real unsymmetric, 8192 by 8192, 41746 entries)

DWA512 (real unsymmetric, 512 by 512, 2480 entries)

DWB512 (real unsymmetric, 512 by 512, 2500 entries)