We consider the solution of the Helmholtz equation−∆ u (x)− n (x) 2ω2u (x)= f (x), x=(x, y), in
a domain Ω which is infinite in x and bounded in y. We assume that f (x) is supported in …

We consider the solution of the Helmholtz equation with absorption− Δu (x)− n (x) 2 (ω2+ ıε)
u (x)= f (x), x=(x, y), in a 2D periodic medium Ω= R2. We assume that f (x) is supported in a …

In this work we present a new numerical technique for solving periodic structure problems.
This new approach possesses several advantages. First, it allows for a fast evaluation of the …

We present a new computational approach for a class of large-scale nonlinear eigenvalue
problems (NEPs) that are nonlinear in the eigenvalue. The contribution of this paper is …

We present NEP-PACK a novel open-source library for the solution of nonlinear eigenvalue
problems (NEPs). The package provides a framework to represent NEPs, as well as efficient …

Based on the work of Zheng on the artificial boundary condition for the Schrödinger equation
with sinusoidal potentials at infinity, an analytical impedance expression is presented for …

Let T:Ω→C^n*n be a matrix-valued function that is analytic on some simply connected
domain Ω⊂C. A point λ∈Ω is an eigenvalue if the matrix T(λ) is singular. In this paper, we …

A method of calculating eigenvalues in the spectral gaps of self-adjoint elliptic partial
differential equations on waveguides is presented. It is based on approximating the problem …

We consider a nonlinear eigenvalue problem (NEP) arising from absorbing boundary
conditions in the study of a partial differential equation (PDE) describing a waveguide. We …

We investigate a technique to transform a linear two-parameter eigenvalue problem into a
nonlinear eigenvalue problem (NEP). The transformation stems from an elimination of one of …