2,771 research outputs found
On the use of Perfectly Matched Layers at corners for scattering problems with sign-changing coefficients
International audienceWe investigate in a 2D setting the scattering of time-harmonic electromagnetic waves by a plasmonic device, represented as a non dissipative bounded and penetrable obstacle with a negative permittivity. Using the -coercivity approach, we first prove that the problem is well-posed in the classical framework if the negative permittivity does not lie in some critical interval whose definition depends on the shape of the device. When the latter has corners, for values inside the critical interval, unusual strong singularities for the electromagnetic field can appear. In that case, well-posedness is obtained by imposing a radiation condition at the corners to select the outgoing black-hole plasmonic wave, that is the one which carries energy towards the corners. A simple and systematic criterion is given to define what is the outgoing solution. Finally, we propose an original numerical method based on the use of Perfectly Matched Layers at the corners. We emphasize that it is necessary to design an technique because the field is too singular to be captured with standard finite element methods
On a Helmholtz transmission problem in planar domains with corners
A particular mix of integral equations and discretization techniques is
suggested for the solution of a planar Helmholtz transmission problem with
relevance to the study of surface plasmon waves. The transmission problem
describes the scattering of a time harmonic transverse magnetic wave from an
infinite dielectric cylinder with complex permittivity and sharp edges.
Numerical examples illustrate that the resulting scheme is capable of obtaining
total magnetic and electric fields to very high accuracy in the entire
computational domain.Comment: 28 pages, 8 figure
Oscillating behaviour of the spectrum for a plasmonic problem in a domain with a rounded corner
We investigate the eigenvalue problem in a 2D domain divided into two regions
. We are interested in situations where takes positive
values on and negative ones on . Such problems appear
in time harmonic electromagnetics in the modeling of plasmonic technologies. In
a recent work [15], we highlighted an unusual instability phenomenon for the
source term problem associated with : for certain
configurations, when the interface between the subdomains
presents a rounded corner, the solution may depend critically on the value of
the rounding parameter. In the present article, we explain this property
studying the eigenvalue problem . We provide an asymptotic
expansion of the eigenvalues and prove error estimates. We establish an
oscillatory behaviour of the eigenvalues as the rounding parameter of the
corner tends to zero. We end the paper illustrating this phenomenon with
numerical experiments.Comment: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN),
09/12/2016. arXiv admin note: text overlap with arXiv:1304.478
Nonlocal models for interface problems between dielectrics and metamaterials
International audienceConsider two materials with permittivities/diffusivities of opposite sign, and separated by an interface with a corner. Then, when solving the classic (local) models derived from electromagnetics theory, strong singularities may appear. For instance the scalar problem may be ill-posed in H1. To address this difficulty, we study here a nonlocal model for scalar problems with sign-changing coefficients. Numerical results indicate that the proposed nonlocal model has some key advantages over the local one
Numerical methods for computing Casimir interactions
We review several different approaches for computing Casimir forces and
related fluctuation-induced interactions between bodies of arbitrary shapes and
materials. The relationships between this problem and well known computational
techniques from classical electromagnetism are emphasized. We also review the
basic principles of standard computational methods, categorizing them according
to three criteria---choice of problem, basis, and solution technique---that can
be used to classify proposals for the Casimir problem as well. In this way,
mature classical methods can be exploited to model Casimir physics, with a few
important modifications.Comment: 46 pages, 142 references, 5 figures. To appear in upcoming Lecture
Notes in Physics book on Casimir Physic
A Finite Difference Representation of Neutrino Radiation Hydrodynamics in Spherically Symmetric General Relativistic Space-Time
We present an implicit finite difference representation for general
relativistic radiation hydrodynamics in spherical symmetry. Our code,
Agile-Boltztran, solves the Boltzmann transport equation for the angular and
spectral neutrino distribution functions in self-consistent simulations of
stellar core collapse and postbounce evolution. It implements a dynamically
adaptive grid in comoving coordinates. Most macroscopically interesting
physical quantities are defined by expectation values of the distribution
function. We optimize the finite differencing of the microscopic transport
equation for a consistent evolution of important expectation values. We test
our code in simulations launched from progenitor stars with 13 solar masses and
40 solar masses. ~0.5 s after core collapse and bounce, the protoneutron star
in the latter case reaches its maximum mass and collapses further to form a
black hole. When the hydrostatic gravitational contraction sets in, we find a
transient increase in electron flavor neutrino luminosities due to a change in
the accretion rate. The muon- and tauon-neutrino luminosities and rms energies,
however, continue to rise because previously shock-heated material with a
non-degenerate electron gas starts to replace the cool degenerate material at
their production site. We demonstrate this by supplementing the concept of
neutrinospheres with a more detailed statistical description of the origin of
escaping neutrinos. We compare the evolution of the 13 solar mass progenitor
star to simulations with the MGFLD approximation, based on a recently developed
flux limiter. We find similar results in the postbounce phase and validate this
MGFLD approach for the spherically symmetric case with standard input physics.Comment: reformatted to 63 pages, 24 figures, to be published in ApJ
Uni- and omnidirectional simulation tools for integrated optics
This thesis presents several improvements on simulation methods in integrated optics, as well as some new methods. Both uni- and omnidirectional tools are presented; for the unidirectional methods, the emphasis is on higher-order accuracy; for the omnidirectional methods, the boundary conditions are extremely important, and care must be taken with the incoming field definition. The omnidirectional methods are applied to two different types of structures, a cylindrical microcavity and photonic bandgap crystals
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