Pseudospectra implementation in multi-domain spectral method

Abstract

Pseudospectra and minimal perturbation approach (MPA) principles are used and implemented to provide more rigorous mathematical foundations for functional expansion multi domain spectral method (MDSM). The implemented formulation is used to analyze optical waveguide and semiconductor quantum well. The results show that MDSM formulation based on MPA is very stable and slightly more accurate when compared to Tau MDSM. Pseudospectra provides more rigorous mathematical foundations for approximated eigenvalues of overdetermined systems (nonsquare matrix pencil), which is common in numerical formulations. © 2010 IEEE.