27,165 research outputs found
An integral equation based numerical solution for nanoparticles illuminated with collimated and focused light
To address the large number of parameters involved in nanooptical problems, a more efficient computational method is necessary. An integral equation based numerical solution is developed when the particles are illuminated with collimated and focused incident beams. The solution procedure uses the method of weighted residuals, in which the integral equation is reduced to a matrix equation and then solved for the unknown electric field distribution. In the solution procedure, the effects of the surrounding medium and boundaries are taken into account using a Green’s function formulation. Therefore, there is no additional error due to artificial boundary conditions unlike differential equation based techniques, such as finite difference time domain and finite element method. In this formulation, only the scattering nano-particle is discretized. Such an approach results in a lesser number of unknowns in the resulting matrix equation. The results are compared to the analytical Mie series solution for spherical particles, as well as to the finite element method for rectangular metallic particles. The Richards-Wolf vector field equations are combined with the integral equation based formulation to model the interaction of nanoparticles with linearly and radially polarized incident focused beams
Automated Netlist Generation for 3D Electrothermal and Electromagnetic Field Problems
We present a method for the automatic generation of netlists describing
general three-dimensional electrothermal and electromagnetic field problems.
Using a pair of structured orthogonal grids as spatial discretisation, a
one-to-one correspondence between grid objects and circuit elements is obtained
by employing the finite integration technique. The resulting circuit can then
be solved with any standard available circuit simulator, alleviating the need
for the implementation of a custom time integrator. Additionally, the approach
straightforwardly allows for field-circuit coupling simulations by
appropriately stamping the circuit description of lumped devices. As the
computational domain in wave propagation problems must be finite, stamps
representing absorbing boundary conditions are developed as well.
Representative numerical examples are used to validate the approach. The
results obtained by circuit simulation on the generated netlists are compared
with appropriate reference solutions.Comment: This is a pre-print of an article published in the Journal of
Computational Electronics. The final authenticated version is available
online at: https://dx.doi.org/10.1007/s10825-019-01368-6. All numerical
results can be reproduced by the Matlab code openly available at
https://github.com/tc88/ANTHE
Variational Theory and Domain Decomposition for Nonlocal Problems
In this article we present the first results on domain decomposition methods
for nonlocal operators. We present a nonlocal variational formulation for these
operators and establish the well-posedness of associated boundary value
problems, proving a nonlocal Poincar\'{e} inequality. To determine the
conditioning of the discretized operator, we prove a spectral equivalence which
leads to a mesh size independent upper bound for the condition number of the
stiffness matrix. We then introduce a nonlocal two-domain variational
formulation utilizing nonlocal transmission conditions, and prove equivalence
with the single-domain formulation. A nonlocal Schur complement is introduced.
We establish condition number bounds for the nonlocal stiffness and Schur
complement matrices. Supporting numerical experiments demonstrating the
conditioning of the nonlocal one- and two-domain problems are presented.Comment: Updated the technical part. In press in Applied Mathematics and
Computatio
Some Key Developments in Computational Electromagnetics and their Attribution
Key developments in computational electromagnetics are proposed. Historical highlights are summarized concentrating on the two main approaches of differential and integral methods. This is seen as timely as a retrospective analysis is needed to minimize duplication and to help settle questions of attribution
On a non-isothermal model for nematic liquid crystals
A model describing the evolution of a liquid crystal substance in the nematic
phase is investigated in terms of three basic state variables: the {\it
absolute temperature} \teta, the {\it velocity field} \ub, and the {\it
director field} \bd, representing preferred orientation of molecules in a
neighborhood of any point of a reference domain. The time evolution of the
velocity field is governed by the incompressible Navier-Stokes system, with a
non-isotropic stress tensor depending on the gradients of the velocity and of
the director field \bd, where the transport (viscosity) coefficients vary
with temperature. The dynamics of \bd is described by means of a parabolic
equation of Ginzburg-Landau type, with a suitable penalization term to relax
the constraint |\bd | = 1. The system is supplemented by a heat equation,
where the heat flux is given by a variant of Fourier's law, depending also on
the director field \bd. The proposed model is shown compatible with
\emph{First and Second laws} of thermodynamics, and the existence of
global-in-time weak solutions for the resulting PDE system is established,
without any essential restriction on the size of the data
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