2 citations · 2 across the 4 of their papers we have counts for
7 papers
On spurious solutions encountered in Helmholtz scattering resonance computations in R^d with applications to nano-photonics and acoustics
Juan Carlos Araujo Cabarcas, Christian Engström
In this paper, we consider a sorting scheme for potentially spurious scattering resonant pairs in one- and two-dimensional electromagnetic problems and in three-dimensional acousti…
Accumulation of Complex Eigenvalues of a Class of Analytic Operator Functions
Christian Engström, Axel Torshage
For analytic operator functions, we prove accumulation of branches of complex eigenvalues to the essential spectrum. Moreover, we show minimality and completeness of the correspond…
On Equivalence and Linearization of Operator Matrix Functions with Unbounded Entries
Christian Engström, Axel Torshage
In this paper we present equivalence results for several types of unbounded operator functions. A generalization of the concept equivalence after extension is introduced and used t…
Efficient resonance computations for Helmholtz problems based on a Dirichlet-to-Neumann map
Juan Carlos Araujo-Cabarcas, Christian Engstrom, Elias Jarlebring
We present an efficient procedure for computing resonances and resonant modes of Helmholtz problems posed in exterior domains. The problem is formulated as a nonlinear eigenvalue p…
On spurious solutions in finite element approximations of resonances in open systems
Juan Carlos Araujo-Cabarcas, Christian Engström
In this paper, we discuss problems arising when computing resonances with a finite element method. In the pre-asymptotic regime, we detect for the one dimensional case, spurious so…
Enclosure of the Numerical Range of a Class of Non-Selfadjoint Rational Operator Functions
Christian Engström, Axel Torshage
In this paper we introduce an enclosure of the numerical range of a class of rational operator functions. In contrast to the numerical range the presented enclosure can be computed…
Non-linear eigenvalue problems and applications to photonic crystals
Christian Engström, Heinz Langer, Christiane Tretter
We establish new analytic and numerical results on a general class of rational operator Nevanlinna functions that arise e.g. in modelling photonic crystals. The capability of these…