The nonlinear eigenvalue problem
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 …
and in the past ten years there have been numerous breakthroughs in the development of …
[LIVRE][B] Layer potential techniques in spectral analysis
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 …
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
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 …
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
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 …
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
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 …
ubiquitous role in all domains of physics ruled by wave phenomena, notably in continuum …
Photonics in highly dispersive media: the exact modal expansion
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 …
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 …
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
In this paper, we consider band structure calculations governed by the Helmholtz or Maxwell
equations in piecewise homogeneous periodic materials. Methods based on boundary …
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 …
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
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 …
unstable matrices is provided. The method uses Newton's method to find a two-dimensional …