30 research outputs found
Open Boundaries for the Nonlinear Schrodinger Equation
We present a new algorithm, the Time Dependent Phase Space Filter (TDPSF)
which is used to solve time dependent Nonlinear Schrodinger Equations (NLS).
The algorithm consists of solving the NLS on a box with periodic boundary
conditions (by any algorithm). Periodically in time we decompose the solution
into a family of coherent states. Coherent states which are outgoing are
deleted, while those which are not are kept, reducing the problem of reflected
(wrapped) waves. Numerical results are given, and rigorous error estimates are
described.
The TDPSF is compatible with spectral methods for solving the interior
problem. The TDPSF also fails gracefully, in the sense that the algorithm
notifies the user when the result is incorrect. We are aware of no other method
with this capability.Comment: 21 pages, 4 figure
Numerical Investigation of Light Scattering off Split-Ring Resonators
Recently, split ring-resonators (SRR's) have been realized experimentally in
the near infrared (NIR) and optical regime. In this contribution we numerically
investigate light propagation through an array of metallic SRR's in the NIR and
optical regime and compare our results to experimental results.
We find numerical solutions to the time-harmonic Maxwell's equations by using
advanced finite-element-methods (FEM). The geometry of the problem is
discretized with unstructured tetrahedral meshes. Higher order, vectorial
elements (edge elements) are used as ansatz functions. Transparent boundary
conditions and periodic boundary conditions are implemented, which allow to
treat light scattering problems off periodic structures.
This simulation tool enables us to obtain transmission and reflection spectra
of plane waves which are incident onto the SRR array under arbitrary angles of
incidence, with arbitrary polarization, and with arbitrary
wavelength-dependencies of the permittivity tensor. We compare the computed
spectra to experimental results and investigate resonances of the system.Comment: 9 pages, 8 figures (see original publication for images with a better
resolution
A rapidly converging domain decomposition method for the Helmholtz equation
A new domain decomposition method is introduced for the heterogeneous 2-D and
3-D Helmholtz equations. Transmission conditions based on the perfectly matched
layer (PML) are derived that avoid artificial reflections and match incoming
and outgoing waves at the subdomain interfaces. We focus on a subdivision of
the rectangular domain into many thin subdomains along one of the axes, in
combination with a certain ordering for solving the subdomain problems and a
GMRES outer iteration. When combined with multifrontal methods, the solver has
near-linear cost in examples, due to very small iteration numbers that are
essentially independent of problem size and number of subdomains. It is to our
knowledge only the second method with this property next to the moving PML
sweeping method.Comment: 16 pages, 3 figures, 6 tables - v2 accepted for publication in the
Journal of Computational Physic
Optical microscopy via spectral modifications of a nano-antenna
The existing optical microscopes form an image by collecting photons emitted
from an object. Here we report on the experimental realization of microscopy
without the need for direct optical communication with the sample. To achieve
this, we have scanned a single gold nanoparticle acting as a nano-antenna in
the near field of a sample and have studied the modification of its intrinsic
radiative properties by monitoring its plasmon spectrum.Comment: 6 pages, 4 figures (color
A bootstrap method for sum-of-poles approximations
A bootstrap method is presented for finding efficient sum-of-poles approximations of causal functions. The method is based on a recursive application of the nonlinear least squares optimization scheme developed in (Alpert et al. in SIAM J. Numer. Anal. 37:1138â1164, 2000), followed by the balanced truncation method for model reduction in computational control theory as a final optimization step. The method is expected to be useful for a fairly large class of causal functions encountered in engineering and applied physics. The performance of the method and its application to computational physics are illustrated via several numerical examples