The Matrix Market

Home Search Browse Resources

DWAVE: Square Dielectric Waveguide

from the NEP Collection

Source: H. Dong, University of Minnesota
Discipline: Electrical engineering

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

grad^2H_x+k^2n^2(x,y)H_x=beta^2H_x; grad^2H_y+k^2n^2(x,y)H_y=beta^2H_y,

leads to the nonsymmetric eigenvalue problem of the form

C H = beta^2 B H

where C11 and C22 are penta- or tri-diagonal matrices, C12 and C21 are (tri-)diagonal matrices, and B11 and B22 are nonsingular diagonal matrices. This generalized eigenvalue problem is reduced to a standard eigenvalue problem, A x=x lambda, where A=B^(-1), 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:

The Matrix Market is a service of the Mathematical and Computational Sciences Division / Information Technology Laboratory / National Institute of Standards and Technology.

[ Home ] [ Search ] [ Browse ] [ Resources ]

Last change in this page: Wed Sep 22 13:37:24 US/Eastern 2004 [Comments: ]