The nonlinear eigenvalue problem

S Güttel, F Tisseur - Acta Numerica, 2017 - cambridge.org
Nonlinear eigenvalue problems arise in a variety of science and engineering applications,
and in the past ten years there have been numerous breakthroughs in the development of …

[LIVRE][B] Layer potential techniques in spectral analysis

H Ammari, H Kang, H Lee - 2009 - books.google.com
Since the early part of the twentieth century, the use of integral equations has developed into
a range of tools for the study of partial differential equations. This includes the use of single …

[LIVRE][B] Mathematical and computational methods in photonics and phononics

H Ammari, B Fitzpatrick, H Kang, M Ruiz, S Yu… - 2018 - books.google.com
The fields of photonics and phononics encompass the fundamental science of light and
sound propagation and interactions in complex structures, as well as its technological …

The complex Bloch bands of a 2D plasmonic crystal displaying isotropic negative refraction

M Davanço, Y Urzhumov, G Shvets - Optics Express, 2007 - opg.optica.org
The propagation characteristics of a subwavelength plasmonic crystal are studied based on
its complex Bloch band structure. Photonic crystal bands are generated with an alternative …

Physically agnostic quasi normal mode expansion in time dispersive structures: From mechanical vibrations to nanophotonic resonances

A Nicolet, G Demésy, F Zolla, C Campos… - European Journal of …, 2023 - Elsevier
Resonances, also known as quasi normal modes (QNM) in the non-Hermitian case, play an
ubiquitous role in all domains of physics ruled by wave phenomena, notably in continuum …

Photonics in highly dispersive media: the exact modal expansion

F Zolla, A Nicolet, G Demésy - Optics letters, 2018 - opg.optica.org
We present exact modal expansions for photonic systems including highly dispersive media.
The formulas, based on a simple version of the Keldyš theorem, are very general since both …

Variational characterization and Rayleigh quotient iteration of 2D eigenvalue problem with applications

T Lu, Y Su, Z Bai - SIAM Journal on Matrix Analysis and Applications, 2024 - SIAM
A two dimensional eigenvalue problem (2DEVP) of a Hermitian matrix pair is introduced in
this paper. The 2DEVP can be regarded as a linear algebra formulation of the well-known …

A new integral representation for quasi-periodic fields and its application to two-dimensional band structure calculations

A Barnett, L Greengard - Journal of Computational Physics, 2010 - Elsevier
In this paper, we consider band structure calculations governed by the Helmholtz or Maxwell
equations in piecewise homogeneous periodic materials. Methods based on boundary …

[PDF][PDF] Nonlinear eigenvalue problems: Newton-type methods and nonlinear Rayleigh functionals

K Schreiber - 2008 - depositonce.tu-berlin.de
Nonlinear eigenvalue problems arise in many fields of natural and engineering sciences.
Theoretical and practical results are scattered in the literature and in most cases they have …

A Newton-based method for the calculation of the distance to instability

MA Freitag, A Spence - Linear Algebra and its Applications, 2011 - Elsevier
In this paper, a new fast algorithm for the computation of the distance of a stable matrix to the
unstable matrices is provided. The method uses Newton's method to find a two-dimensional …