Sensitivity analysis of waveguide eigenvalue problems

Methods for Large Sparse Eigenvalue Problems from Waveguide Analysis

We discuss several techniques for nding leading eigenvalues and eigenvectors for large sparse matrices. The techniques are demonstrated on a scalar Helmholtz equation derived from a model semiconductor rib waveguide problem. We compare the simple inverse iteration approach with more sophisticated methods, including minimum degree reordering, Arnoldi and Lanczos methods. We then propose a new Ar...

II. Eigenvalue Sensitivity Analysis

Numerical Analysis of Nonlinear Eigenvalue Problems

We provide a priori error estimates for variational approximations of the ground state eigenvalue and eigenvector of nonlinear elliptic eigenvalue problems of the form −div(A∇u) + V u + f(u)u = λu, ‖u‖L2 = 1. We focus in particular on the Fourier spectral approximation (for periodic problems) and on the P1 and P2 finite-element discretizations. Denoting by (uδ, λδ) a variational approximation o...

Sensitivity analysis for the multivariate eigenvalue problem

This paper concerns with the sensitivity analysis for the multivariate eigenvalue problem (MEP). The concept of a simple multivariate eigenvalue of a matrix is generalized to the MEP and the first-order perturbation expansions of a simple multivariate eigenvalue and the corresponding multivariate eigenvector are presented. The explicit expressions of condition numbers, perturbation upper bounds...

SENSITIVITY ANALYSIS IN LINEAR-PLUS-LINEAR FRACTIONAL PROGRAMMING PROBLEMS

In this paper, we study the classical sensitivity analysis when the right - hand – side vector, and the coefficients of the objective function are allowed to vary.